Jim Sterk replaces Mack Rhoades, whose tenure lasted just 15 months.
COLUMBIA - New athletic director Jim Sterk did not shy away from addressing the social issues that have beset the Missouri campus the last 12 months, saying Thursday that he wants to foster an "inclusive, diverse and successful" environment.
Interim Chancellor Hank Foley introduced Sterk and his wife, Debra, to a room of Tiger faithful that included former football coach Gary Pinkel and current coach Barry Odom.
Sterk replaces Mack Rhoades, whose tenure lasted just 15 months. It was marked by campus upheaval that resulted in the removal of the university system president and chancellor following student protests, including a prominent promise of a boycott from members of the football team, a stance Pinkel supported. Rhoades is taking over at Baylor.
In his opening remarks, Sterk called Missouri a "destination" job, stressing a long-term commitment to the program.
Sterk served as athletic director at Portland State from 1995-2000 and at Washington State from 2000-2010 before stepping into the same position at San Diego State. His official start date is Aug. 22.
Foley led the search for Rhoades' replacement in conjunction with the Collegiate Sports Associates search firm.
"In thinking about this hire, I looked for people who would tell me that Jim's reputation was too good to be true, but to honest I couldn't find them," Foley said.
Sterk is regarded as an exceptional fundraiser, having more than doubled San Diego State's athletic scholarship fund during his seven-year tenure with the school.
Sterk was named 2016 AD of the year by the National Association of Collegiate Directors of Athletics and holds a seat on the NCAA Division I Men's Basketball Committee. However, he revealed Thursday he will have to vacate that seat. Kentucky's Mitch Barnhart already holds a seat on the committee, and per NCAA rules, only one representative from each conference may occupy a seat on the committee at a time.


We are looking for a parent or two with some time over the next couple of weeks who could go into the school and take some candid grad pictures. Please let us know via the sign up below.
If you would like to help out with the planning or set up of the graduation night, here is the volunteer sign up – Grade 6 Grad Party Sign Up – please sign up for something of interest to you.


Pop artist Jordan LaFaver is preparing to release his first single of 2016, and the second song of his solo career. Coming almost a year after his moderately successful first single Lipstick Stains, he plans to release the appropriately titled Salem this Halloween.
Salem is scheduled to release at midnight on October 31st to all major online music retailers and streaming services. Snowbound Records will also release it for streaming on Youtube at the same time.
Learn more about Jordan LaFaver at www.facebook.com/jordanlafaver, and be sure to subscribe to Snowbound Records on Youtube!


text:
/**
 * Expose `Collection`.
 */

module.exports = Collection;

/**
 * Initialize a new route `Collection`
 * with the given `router`.
 *
 * @param {Router} router
 * @api private
 */

function Collection(router) {
  Array.apply(this, arguments);
  this.router = router;
}

/**
 * Inherit from `Array.prototype`.
 */

Collection.prototype.__proto__ = Array.prototype;

/**
 * Remove the routes in this collection.
 *
 * @return {Collection} of routes removed
 * @api public
 */

Collection.prototype.remove = function(){
  var router = this.router
    , len = this.length
    , ret = new Collection(this.router);

  for (var i = 0; i < len; ++i) {
    if (router.remove(this[i])) {
      ret.push(this[i]);
    }
  }

  return ret;
};

redpajama_set_name: RedPajamaGithub


CATALOGUE DESCRIPTION Rectangular flat tile, with white slip. A semi-circular element on each half forms a circle containing linear and globular details. A pointed arching element on left side with two parallel lines at each end. Black border. Made in a mold. CONDITION: Holes at top and bottom center.


text:
Philip Oakey, född 2 oktober 1955 i Sheffield, England, är en sångare mest känd som vokalist i synthpopgruppen The Human League. Han har också gett ut skivan "Philip Oakey & Giorgio Moroder" tillsammans med Giorgio Moroder som innehöll hitlåten "Together in Electric Dreams". I början av 80-talet var han mest känd för sin ovanliga frisyr med långt hår på ena sidan och kort på den andra. Han har hävdat att frisyren var inspirerad av hollywoodstjärnan Veronica Lake.
2003 var han med på singeln "LA Today" av Alex Gold.

Diskografi

Med The Human League
Studioalbum
Reproduction (1979)
Travelogue (1980)
Dare (1981)
Love and Dancing (1982)
Hysteria (1984)
Crash (1986)
Romantic? (1990)
Octopus (1995)
Secrets (2001)
Credo (2011)

Hitsinglar
"Don't You Want Me" – 1981 (UK #1, U.S #1, AUS #1, NZ #1)
"Human" – 1986 (U.S #1)

Solo
Studioalbum
Philip Oakey & Giorgio Moroder (1985)

Singlar (med Giorgio Moroder)
"Together in Electric Dreams" (1984)
"Good-Bye Bad Times" (1985)
"Be My Lover Now" (1985)

Singlar (som bidragande artist)
"What Comes After Goodbye"  (1990)
"1st Man in Space"  (1999)
"Rock and Roll is Dead"  (2003)
"LA Today"  (2003)

Referenser

Externa länkar

Brittiska sångare
Synthpopsångare
Födda 1955
Män
Levande personer

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}

The iron pnictides and chalcogens have been the subject of intense study since 2008, when it was discovered that they are superconducting at relatively high critical temperatures~\cite{hosono}.
 Understanding their gap structure is an important step toward identifying the mechanism responsible for superconductivity in these materials. Although the multi-band nature of Fe pnictides/chalcogenides allows for many different gap structures, the  prevailing scenario is that the pairing occurs between electrons on the same Fermi surface (FS) and the superconducting gap function has $s^{+-}$ symmetry, i.e., the gap  changes sign between hole and electron pockets.
 There is experimental evidence that in some members of the family, like BaFe$_2$(As$_{1-x}$P$_x$)$_2$,\cite{BaFeAsP} LaOFeP,\cite{LaOFeP} and LiFeP,\cite{LiFeP} the gap has nodes, likely on the electron pockets.

Previous studies of the gap structure were mostly restricted to an Fe-only approach, in which a generic model of the band structure consists of two nearly circular hole pockets centered at $(0,0)$ and two elliptical electron pockets centered at $(\pi,0)$ and $(0,\pi)$ in the first Brillouin zone (BZ) (see Figure \ref{fig:multipocket_nodes}). In some systems there exists, at least for some $k_z$, a third hole pocket, centered at $(\pi,\pi)$.
The $s^{+-}$ superconductivity is believed to be chiefly caused by a magnetically enhanced interaction between hole and electron pockets~\cite{review}.
 The nodes on the two electron pockets come about because by symmetry the $s$-wave gap on these pockets has the form $\Delta (1 \pm \alpha\cos 2 \theta_k)$
 (plus higher harmonics), and if $\alpha >1$, the gap vanishes at $\cos 2 \theta_k = \pm 1/\alpha$.~\cite{Kemper2010,vavilov,Maiti2011}.

\begin{figure}[htb]
	\centering
		\includegraphics[width=0.3\textwidth]{multipocket_nodes_Q.pdf}
	\caption{Unfolded Brillouin zone with one Fe atom per unit cell (with no hybridization). Holes and electron pockets are labeled by $h$ and $e$, respectively. The crosses on the electron pockets indicate where the nodal lines of the gap function intersect the Fermi surface.
	\label{fig:multipocket_nodes}
\end{figure}

However, this Fe-only scenario is incomplete because the electron hopping between Fe atoms predominantly occurs via pnictogen or chalcogen sites, half of which
  are located above and half below each Fe layer in a checkerboard pattern~\cite{hybrid}. As a result, the actual symmetry is lower than that of the Fe-only lattice, and the correct unit cell contains two Fe atoms.  The non-equivalence of hopping from above and from below an iron layer causes the electron pockets to hybridize. In this paper we will study the effect of this hybridization on the gap structure.

  In order to incorporate this effect into models with one Fe atoms, one has to include additional terms in the Hamiltonian with excess momentum $\mathbf{Q}=(\pi,\pi)$. This does not actually violate conservation of momentum because this vector folds into a reciprocal lattice vector in the actual BZ with two Fe atoms per unit cell.  The momentum $\mathbf{Q}$ connects the two electron FSs and also the hole pocket centered at $(\pi,\pi)$ with the other two hole pockets. Our primary goal will be to study how the accidental nodes on the electron pockets evolve once we include hybridization. Therefore, we focus on the effect of hybridization on the electron pockets.

  The hybridization gives rise to two effects.   First, hopping via a pnictogen/chalcogen sites gives rise to an additional quadratic term in the Hamiltonian for two electron pockets
\begin{equation}\label{eq:Hlambda}
\mathcal{H}_\lambda=\sum_\mathbf{k}\[ \lambda_k c^\dagger_{\mathbf{k}\alpha} d_{\mathbf{k+Q}\alpha}+ \lambda^*_k d^\dagger_{\mathbf{k}\alpha} c_{\mathbf{k+Q}\alpha}\],
\end{equation}
where $c$ and $d$ are operators for electrons near each of the two electron FSs (we discuss the form of $\lambda_k$ in the next section)
 and the sum over repeated spin indices is implied.
 This cross-term mixes the two electron pockets and reconstructs the electron FSs.
 Second, there appear new four-fermion interaction terms in which incoming and outgoing momenta differ by $\mathbf{Q}$.
  In the superconducting state, in which we are  interested, two out of four fermions can be put into the condensate and the four-fermion terms with excess momentum $\mathbf{Q}$
	reduce to  quadratic terms with prefactors proportional to the superconducting gap. These new terms describe inter-pocket pairing between fermions from two different electron pockets:
 \begin{equation}
	\mathcal{H}_\beta =\frac{1}{2}\sum_{\mathbf{k}} \beta_k \left[c^\dagger_{\mathbf{k}\alpha}d^\dagger_{-\mathbf{k}-Q\beta}+d^\dagger_{\mathbf{k}\alpha}c^\dagger_{-\mathbf{k}-Q\beta}\right]i\sigma^y_{\alpha\beta}+\mathrm{H.c.}
	\end{equation}
In other words, due to hybridization, the non-zero intra-pocket pairing condensates   $\langle c^\dagger_{\mathbf{k}\alpha}c^\dagger_{-\mathbf{k}\beta}\rangle$ and $\langle d^\dagger_{\mathbf{k+Q}\alpha}d^\dagger_{-\mathbf{k-Q}\beta}\rangle$ induce inter-pocket pairing between the two electron pockets.

In this paper we study how the additional terms $\mathcal{H}_\lambda$ and $\mathcal{H}_\beta$  affect the gap structure when nodes are present on the electron pockets. The effect of the hopping $\lambda_\mathbf{k}$ term alone has been studied before\cite{Khodas2012b}, but not its interplay with the pairing term. We find that the hopping and inter-pocket pairing terms generally pull the nodal points in opposite direction. If the $\lambda_\mathbf{k}$ term dominates and reaches a certain threshold value, the nodes merge and disappear at particular symmetry points, and the gap  acquires a uniform and equal phase on the two electron pockets (opposite to the phase on the hole pockets). In contrast, when $\beta_k$ dominates and  reaches a threshold value, the nodes merge and disappear at a different set of symmetry points and the phase of the superconducting order parameter becomes  opposite on the hybridized electron pockets. This is the same gap structure
  that was recently found in the analysis of pairing in the orbital formalism\cite{Kotliar2014} and dubbed orbital anti-phase $s^{+-}$ state.
   The state  with opposite signs of the gaps on the two electron pockets has also been found in the analysis of possible superconducting states in LiFeAs, albeit for a different reason~\cite{ilya_li}.
     As an interesting peculiarity, we found that for elliptical pockets nodes disappear in a rather non-trivial way --
      first new nodes appear and the number of nodes doubles, and then the new and already existing nodes merge and disappear.
         Such behavior has not been found before in the studies of multi-band superconductors, as far as  we know.

\begin{figure}[htb]
	\centering
		\includegraphics[width=0.5\textwidth]{BZ_fold_unfold_v3.pdf}
	\caption{Fermi surface folding. a) Unfolded Brillouin zone corresponding to a 1Fe unit cell. b) Folded Brillouin zone corresponding to a 2Fe unit cell.  The electron Fermi surfaces overlap and are reconstructed into outer and inner parts. Depending on their original location, the nodes of the gap function are either all located on the outer surface, as shown in c), or on the inner surface, as shown in d).}
	\label{fig:folding}
\end{figure}

The hybridization between electron pockets, either due to $\mathcal{H}_\lambda$ or to $\mathcal{H}_\beta$, has to be distinguished from the
effect of the folding of the 1Fe BZ into the 2Fe BZ.  Upon folding, fermionic momenta transform as  ${\tilde k}_x = k_x + k_y, {\tilde k}_y = k_y-k_x$,
  and the two electron FSs, originally centered at $(0,\pi)$ and $(\pi,0)$, merge around $(\pi,\pi)$ (see Fig. \ref{fig:folding}).  The inner and outer FSs touch each other along ${\tilde k}_x = \pi$ or ${\tilde k}_y = \pi$. The merging can be viewed as ``reconstruction'' of the two electron FSs into
   an inner FS with no nodes and an outer FS with 8 nodes, or vice versa.  However, this ``reconstruction" is just a rotation in momentum space and a re-branding.
   The $k_F$ remains the same and the location of the nodes remains at exactly the same
	angles as without
folding, only the reference axis rotates by $45^o$.   The hybridization is a different phenomenon -- it actually reconstructs the original FSs into
 an inner and an outer FSs at {\it new} $k_F$  and creates a pairing component between them. As a consequence, the position of the nodal points shifts.

The paper is organized as follows: In Section \ref{sec:model} we discuss our model. In Section \ref{sec:circular}, we consider, as a warm-up,
 the limiting case of circular electron pockets and analyze the two effects of hybridization first separately and then together and study their interplay. Section \ref{sec:elliptical} extends the analysis to the more general case of elliptical pockets. We summarize our findings in Section \ref{sec:conclusions}.

\section{The model}\label{sec:model}

 We consider a two-dimensional multi-band model with hole pockets centered at $(0,0)$ and elliptical electron pockets centered at $(0,\pi)$ and $(\pi,0)$ in the unfolded BZ.  In the normal state, the Hamiltonian describing the two non-hybridized electron pockets is simply
\begin{equation}
	\mathcal{H}_0 =\sum_{\mathbf{k}} \left[\xi^c_\mathbf{k}c^\dagger_{\mathbf{k}\alpha}c_{\mathbf{k}\alpha}+\xi^d_\mathbf{k}d^\dagger_{\mathbf{k}\alpha}d_{\mathbf{k}\alpha}\right].
\end{equation}

We assume that the dominant interaction which leads to $s^{+-}$ superconductivity
   is the repulsion between electron and hole pockets, enhanced by $(\pi,\pi)$ spin fluctuations (in the 2Fe BZ).
      The s-wave gap on the hole pockets is invariant under rotations by $\pi/2$, so it can be expanded in $\cos 4n\phi$ harmonics, where $\phi$ is the angle along the hole pocket and $n$ is an integer. On the electron pockets the expansion of the $s-$wave gap contains $\cos 2n\theta$ terms, where $\theta$ is the angle along the electron pockets and the components with odd $n = 1,3,\ldots$ have opposite signs on the two electron pockets, if we measure $\theta$ from the same direction for both pockets~\cite{vavilov}.
        These odd multiples  of $2\theta$ are allowed because the electron pockets transform into each other under a rotation by $\pi/2$.  Numerical analysis\cite{Kemper2010, Maiti2011} shows that the gap on the electron pockets can be well-approximated
         by the two first harmonics $n=0$ and $n=1$, whose magnitudes are generally comparable to each other.
          Accordingly, we set $\Delta_{e1} (\theta_\mathbf{k})= \Delta (1- \alpha\cos 2\theta_\mathbf{k})$, $\Delta_{e2} (\theta_\mathbf{k+Q})= \Delta (1+ \alpha\cos 2\theta_\mathbf{k+Q})$.  The corresponding term in the Hamiltonian is thus
\begin{align}
	\mathcal{H}_\Delta &=\frac{1}{2}\sum_{\mathbf{k}} \Delta \left[(1-y_\mathbf{k})c^\dagger_{\mathbf{k}\alpha}c^\dagger_{-\mathbf{k}\beta}\right.\\
	&\quad\quad\quad\quad\quad+ \left.(1+y_\mathbf{k+Q})d^\dagger_{\mathbf{k+Q}\alpha}d^\dagger_{-\mathbf{k-Q}\beta}\right]i\sigma^y_{\alpha\beta}+\mathrm{H.c.},\nonumber
\end{align}
where $y_\mathbf{k}\equiv \alpha \cos 2\theta_\mathbf{k}$ and $y_\mathbf{k+Q}\equiv \alpha \cos 2\theta_\mathbf{k+Q}$.

Our goal is to analyze how accidental nodes on electron pockets evolve with increasing hybridization.   For this we assume from the beginning that $|\alpha| >1$ in which case the gaps on electron pockets have nodes when $y_\mathbf{k} = 1$ (for $c-$fermions) and $y_\mathbf{k+Q} =-1$ for $d-$fermions.

To simplify the presentation, we fold the 1Fe BZ into the 2Fe BZ and replace the momentum ${\bf k} + {\bf Q}$ of d-fermions  by ${\bf k}$.  The momenta ${\bf k}$ below are defined as a deviation from ${\bf Q}$, which is the location of the electron pockets in the folded BZ.
In order to preserve the $\cos 2\theta_\mathbf{k}$ form of the gap function, we  define $\theta_\mathbf{k}$ relative to the minor axis of the $c$ pocket.

In the normal state, the inclusion of hopping via pnictogen/chalcogen atoms generates  mixing between $c$ and $d$ fermions:
\begin{align}
	\mathcal{H}_\lambda &=\sum_\mathbf{k}\[ \lambda_k c^\dagger_{\mathbf{k}\alpha} d_{\mathbf{k}\alpha}+ \lambda^*_k d^\dagger_{\mathbf{k}\alpha} c_{\mathbf{k}\alpha}\],
\end{align}

A microscopic derivation  of $\lambda_\mathbf{k}$ shows~\cite{oskar,mazin_i,sadovskii,Khodas2012b}  that in 1111 systems (in which the configuration of pnictide atoms around every Fe layer is the same), $\lambda_\mathbf{k}$ vanishes along the lines $k_x=\pm k_y$ and has some weak $k_z$ dependence. In 122 structures (in which the ``above/below" configuration of pnictogen/chalcogen atoms is inverted from one Fe layer to the other), $\lambda_\mathbf{k}$ has minima but does not vanish along any direction. In the presence of a spin-orbit interaction $\lambda_\mathbf{k}$  does not have zeros even in 1111 systems~\cite{oskar,mazin_i}.  Because our goal is to understand the generic effect of the hybridization between the two bands, we will treat $\lambda_\mathbf{k}$ as a constant $\lambda$ \cite{mazin_i,Coldea}. Earlier analysis of the effect of $\lambda_\mathbf{k}$ including its angular dependence (but without interplay with inter-pocket pairing) has shown that the results are qualitatively the same as for constant $\lambda$\cite{Khodas2012b}.

   We next consider how hybridization affects the  pairing terms.  They can be subdivided into two types.
Terms of the first type  describe an interaction with excess momentum $\mathbf{Q}$ between electron pockets and contain three fermionic operators from one pocket and one from the other pocket\cite{Khodas2012a}, e.g.,
 \begin{align}\label{eq:HQ1}
	\mathcal{H}_1= u_1 \sum_{\mathbf{k},\mathbf{p},\mathbf{q}}&\bigg[\(c^\dagger_{\mathbf{k}\alpha} d_{\mathbf{k}-\mathbf{q},\alpha}+d^\dagger_{\mathbf{k}\alpha} c_{\mathbf{k}-\mathbf{q},\alpha}\) \nonumber\\
	&\times \(c^\dagger_{\mathbf{p}\beta} c_{\mathbf{p}+\mathbf{q},\beta}+d^\dagger_{\mathbf{p}\beta} d_{\mathbf{p}+\mathbf{q},\beta}\)\bigg].
\end{align}
Terms of the second type  contain an interaction with excess momentum $\mathbf{Q}$ involving two fermions from a hole pocket and two from different electron pockets, e.g.,
\begin{align}\label{eq:HQ2}
	\mathcal{H}_2= u_2 \sum_{\mathbf{k},\mathbf{p},\mathbf{q}}&\bigg[\(c^\dagger_{\mathbf{k}\alpha} h_{\mathbf{k}-\mathbf{q},\alpha}+h^\dagger_{\mathbf{k}\alpha} c_{\mathbf{k}-\mathbf{q},\alpha}\) \nonumber\\
	&\times \(d^\dagger_{\mathbf{p}\beta} h_{\mathbf{p}+\mathbf{q},\beta}+h^\dagger_{\mathbf{p}\beta} d_{\mathbf{p}+\mathbf{q},\beta}\)\bigg],
\end{align}
where the operator $h_{\mathbf{p}\alpha}$ describes fermions near one of the hole pockets.  The two types of terms are different,  yet
  their effect on the $s^{+-}$ superconducting  state is the same -- both induce an additional pairing interaction between fermions belonging to different electron pockets. Indeed, in the superconducting state $\langle c^\dagger_{\mathbf{k}\alpha}c^\dagger_{-\mathbf{k}\beta}\rangle$, $\langle d^\dagger_{\mathbf{k}\alpha}d^\dagger_{-\mathbf{k}\beta}\rangle$, and $\langle h^\dagger_{\mathbf{k}\alpha}h^\dagger_{-\mathbf{k}\beta}\rangle$ are all non-zero. Decoupling  four-fermion terms in (\ref{eq:HQ1}) and (\ref{eq:HQ2}) using these averages, we obtain anomalous quadratic terms involving $c$ and $d$ fermions:
 \begin{equation}
	\mathcal{H}_\beta =\frac{1}{2}\sum_{\mathbf{k}} \beta_k \left[c^\dagger_{\mathbf{k}\alpha}d^\dagger_{-\mathbf{k}\beta}+d^\dagger_{\mathbf{k}\alpha}
c^\dagger_{-\mathbf{k}\beta}\right]i\sigma^y_{\alpha\beta}+\mathrm{H.c.}.	\end{equation}
The coupling $\beta_k$ is proportional to the magnitude of the $s^{+-}$ gap $\Delta$ and has some non-singular  angular dependence  which we can safely neglect.

We assume without loss of generality that the parameters $\Delta$ and $\lambda$ are real and positive. The parameter $\beta \propto \Delta$ is then also real, but its sign can be either positive or negative.

 Below we consider various ratios of $\lambda/\beta$  and two  FS geometries. In each case we compute the  quasi-particle dispersion in the superconducting state and determine the position of the nodal points.  In all cases we find two different dispersions: One is gapped over the entire BZ, while the other contains nodal points in a subset of the parameter space.

\section{Circular pockets}\label{sec:circular}

As a warm-up, consider the limiting case when the two electron pockets are identical and have full rotational symmetry, i.e., $\xi^c_\mathbf{k}=\xi^f_\mathbf{k}\equiv \xi_\mathbf{k}$.

\subsection{Inter-pocket pairing only ($\beta\neq 0$, $\lambda= 0$)}

\begin{figure*}[htb]
	\centering
		\includegraphics[width=0.8\textwidth]{sequence_cb_v3.pdf}
	\caption{Gap structure for circular electron pockets with inter-pocket pairing. The crosses represent the location of the nodal points of the quasi-particle dispersions in the superconducting state. In a) and b) we show the unfolded and folded zones, respectively. In the folded zone, the pockets should overlap but we separate them for clarity. As we increase the inter-pocket pairing, keeping the conventional intra-pocket pairing fixed, the nodal points shift toward the diagonal lines $k_x=\pm k_y$, as seen in c). If the inter-pocket pairing reaches a critical value, the nodes merge and disappear, resulting in electron Fermi surfaces with opposite signs of the gap function.}
	\label{fig:circular_beta}
\end{figure*}

In this special case, we find, after straightforward diagonalization of the quadratic form,
 that the two dispersions in the superconducting state are
\begin{equation}
	\left(E_\mathbf{k}^\pm\right)^2 = \xi_\mathbf{k}^2+\(\Delta \pm \sqrt{\Delta^2 y_\mathbf{k}^2+\beta^2} \)^2,
\end{equation}
where the expression in parenthesis represents an effective gap function. At $\beta =0$, $E^+_\mathbf{k} = \pm \sqrt{\xi^2_\mathbf{k} + \Delta^2 (1 + |y_\mathbf{k}|)^2}$ and $E^-_\mathbf{k} = \pm \sqrt{\xi^2_\mathbf{k} + \Delta^2 (1 - |y_\mathbf{k}|)^2}$. This corresponds
 to the gap structure in the folded BZ:  one band has no nodes and the other band has 8 nodes (see Fig. \ref{fig:circular_beta}).

At $\beta \neq 0$, both dispersions evolve. The nodal points are still located on the FS (the locus of zero energy points in the normal state, given by $\xi_\mathbf{k}=0$).
 The band with energy $E^+_\mathbf{k}$ is shifted up at a non-zero $\beta$  and its effective gap function is definitely nodeless.
  In contrast, the band with energy $E^-_\mathbf{k}$ is shifted down and the positions of the 8 nodes shift to
\begin{equation}
	\cos(2\theta_\mathbf{k})=\pm\frac{\sqrt{\Delta^2-\beta^2}}{\alpha\Delta}.
\end{equation}
As $\beta$ increases, the nodal points move toward the diagonals $k_x=\pm k_y$, as shown in Fig. \ref{fig:circular_beta}. At a critical value $\beta_c=\Delta$ they meet along the BZ diagonals. At larger $\beta>\beta_c$ the nodes disappear.  At the same, because the nodes merge along the BZ diagonals, the sign of the gap on one FS is opposite to that on another FS. Such a gap structure has been obtained before in the analysis of possible gap configurations in LiFeAs both in orbital formalism and in band formalism~\cite{Kotliar2014,ilya_li}. In the orbital formalism, such a state was termed ``orbital antiphase'' $s^{+-}$  state\cite{Kotliar2014}.

\begin{figure}[htb]
	\centering
		\includegraphics[width=0.47\textwidth]{Delta_b.pdf}
	\caption{Nodal gap function with inter-pocket pairing $\beta$ evaluated over the FS. As $\beta$ increases, the function shifts downward and its zeroes move toward the angles $n\pi/2$, where $n$ is an integer, which correspond to the directions given by $k_x=\pm k_y$. At $\beta=\Delta$, pairs of zeroes merge at those angles. For $\beta>\Delta$, the function is negative and has no zeroes.}
	\label{fig:Delta_b}
\end{figure}

An intuitive way to understand this behavior is the following: the gap function at the upper band is positive, while the one  at the lower band has a roughly sinusoidal shape that crosses zero eight times, and its maxima occur at the diagonal directions $k_x=k_y$ and $k_x=-k_y$. As $|\beta|$ increases, the gap function shifts downward and thus the nodes  move towards the BZ diagonals, until $|\beta|$ reaches the critical value $\beta_c$. At this point, pairs of nodal points meet and annihilate. At larger
  $|\beta|>\Delta$ the maxima of the gap function are located below zero, i.e., the gap is negative for all angles.
This behavior is illustrated in Fig. \ref{fig:Delta_b}.

\subsection{Inter-pocket hopping only ($\lambda\neq 0$, $\beta=0$)}

\begin{figure*}[htb]
	\centering
		\includegraphics[width=0.8\textwidth]{sequence_cl_v3.pdf
	\caption{Gap structure for circular pockets with inter-pocket hopping. In a) and b) we show the unfolded and folded gap structure in the absence of hybridization, respectively. Inter-pocket hopping reconstructs the FSs as shown in c). The dashed line represents the original pockets, while the solid lines are the new set of two pockets. As the hopping parameter increases, the inner FS shrinks and the outer one becomes larger. In the superconducting state, the nodal points (represented as crosses) lie on the unhybridized FSs and shift toward the $k_x$ and $k_y$ axis as the hopping increases. At a critical value of this parameter the nodes meet and merge in pairs. For greater values of the parameter they vanish and the sign of the gap function becomes the same on both FSs. The separation between the FSs is purely schematic and has been exaggerated for clarity.}
	\label{fig:circular_lambda}
\end{figure*}

This case has been studied before,\cite{Khodas2012b} and we briefly summarize the results for completeness. The hybridization of the electron pockets
reconstructs the FSs. In order to study this effect we diagonalize the Hamiltonian $\mathcal{H}_0+\mathcal{H}_\lambda$ by introducing new quasi-particles $a$ and $b$  via
\begin{equation}
	c_{\mathbf{k}\alpha}=\frac{a_{\mathbf{k}\alpha}-b_{\mathbf{k}\alpha}}{\sqrt{2}},\quad
	d_{\mathbf{k}\alpha}=\frac{a_{\mathbf{k}\alpha}+b_{\mathbf{k}\alpha}}{\sqrt{2}}.\label{eq:transformation}
\end{equation}
After diagonalization, the non-pairing part of the Hamiltonian takes the form
\begin{equation}
	\mathcal{H}_0' =\sum_{\mathbf{k}} \left[\xi^a_\mathbf{k}a^\dagger_{\mathbf{k}\alpha}a_{\mathbf{k}\alpha}+\xi^b_\mathbf{k}b^\dagger_{\mathbf{k}\alpha}b_{\mathbf{k}\alpha}\right],
\end{equation}
where the dispersions are $\xi^a_\mathbf{k}=\xi_\mathbf{k}+\lambda$ and $\xi^b_\mathbf{k}=\xi_\mathbf{k}-\lambda$. The new FSs are concentric circles. The $a$ pocket is smaller and the $b$ pocket is larger than the unhybridized pockets.

In order to study the superconducting state, it is convenient to first rewrite $\mathcal{H}_\Delta$ in terms of the new operators $a$ and $b$ as
\begin{align}\label{eq:H_Delta_1}
	\mathcal{H}_{\Delta}' &=\frac{1}{2}\sum_{\mathbf{k}} \Delta\left[ a^\dagger_{\mathbf{k}\alpha}a^\dagger_{-\mathbf{k}\beta}+ b^\dagger_{\mathbf{k}\alpha}b^\dagger_{-\mathbf{k}\beta}\right]i\sigma^y_{\alpha\beta}\\
	&+\frac{1}{2}\sum_{\mathbf{k}} \Delta y_\mathbf{k} \left[a^\dagger_{\mathbf{k}\alpha}b^\dagger_{-\mathbf{k}\beta}+b^\dagger_{\mathbf{k}\alpha}a^\dagger_{-\mathbf{k}\beta}\right]\nonumber
i\sigma^y_{\alpha\beta}+\mathrm{H.c.}
\end{align}

 Note that the inter-pocket pairing component $\Delta y_\mathbf{k}$ emerges. Diagonalizing the new Hamiltonian $\mathcal{H}_0'+\mathcal{H}_{\Delta}'$, we find the two dispersions for the quasi-particles in the superconducting state given by
\begin{equation}
	\left(E_\mathbf{k}^\pm\right)^2 = A_\mathbf{k}\pm\sqrt{B_\mathbf{k}},
\label{eq:H_Delta_2}
\end{equation}
where
\begin{align}
	A_\mathbf{k}=&\xi_\mathbf{k}^2+\Delta^2 (1+y_\mathbf{k}^2)+\lambda^2,\\
	B_\mathbf{k}=&4\left[ (\xi_\mathbf{k}\lambda)^2 +\Delta^2 y_\mathbf{k}^2 (\Delta^2+\lambda^2)\right],
\end{align}

 The dispersion $E^+_\mathbf{k}$, as defined in (\ref{eq:H_Delta_2}), is positive for all $\mathbf{k}$ even when evaluated at $\Delta=0$, so it has no locus of the nodal points. Both FS lines $\xi_\mathbf{k} = \pm \lambda$ in the normal state are part of the other dispersion $E^{-}_\mathbf{k}$. Once $\Delta$ becomes non-zero,
 one can easily check that $E^{-}_k$ is non-zero along the normal state FSs. However, on the original, non-reconstructed FS,
\begin{equation}
  E_\mathbf{k}^- = \sqrt{\Delta^2 + \lambda^2} - \Delta |y_\mathbf{k}|
\end{equation}
 This function contains 8 nodal points located at
\begin{equation}
	\cos(2\theta_\mathbf{k})=\pm\frac{\sqrt{\Delta^2+\lambda^2}}{\alpha\Delta}.
\end{equation}
As one increases $\lambda$, the nodes stay on the unhybridized FSs,
 but move toward the $k_x$ or $k_y$ axes (whichever is closer), until $\lambda$ reaches a critical value $\lambda_c=\Delta \sqrt{\alpha^2-1}$. At this value of $\lambda$, pairs of nodal points merge  and then disappear at larger $\lambda$.
We show this schematically in Fig. \ref{fig:circular_lambda}.

The analysis of the signs of the gap requires some care.
  For $\lambda \gg \Delta$, the inter-pocket pairing term becomes irrelevant as the two reconstructed FSs are far apart from each other. In this limit, the gap on each reconstructed pocket is given by the fist line in (\ref{eq:H_Delta_1}) and is just $\Delta$ for both pockets.
In this limit,  the sign of the gap is indeed the same on both FSs.
At intermediate $\lambda$, however, one
    cannot define the phase of the gap function on the two FSs because in terms of the hybridized
  fermions the gap has contributions from both inter-pocket and inter-pocket condensates $\langle a_{\mathbf{k},\alpha} a_{-\mathbf{k},\beta} \rangle i \sigma^y_{\alpha \beta}$
  and $\langle a_{\mathbf{k},\alpha} b_{-\mathbf{k},\beta} \rangle i \sigma^y_{\alpha \beta}$, respectively. Because the limiting behavior at large $\lambda$ is known, it is ``natural'' to define both finite gaps with the same sign, as in Eq. (\ref{eq:H_Delta_1}),
   but we caution that this is rigorously justified only in the limit of very large $\lambda$.

\subsection{Inter-pocket pairing and hopping ($\beta\neq0$, $\lambda\neq 0$)}

\begin{figure*}[htb]
	\centering
		\includegraphics[width=0.8\textwidth]{sequence_clb_v2.pdf}
	\caption{Gap structure for circular pockets with inter-pocket hopping and pairing interaction. The solid outer and inner circles represent the reconstructed FSs after hybridization. In the superconducting state, the nodal points (represented as crosses) lie on a circle (dashed line) but no longer on the unhybridized Fermi surface. As the hopping parameter $\lambda$ increases, the nodes move toward the $k_x$ and $k_y$ axis, where they can merge and disappear. In this scenario the gap function has the same sign on both electron pockets. Increasing the pairing strength $\beta$ shifts the nodes toward the diagonal lines $k_x=\pm k_y$ instead. The nodes can merge and vanish, in which case the gap function acquires opposite signs on the outer and inner pockets.}
	\label{fig:circular_both}
\end{figure*}

Once more, the first step is to diagonalize the Hamiltonian $\mathcal{H}_0+\mathcal{H}_\lambda$ by introducing new pockets $a$ and $b$ exactly as in the case with $\beta=0$. We then rewrite the remaining Hamiltonian in terms of the $a$ and $b$ operators and obtain
\begin{align}\label{eq:H_cbl}
	\mathcal{H}_{\Delta+\beta}' &=\frac{1}{2}\sum_{\mathbf{k}} \left[(\Delta+\beta)a^\dagger_{\mathbf{k}\alpha}a^\dagger_{-\mathbf{k}\beta}+(\Delta-\beta)b^\dagger_{\mathbf{k}\alpha}b^\dagger_{-\mathbf{k}\beta}\right]i\sigma^y_{\alpha\beta}\nonumber\\
	&+\frac{1}{2}\sum_{\mathbf{k}} \Delta y_\mathbf{k} \left[a^\dagger_{\mathbf{k}\alpha}b^\dagger_{-\mathbf{k}\beta}+b^\dagger_{\mathbf{k}\alpha}a^\dagger_{-\mathbf{k}\beta}\right]i\sigma^y_{\alpha\beta}+\mathrm{H.c.}
\end{align}
 Observe that the coefficient $\beta$ appears only in the intra-pocket terms. We  diagonalize the Hamiltonian $\mathcal{H}_0'+\mathcal{H}_{\Delta+\beta}'$ and again find dispersions of the form $E_\mathbf{k}^\pm= \sqrt{A_\mathbf{k}\pm\sqrt{B_\mathbf{k}}}$, where
\begin{align}
	A_\mathbf{k}=&\xi_\mathbf{k}^2+\Delta^2 (1+y_\mathbf{k}^2)+\lambda^2+\beta^2,\\
	B_\mathbf{k}=&4\left[ (\xi_\mathbf{k}\lambda+\Delta\beta)^2 +\Delta^2 y_\mathbf{k}^2 (\Delta^2+\lambda^2)\right].
\end{align}
The dispersion $E^+_\mathbf{k}$ is fully gapped, but $E^-_\mathbf{k}$ has nodal points at momenta given by
\begin{align}
	\xi_\mathbf{k} &=\lambda\beta/\Delta,\\
	\cos 2\theta_\mathbf{k} &=\pm \frac{\sqrt{\Delta^2+\lambda^2-\beta^2-\lambda^2\beta^2/\Delta^2}}{\alpha\Delta}.
\end{align}
Note that  the nodal points are now shifted from the unhybridized FS. The direction of the shift depends
on the sign of $\beta$. If $\beta>0$ ($\beta<0$) the nodes appear between the original FSs (the ones before hybridization)
and the outer (inner) hybridized FS. The nodes exist in the parameter range given by
\begin{equation}
	0\leq\Delta^2+\lambda^2-\beta^2-\lambda^2\beta^2/\Delta^2\leq\alpha^2\Delta^2.
\label{ll}
\end{equation}
The lower bound is reached when we keep $\lambda$ fixed and increase $|\beta|$ towards critical $\beta_c = \Delta$.  In this case the nodes merge at the diagonals $k_x=k_y$ or $k_x=-k_y$. The nodes disappear when $|\beta|>\beta_c$ and the intra-pocket gap components in the first line of Eq. (\ref{eq:H_cbl}) have different signs. In the limit of $\lambda\gg \Delta$, the inter-pocket gap component becomes irrelevant since the reconstructed FSs are far apart and in this sense the gap function has opposite signs on the two electron pockets.

 The upper boundary in (\ref{ll}) is reached when we set $|\beta| < \Delta$  and increase $\lambda$. In this situation the nodes merge along  the $k_x$ and $k_y$ directions at a critical value of $\lambda$ given by
\begin{equation}
	\lambda_c = \Delta \sqrt{\frac{(\alpha^2-1)\Delta^2+\beta^2}{\Delta^2-\beta^2}}.
\end{equation}
 At $\lambda > \lambda_c$, the nodes disappear and the gap function has the same sign on each electron pocket, as can be clearly seen in the limit of $\lambda\gg\Delta$. Note that $\lambda_c$  grows with $\beta$, i.e., the inter-pocket pairing allows the nodes to exist in a greater range of values of $\lambda$. In this sense the pairing partially protects the nodes from disappearing due to hopping, as long as $|\beta|<\Delta$. The behavior of the nodes when both $\lambda$ and $\beta$ are present is summarized in Fig. \ref{fig:circular_both}.

\section{Elliptical pockets}\label{sec:elliptical}
Now we consider the more realistic case where the electron pockets are elliptical. We will take the dispersions in the form
\begin{align}
	\xi^c_\mathbf{k} &= -\mu +\frac{k_x^2}{2m_1}+\frac{k_y^2}{2m_2},\\
	\xi^d_\mathbf{k} &= -\mu +\frac{k_x^2}{2m_2}+\frac{k_y^2}{2m_1}.
\end{align}
 It is convenient to rewrite the dispersions as $\xi^{c,d}_\mathbf{k}=\xi_\mathbf{k}\pm\delta_\mathbf{k} \cos 2\theta_\mathbf{k}$, where the $+$ sign corresponds to $\xi^c_\mathbf{k}$, $\xi_\mathbf{k}\equiv (\xi_\mathbf{k}^c+\xi_\mathbf{k}^d)/2$, and $\delta_\mathbf{k}\equiv \mathbf{k}^2(m_1^{-1}-m_2^{-1})/4$. Without loss of generality, we will take $\delta_\mathbf{k}$ to be positive.

\subsection{Inter-pocket pairing only ($\beta\neq 0$, $\lambda= 0$)}

\begin{figure*}[htb]
	\centering
		\includegraphics[width=\textwidth]{sequence_eb_v3.pdf}
	\caption{Gap structure for elliptical pockets with inter-pocket pairing. In a) we show the folded electron pockets overlapping. The crosses indicate the position of the nodal points, while the solid and dashed lines indicate opposite signs of the gap function. The evolution of the nodal points as obtained by a numerical calculation is shown in b) through f). First, b) shows the nodal points with no hybridization. If the ellipticity is below a threshold, increasing the inter-pocket pairing simply shifts the nodes toward the diagonal lines $k_x=\pm k_y$ as seen in c) and d). The nodes merge and disappear after reaching the diagonal lines and the gap structure becomes nodeless as shown in g). If this occurs, the gap function has opposite signs on the inner and outer edges of the FSs. Alternatively, if the ellipticity is higher than the threshold, the nodes do not reach the diagonal lines, but instead a node emerges at that symmetry point. As we further increase the inter-pocket pairing the node splits into two nodes which move toward the original nodes, as shown in e) and f). Eventually, the new and old nodes meet and merge, resulting again in the structure shown in g).}
	\label{fig:elliptical_beta}
\end{figure*}

The dispersions after diagonalizing the Hamiltonian are given by $(E_\mathbf{k}^\pm)^2= A_\mathbf{k}\pm\sqrt{B_\mathbf{k}}$, where
\begin{align}
	A_\mathbf{k}=&\frac{1}{2}\Big[(\xi^c_\mathbf{k})^2+(\xi^d_\mathbf{k})^2+2\Delta^2 (1+y_\mathbf{k}^2)+2\beta^2\Big],\\
	B_\mathbf{k}=&\frac{1}{4}\Big[\left((\xi^d_\mathbf{k})^2-(\xi^c_\mathbf{k})^2+4\Delta^2 y_\mathbf{k}\right)^2 \nonumber\\
	&\quad+ 4|\beta|^2\left((\xi^c_\mathbf{k}-\xi^d_\mathbf{k})^2 +4\Delta^2\right) \Big].
\end{align}
Once again, $E^+_\mathbf{k}$ is fully gapped but $E^-_\mathbf{k}$ may contain nodes. Unlike the circular case, the nodes are not located on the original FSs, but at momenta $|\mathbf{k}|$ which are solutions of
\begin{equation}\label{eq:k_beta}
\(\delta_\mathbf{k}+\alpha \xi_\mathbf{k}\) \(\xi_\mathbf{k} \delta_\mathbf{k}-\alpha \Delta^2\) +\alpha \beta^2 \delta_\mathbf{k}=0.
\end{equation}
Let the solutions to this equation be $\xi_\mathbf{k}=\bar{\xi}$ and $\delta_\mathbf{k}=\bar{\delta}$. The angular positions of the nodal points are given by
\begin{equation}
	\cos^2 2\theta_\mathbf{k}= \frac{F(\bar{\xi}, \bar{\delta})}{(\bar{\delta}^2+\alpha^2\Delta^2)^2},
\end{equation}
where
\begin{align}\label{eq:theta_beta}
	F(\bar{\xi}, \bar{\delta}) &=\(\bar{\delta}^2-\alpha^2\Delta^2\) \(\bar{\xi}^2+\beta^2-\Delta^2\) \nonumber\\
		&\quad-4\alpha\Delta^2\bar{\xi}\bar{\delta}.
\end{align}
Note that for each solution to Eq. (\ref{eq:k_beta}) there exist 8 nodal points in the dispersion. One may solve
  for ${\bar \xi}$ and ${\bar \delta}$ exactly  but the solution is not very illuminating.  It is more useful
   to solve for $\bar{\xi}$ in terms of $\bar{\delta}$ and analyze how the nodal points evolve when we change ${\bar \delta}$.
   Expressing ${\bar \xi}$ in terms of ${\bar \delta}$ we obtain
\begin{equation}
\bar{\xi}=\frac{\bar{\delta} ^2-\alpha ^2 \Delta ^2 \pm\sqrt{\left(\alpha ^2 \Delta ^2+\bar{\delta} ^2\right)^2-4 \alpha ^2 \beta^2 \bar{\delta} ^2}}{2 \alpha  \bar{\delta} }.
\end{equation}
Substitution of these solutions into Eq. (\ref{eq:theta_beta}) yields
\begin{equation}
\cos^2 2\theta_\mathbf{k}=\frac{\bar{\delta} ^2-\alpha ^2 \Delta ^2 \mp\sqrt{\left(\alpha ^2 \Delta ^2+\bar{\delta} ^2\right)^2-4 \alpha ^2 \beta^2 \bar{\delta} ^2}}{2 \alpha^2  \bar{\delta}^2 }
\label{a_3}
\end{equation}

 Analyzing (\ref{a_3}) we find new interesting physics. Namely, depending on the parameters, there may be 0, 8, or 16 nodal points in the dispersion. When
  $\bar{\delta}<\alpha\Delta$,  there are either 8 or zero nodes, as one can immediately verify.  At small $\beta$, there are 8 nodes.
      As $|\beta|$  increases, the nodes move toward the diagonals $k_x=\pm k_y$, like in the circular case. At $|\beta|=\Delta$, pairs of nodes merge,
        and for $|\beta|>\Delta$ they disappear.   The outcome of the disappearance of the nodes is the effective $s^{+-}$ superconducting state
          with different signs of the gap on the inner and outer electron pockets, see Fig. \ref{fig:elliptical_beta}.

 When $\bar{\delta}>\alpha\Delta$, the evolution of the nodes is more interesting. At small $\beta$, there are again 8 nodes. As $|\beta|$ increases, the nodes shift towards diagonals but they do not reach $k_x=\pm k_y$ at $|\beta| =\Delta$. Instead, at this $\beta$, a new quadratic node appears in in each quadrant at the point where zone diagonals intersect the original FS.  At $|\beta| > \Delta$, each quadratic node splits into two, one to the right and one to the left of a diagonal, and each new node moves toward the already existing nodes (see Fig. \ref{fig:elliptical_beta}).  Thus, there is a total of 16 nodal points.
  As  $|\beta|$ continues increasing,  the old and new nodes merge
  at a critical value $|\beta|=\beta_c$ given by
  \begin{equation}
  \beta_c=\left(\alpha ^2 \Delta ^2+\bar{\delta} ^2\right)/ (2|\alpha|  \bar{\delta}).
   \end{equation}
   The nodes disappear when $|\beta|$ exceeds this critical value and the end result of the evolution of the nodes is the same minus-plus gap on the inner and outer electron pockets.

We verified this behavior numerically (Fig. \ref{fig:elliptical_beta} actually shows the results of numerical calculations).
 In all numerical examples here and below we have set $\mu=10\Delta$ and $\alpha=-1.5$.
Note in passing that while the relationships presented in this analysis are exact, one must keep in mind that in general $\bar{\delta}$ by itself depends on $\beta$.

\subsection{Inter-pocket hopping only ($\lambda\neq 0$, $\beta=0$)}

\begin{figure*}[htb]
	\centering
		\includegraphics[width=0.8\textwidth]{sequence_el.pdf}
	\caption{Gap structure for elliptical pockets with inter-pocket hopping. In a) we show the gap structure in the absence of hybridization. Inter-pocket hopping reconstructs the FSs as shown in b). As the hopping parameter increases, the inner FS shrinks and the outer one becomes larger. In the superconducting state, the nodal points (represented as crosses) lie near, but not exactly on FSs and shift toward the $k_x$ and $k_y$ axis as the hopping increases, as shown in b) and c). At a critical value of the hopping the nodes meet and merge in pairs as in d). Finally, for greater values of the parameter they vanish and the sign of the gap function becomes the same on both FSs. Subfigures b) through e) are the result of numerical calculations.}

\label{fig:elliptical_lambda}
\end{figure*}

This case has been studied before~\cite{Khodas2012b}  and we present it here for completeness, using a somewhat different computation scheme.
 The first step is to diagonalize the Hamiltonian $\mathcal{H}_0+\mathcal{H}_\lambda$ by introducing new operators $a$ and $b$ such that
\begin{align}
	c_{\mathbf{k}\alpha} &=u_\mathbf{k}c_{\mathbf{k}\alpha}+v_\mathbf{k}b_{\mathbf{k}\alpha}, \nonumber\\
	d_{\mathbf{k}\alpha} &=-v_\mathbf{k}a_{\mathbf{k}\alpha}+u_\mathbf{k}b_{\mathbf{k}\alpha},
\end{align}
where $u_\mathbf{k}=\cos \psi$ and $v_\mathbf{k}=-\sin \psi$, and this angle $\psi$ satisfies $\cos 2\psi=(\xi_\mathbf{k}^c-\xi_\mathbf{k}^d)/\sqrt{(\xi_\mathbf{k}^c-\xi_\mathbf{k}^d)^2+4\lambda^2}$ and $\sin 2\psi=2\lambda/\sqrt{(\xi_\mathbf{k}^c-\xi_\mathbf{k}^d)^2+4\lambda^2}$. The new Hamiltonian is
\begin{equation}
	\mathcal{H}_0' =\sum_{\mathbf{k}} \left[\xi^a_\mathbf{k}a^\dagger_{\mathbf{k}\alpha}a_{\mathbf{k}\alpha}+\xi^b_\mathbf{k}b^\dagger_{\mathbf{k}\alpha}b_{\mathbf{k}\alpha}\right],
\end{equation}
where $\xi^{a,b}_\mathbf{k}=\frac{1}{2}(\xi^c_\mathbf{k}+\xi^d_\mathbf{k})\pm\sqrt{\lambda^2+(\xi_\mathbf{k}^c-\xi_\mathbf{k}^d)^2/4}$. These new dispersions define the reconstructed FSs  shown in Fig. \ref{fig:elliptical_lambda}. As the hopping parameter $\lambda$ increases, the outer FS (associated with $b$ fermions) becomes larger, while the inner FS (associated with $a$ fermions) shrinks.

Now we consider the superconducting state. Rewriting the pairing part of the Hamiltonian in terms of the new operators we find
\begin{align}
	\mathcal{H}_{\Delta}' &=\frac{1}{2}\sum_{\mathbf{k}} \Big[\Delta(1-f_\mathbf{k} y_\mathbf{k})a^\dagger_{\mathbf{k}\alpha}a^\dagger_{-\mathbf{k}\beta} \Big.\nonumber\\
	&\quad\quad\quad+\Big.\Delta(1+f_\mathbf{k} y_\mathbf{k})b^\dagger_{\mathbf{k}\alpha}b^\dagger_{-\mathbf{k}\beta}\Big]i\sigma^y_{\alpha\beta}\\
	&-\frac{1}{2}\sum_{\mathbf{k}} \Delta g_\mathbf{k}y_\mathbf{k} \left[c^\dagger_{\mathbf{k}\alpha}d^\dagger_{-\mathbf{k}\beta}+d^\dagger_{\mathbf{k}\alpha}c^\dagger_{-\mathbf{k}\beta}\right]i\sigma^y_{\alpha\beta}+\mathrm{H.c.},	\nonumber
\end{align}
where $f_\mathbf{k}\equiv \cos 2\psi$ and $g_\mathbf{k}\equiv -\sin 2\psi$. The diagonalization of this Hamiltonian again yields dispersions in the superconducting state in
 the form $(E_\mathbf{k}^\pm)^2= A_\mathbf{k}\pm\sqrt{B_\mathbf{k}}$. In this particular case
\begin{align}
	A_\mathbf{k}=&\frac{1}{2}\Big[(\xi^a_\mathbf{k})^2+(\xi^b_\mathbf{k})^2+2\Delta^2 (1+y_\mathbf{k}^2)\Big],\\
	B_\mathbf{k}=&\frac{1}{4}\Big[\left((\xi^b_\mathbf{k})^2-(\xi^a_\mathbf{k})^2+4\Delta^2 f_\mathbf{k}y_\mathbf{k}\right)^2 \nonumber\\
	&\quad+ 4\Delta^2 y^2_\mathbf{k}g^2_\mathbf{k}\left((\xi^a_\mathbf{k}-\xi^b_\mathbf{k})^2 +4\Delta^2\right) \Big].
\end{align}

As usual, the dispersion $E^+_\mathbf{k}$ is nodeless, but $E^-_\mathbf{k}$ has nodes at momenta which are the solutions of the equation
\begin{equation}\label{eq:k_lambda}
\(\delta_\mathbf{k}+\alpha \xi_\mathbf{k}\) \(\xi_\mathbf{k} \delta_\mathbf{k}-\alpha \Delta^2\) -\alpha \lambda^2 \delta_\mathbf{k}=0.
\end{equation}

Each solution to this equation defines a pair ($\bar{\xi}$, $\bar{\delta}$) and determines the radial position of the nodal point. The angular position is then given by
\begin{equation}\label{eq:theta_lambda}
	\cos^2 2\theta_\mathbf{k}= \frac{F(\bar{\xi}, \bar{\delta})}{(\bar{\delta}^2+\alpha^2\Delta^2)^2},
\end{equation}
where
\begin{align}
	F(\bar{\xi}, \bar{\delta}) &=\(\bar{\delta}^2-\alpha^2\Delta^2\) \(\bar{\xi}^2-\lambda^2-\Delta^2\) \nonumber\\
		&\quad-4\alpha\Delta^2\bar{\xi}\bar{\delta}.
\end{align}

Like before, we solve for $\bar{\xi}$ in terms of $\bar{\delta}$. The solution is
\begin{equation}
\bar{\xi}=\frac{-\bar{\delta} ^2+\alpha ^2 \Delta ^2 -\sqrt{\left(\alpha ^2 \Delta ^2+\bar{\delta} ^2\right)^2+4 \alpha ^2 \lambda^2 \bar{\delta} ^2}}{2 \alpha  \bar{\delta} }.
\end{equation}
When we substitute this solution into Eq. (\ref{eq:theta_lambda}) we find that the angular position of the nodes is given by
\begin{equation}
\cos^2 2\theta_\mathbf{k}=\frac{\bar{\delta} ^2-\alpha ^2 \Delta ^2 +\sqrt{\left(\alpha ^2 \Delta ^2+\bar{\delta} ^2\right)^2+4 \alpha ^2 \lambda^2 \bar{\delta} ^2}}{2 \alpha^2  \bar{\delta}^2 }.
\end{equation}

The analysis of these equations shows that nodal points appear in a set of 8 and that they are not located on the FSs of the normal state, although our numerical calculations show that they remain very close to it. The location of the nodes with respect to the original FSs varies depending on the sign of $\alpha$. If $\alpha>0$, the nodes are located inside of both unhybridized FSs but outside of the smaller FS. Instead, if $\alpha<0$ the nodes are outside the unhybridized FSs but inside the larger reconstructed FS.

In both cases, the behavior is qualitatively the same as in the limiting case of circular pockets and is summarized in Fig. \ref{fig:elliptical_lambda}, where we show the result of numerical calculations. Increasing $\lambda$ shifts the nodes toward the $k_x$ and $k_y$ axes. The critical value of $\lambda$ that causes the nodes to merge along these directions is enhanced by the ellipticity and is given by $\lambda_c=\sqrt{\(\Delta^2+\bar{\delta}^2\) \(\alpha^2-1\)}$. At any larger $\lambda$ the nodes disappear.
In this sense, the eccentricity of the pockets tries to prevent the disappearance of the nodes.

Regarding the gap structure, we note that for large $\lambda$ the inter-pocket pairing term is irrelevant as the reconstructed FSs are far apart from each other. In this limit, the gap on the reconstructed pockets is given by $\Delta(1\pm f_\mathbf{k}y_\mathbf{k})$,
 where $|f_\mathbf{k}y_\mathbf{k}|\ll 1$. Thus, the phase of the gap function is equal and uniform over the the reconstructed FSs.
 At smaller $\lambda$, the phase of the gap along the FSs cannot be determined as the pairing involves both intra-pocket and inter-pocket terms.
Judging from the large $\lambda$ limit, it seems natural to define the gap with equal sign on both FSs also at intermediate $\lambda$, see Fig. \ref{fig:elliptical_lambda}.

\subsection{Inter-pocket pairing and hopping ($\beta\neq0$, $\lambda\neq 0$)}

\begin{figure*}[htb]
	\centering
		\includegraphics[width=0.8\textwidth]{sequence_e_all.pdf}
	\caption{Gap structure for elliptical pockets with inter-pocket hopping and pairing. This case incorporates all the features seen in Figs. \ref{fig:elliptical_beta} and \ref{fig:elliptical_lambda}. The main difference is that the condition for additional nodes does not depend solely on the ellipticity, but also on the hopping parameter and the sign of the inter-pocket pairing.}
	\label{fig:elliptical_all}
\end{figure*}

This case is the most generic one. Like before, we switch to the reconstructed $a$ and $b$ pockets after hybridization. The pairing terms in the Hamiltonian can be rewritten in terms of $a$ and $b$  operators and take the form
\begin{align}
	\mathcal{H}_{\Delta+\beta}' &=\frac{1}{2}\sum_{\mathbf{k}} \left[\Delta_{aa}(\mathbf{k})a^\dagger_{\mathbf{k}\alpha}a^\dagger_{-\mathbf{k}\beta}+\Delta_{bb}(\mathbf{k})b^\dagger_{\mathbf{k}\alpha}b^\dagger_{-\mathbf{k}\beta}\right]i\sigma^y_{\alpha\beta}\nonumber\\
	&+\frac{1}{2}\sum_{\mathbf{k}} \Delta_{ab}(\mathbf{k}) \left[a^\dagger_{\mathbf{k}\alpha}b^\dagger_{-\mathbf{k}\beta}+b^\dagger_{\mathbf{k}\alpha}a^\dagger_{-\mathbf{k}\beta}\right]i\sigma^y_{\alpha\beta}+\mathrm{H.c.},
\end{align}
where
\begin{align}
	\Delta_{aa}(\mathbf{k}) &=\Delta(1-y_\mathbf{k}f_\mathbf{k}) -\beta g_\mathbf{k},\\
	\Delta_{bb}(\mathbf{k}) &=\Delta(1+y_\mathbf{k}f_\mathbf{k}) +\beta g_\mathbf{k},\\
	\Delta_{ab}(\mathbf{k}) &=-\Delta y_\mathbf{k}g_\mathbf{k} +\beta f_\mathbf{k}.
\end{align}

The dispersions are given by $(E_\mathbf{k}^\pm)^2= A_\mathbf{k}\pm\sqrt{B_\mathbf{k}}$,
where
\begin{align}
	A_\mathbf{k}=&\frac{1}{2}\Big[\(\xi^a_\mathbf{k}\)^2+\(\xi^b_\mathbf{k}\)^2+2\Delta^2 \(1+y_\mathbf{k}^2\) +2\beta^2\Big],\\
	B_\mathbf{k}=&\frac{1}{4}\Big[\left(\(\xi^b_\mathbf{k}\)^2-\(\xi^a_\mathbf{k}\)^2+4\Delta^2 f_\mathbf{k}y_\mathbf{k}\right)^2 \nonumber\\
	&\quad+ 4\Delta^2 y^2_\mathbf{k}g^2_\mathbf{k}\left((\xi^a_\mathbf{k}-\xi^b_\mathbf{k})^2 +4\Delta^2\right) \Big]\nonumber\\
	-&2\beta\Delta  g_\mathbf{k} \(\xi_\mathbf{k}^a-\xi_\mathbf{k}^b\) \[ \xi^a_\mathbf{k} +\xi^b_\mathbf{k} +\(\xi^a_\mathbf{k}-\xi^b_\mathbf{k}\) f_\mathbf{k} y_\mathbf{k}\]\nonumber\\
	+&\beta^2 \[4\Delta^2+\(\xi^a_\mathbf{k}-\xi^b_\mathbf{k}\)^2 f^2_\mathbf{k}\].
\end{align}

Once more, we search for nodes in the dispersion $E^-_\mathbf{k}$. The radial position of the nodes is determined by the condition
\begin{align}\label{eq:k_both}
\left(\delta_\mathbf{k}  \xi_\mathbf{k} -\alpha  \Delta^2\right)(\delta_\mathbf{k}+\alpha  \xi_\mathbf{k}) &\nonumber\\
+\frac{\beta  \lambda}{\Delta}  \(\alpha^2 \Delta^2-\delta^2_\mathbf{k}\)
+\alpha \(\beta^2-\lambda^2\)\delta_\mathbf{k} & =0.
\end{align}
The solutions to this equation $(\bar{\xi},\bar{\delta})$ are needed to find the angular position of the nodes:
\begin{equation}\label{eq:theta_both}
	\cos^2 2\theta_\mathbf{k}= \frac{F(\bar{\xi}, \bar{\delta})}{(\bar{\delta}^2+\alpha^2\Delta^2)^2},
\end{equation}
where
\begin{align}
	F(\bar{\xi}, \bar{\delta}) &=\(\bar{\delta}^2-\alpha^2\Delta^2\) \(\bar{\xi}^2+\beta^2-\lambda^2-\Delta^2\) \nonumber\\
		&\quad+4\alpha\Delta\bar{\delta}\(\beta\lambda-\Delta\bar{\xi}\).
\end{align}

\begin{widetext}
Solving for $\bar{\xi}$ in terms of $\bar{\delta}$, we find that the solutions to Eq. (\ref{eq:k_both}) are
\begin{equation}
\bar{\xi} =\frac{1}{2 \alpha  \bar{\delta}} \Bigg\{-\bar{\delta} ^2+\alpha ^2 \Delta ^2 \pm\Bigg[\left(\alpha ^2 \Delta ^2+\bar{\delta} ^2\right)^2+4\alpha\bar{\delta}\bigg(\(\bar{\delta}^2-\alpha^2\Delta^2\) \frac{\lambda\beta}{\Delta}+ \alpha\bar{\delta}\(\lambda^2-\beta^2\)\bigg)\Bigg]^{1/2}\Bigg\}.
\end{equation}
The angular location of the nodes for these solutions is given by
\begin{equation}
\cos^2 2\theta_\mathbf{k} =\frac{1}{2 \alpha^2  \bar{\delta}^2} \Bigg\{\bar{\delta} ^2-\alpha ^2 \Delta ^2 +2\alpha\delta\beta\lambda/\Delta\mp\Bigg[\left(\alpha ^2 \Delta ^2+\bar{\delta} ^2\right)^2+4\alpha\bar{\delta}\bigg(\(\bar{\delta}^2-\alpha^2\Delta^2\) \frac{\lambda\beta}{\Delta}+ \alpha\bar{\delta}\(\lambda^2-\beta^2\)\bigg)\Bigg]^{1/2}\Bigg\}.
\end{equation}
\end{widetext}

In this general case the interplay of the different parameters is considerably more complicated that in the previous limiting cases, but it does not produce any new features. We find that in general the position of the nodal points depends on the signs of both $\beta$ and $\alpha$, not only their magnitudes. The dependence on the sign of $\beta$ comes from bilinear terms of the form $\beta\lambda$, while the dependence on the sign of $\alpha$ is a consequence of the ellipticity of the pockets.

The general behavior of the nodal points is summarized in Fig. \ref{fig:elliptical_all}. We found by numerical analysis that in general increasing $\lambda$ tends to shift the nodes toward the $k_x$ and $k_y$ axis as usual, where they merge and disappear at a critical value of $\lambda$. In this  case, the sign of the order parameter is the same on both FSs. Increasing $|\beta|$ instead shifts the nodes toward the diagonals $k_x=\pm k_y$. At $|\beta|=\Delta$ there are two possibilities, as seen in the limiting case of $\lambda=0$. The first is that the eight nodal points merge in pairs at the diagonal lines, disappearing for $|\beta|>\Delta$.
 This happens at small ${\bar \delta}$, i.e., for small eccentricity.
  The second is that the original nodal points do not reach the diagonal lines at this value of $\beta$, but instead four new nodes appear at those lines. Increasing $|\beta|$ further causes these four new nodal points to split into pairs, and moves the old and new nodes toward each other.
	At a threshold value of $\beta$ they merge and then disappear. This second scenario, with 16 nodal points at intermediate $\beta$, is realized at larger ${\bar \delta}$, i.e., at larger eccentricity. In either case, the merging of nodes caused by large $\beta$ means that the gap function has opposite signs on the electron pockets.

One important difference with the case of $\lambda=0$ is that the condition for developing additional nodal points is more complicated since the sign of $\beta$ and the value of $\lambda$ also play a role. It is clear from the equations that the additional nodes are more likely to develop for $\beta<0$, for $\delta>\alpha\Delta$ and for small $\lambda$. The exact conditions when additional nodes appear are given by rather involved formulas and we refrain from
 presenting them.

\section{Conclusions}\label{sec:conclusions}
In this paper we have investigated the effect of hybridization of the two electron pockets on the gap structure in FeSCs. We considered the case when the dominant pairing interaction is between hole and electron pockets and it yields an $s^{+-}$ gap with accidental nodes on the electron pockets.
Our goal was to understand how accidental nodes move once we include the hybridization.
 We argued that for an $s^{+-}$ superconductor hybridization gives rise to two effects --  hopping between electron FSs and the appearance of an additional pairing term which describes inter-pocket pairing.
  Each of these two effects shifts the position of the nodes and at large enough hybridization the nodes eventually disappear. However, the evolution of the nodes and the gap structure of the resulting no-nodal state is different, depending on whether the inter-pocket hopping or the inter-pocket interaction is stronger.
 In the first case, the resulting state has the same sign of the gap on both reconstructed FSs.  In the second case, there is a sign change of the superconducting gap  between the inner and outer FSs.

  We also found that the evolution of the nodes with increasing inter-pocket pairing interaction is rather non-trivial, and
   in the intermediate regime the number of nodal points may increase from 8 to 16.
 We also found that the eccentricity of the pockets enlarges these critical values, partially protecting the nodal points from disappearing. The bottom line of this analysis is that  strong hybridization lifts accidental nodes, but the  resulting superconducting state may be highly non-trivial, particularly when the dominant effect of hybridization is the emergence of inter-pocket pairing potential.

We acknowledge useful conversations with M. Khodas, P. Coleman, R. Fernandes, K. Haule, A. Kamenev, and G. Kotliar.
The work is supported by the DOE grant DE-FG02-ER46900.

redpajama_set_name: RedPajamaArXiv


text:
Berkeley Bowl Marketplace ("us", "we", or "our") operates the Berkeley Bowl Marketplace website (the "Service").
We use your Personal Information for providing and improving the Service. By using the Service, you agree to the collection and use of information in accordance with this policy. Unless otherwise defined in this Privacy Policy, terms used in this Privacy Policy have the same meanings as in our Terms and Conditions, accessible at https://berkeleybowl.com
Cookies are files with a small amount of data, which may include an anonymous unique identifier. Cookies are sent to your browser from a web site and stored on your computer's hard drive.
Please read these Terms of Use ("Terms", "Terms of Use") carefully before using the https://berkeleybowl.com website (the "Service") operated by Berkeley Bowl Marketplace ("us", "we", or "our").
The Service and its original content, features and functionality are and will remain the exclusive property of Berkeley Bowl Marketplace and its licensors.
Our Service may contain links to third-party web sites or services that are not owned or controlled by Berkeley Bowl Marketplace.
Berkeley Bowl Marketplace has no control over, and assumes no responsibility for, the content, privacy policies, or practices of any third party web sites or services. You further acknowledge and agree that Berkeley Bowl Marketplace shall not be responsible or liable, directly or indirectly, for any damage or loss caused or alleged to be caused by or in connection with use of or reliance on any such content, goods or services available on or through any such web sites or services.
These Terms shall be governed and construed in accordance with the laws of United States without regard to its conflict of law provisions.

redpajama_set_name: RedPajamaCommonCrawl


Welcome to the Madrid Travel Guide, your online travel specialist. Madrid Hotels offers you comprehensive information and online booking facilities for Hotel Puerta de Toledo, car rentals & golf.
As a leading online hotels and travel guide, the volume of hotel reservations that we send to our selected hotels, apartments & resorts in Madrid means that we have negotiated the most competitive rates for our customers. Below you can find more information on the hotel you selected, Hotel Puerta de Toledo.
With a stay at Hotel Puerta de Toledo, you'll be centrally located in Madrid, steps from Gate of Toledo and minutes from El Rastro. This hotel is within close proximity of San Isidro Museum and San Isidro Church.
Make yourself at home in one of the 176 guestrooms. Satellite television is provided for your entertainment. Conveniences include phones, and cribs/infant beds can be requested.
Satisfy your appetite at a coffee shop/café serving guests of Hotel Puerta de Toledo.


Caching-only name servers are servers not authoritative for any domains except 0.0.127.in-addr.arpa, the localhost. A caching-only name server can look up names inside and outside your zone, as can primary and slave name servers. The difference is that when a caching-only name server initially looks up a name within your zone, it ends up asking one of the primary or slave names servers for your zone for the answer.
In the forwarders line, 208.164.186.1 and 208.164.186.2 are the IP addresses of your Primary Master and Secondary Slave DNS server. They can also be the IP addresses of your ISPs DNS server and another DNS server, respectively.
: To improve the security of your BIND/DNS server you can stop it from even trying to contact an off-site server if their forwarder is down or doesn't respond. With the forward only option set in your named.conf file, the name server doesn't try to contact other servers to find out information if the forwarder doesn't give it an answer.
Configure the /var/named/db.cache file for a simple caching name server before starting your DNS server. You must take a copy of db.cache file and copy this file to the /var/named/ directory. The db.cache tells your server where the servers for the root zone are.
Don't forget to copy the db.cache file to the /var/named/ directory on your server where you're installing DNS server after retrieving it over the Internet.
: Internal addresses like 192.168.1/24 are not included in the DNS configuration files for security reasons. It is very important that DNS doesn't exist between hosts on the corporate network and external hosts.


The gourmet coffee table or probably eileen grey coffee table can be a decorating adornment of which improves your body associated with settees as well as accent chairs, eliminating in the middle of the bedroom for a center point pertaining to minutes associated with conviviality and break. The help system and to provide it's friends drinks in addition to finger foods involving several buddies, laughter, and also joke.
It truly is an enjoyable moment while we are producing small talk with buddies in conjunction with a cup of coffee or maybe tea on coffee stand inside the lifestyle room. Comfy seating on the sofa, amongst experiences, along with eileen grey coffee table, it will make a great opinion about your house. A delicate vase with clean peonies or a greater with fresh adorned cupcakes is going to frame the actual part.
Rectangle coffee table can become common furnishing for just about any house style. Exceedingly particular in its concrete is particularly gray and dark color. It is a bit of good style and unique model, ready to create your home unique and incomparable. Enhance your house with this particular contemporary piece of furniture. It's stated that the king of the family area could be the sofa, however we all mustn't forget the value of an elegant and purposeful furnishing accessory like a espresso table. merger of styles for houses of recent creativity where every aspect coordinates as well as completes the other. The key characteristics which identify each trend regarding furnishings may also be shown within the coffee desk.
Yet another design which is perfect for universally home will be adaptable and contemporary coffee stand with a few legs and circular prime on colored timber, it moves flawlessly with rooms along with pal or relatives but modern design. The help floor is perfect to allow for any kind of item, making this item of good use from a cosmetic as well as useful viewpoint. The timber support design allows maximum security in any kind of surface. Along with practical, espresso table can also be easily obtainable on furniture shops such as for instance target or perhaps Walmart. From a coffee desk in which is smart, contemporary, inexpensive, large, and different design are available. Which we need to contemplate when choosing a coffee dining table style is modify the ground color and style of the couch and internal.
Structure within pickled wood and also glassworks prime or on eileen grey coffee table - dadevoice #f9876154691f inside eileen grey coffee table for a shabby family area within pale colors which enjoys feminine hints. Glossy materials to accomplish a bright couch with small and important characteristics. showcases and shades to get a glamorous fashion living room that really wants to amaze having its refinement. Whatever form of inspiration you select, the coffee desk can conform to how big is the couch, reaching the top of the seat so as to not creatively battle using the remaining portion of the furniture.
Then, any time guests tend to be acquired, the espresso table or might only placing eileen grey coffee table - dadevoice #f9876154691f inside eileen grey coffee table help area should be good and produce the gourmet food prepared for the occasion captivating. On the evening, a ceramic classic vase with sweet flowers will give a pleasing smell whereas a glass milk can reveal the cakes or desserts designed with fondant. A vibrant espresso company or pottery teacups to function hot water. In the evening, for an eleventh hour diy pleased hour, little white ceramic spoon can surprise guests with delightful dishes to style in one single bite. Fine, Let us discover how to make your house much more beautiful.


Dr. Shivan Haran, director of mechanical engineering, initiated an after-school robotics program at the elementary school level in Jonesboro, starting at nearby Valley View. The program was a tremendous success, with more than 60 children participating, predominantly from the second and third grade.
Haran and the Arkansas State University engineering program is set to return to Valley View Elementary this fall. Other schools have already expressed interest for next academic year.
The goal was to introduce and expose the school children to some of the basic concepts in engineering at a very early stage. This way, the children are given an opportunity to learn some unique skills which, in the long run, will help them think through problems. The outcome of such an effort is to increase the children's interest and understanding of basic concepts in engineering, math and programming through hands-on learning. In the long run, the children will be better prepared for college and are more likely to major in engineering or the sciences.
A-State students talk about their experiences in the after-school program.
The seven-week program included student volunteers from the student chapter of the American Society of Mechanical Engineers (ASME) of which Dr. Haran is the faculty mentor. These students, mechanical engineering majors, were responsible for the direct interaction and hands-on instruction with the school children. Some of the teachers also were involved during the weekly sessions.
This initiative will lead to regular summer camps at A-State that will encourage K-12 teachers and parents to be involved, and generally increase knowledge and awareness in the STEM disciplines. We hope that this will spread interest among the K-12 schools in and around Jonesboro to begin with, and statewide in the long run. We also plan to include teacher training at a later stage so that this can be carried out independently by the teachers in various schools, as part of a curriculum or an after-hours activity.


text:
Anaphylaxis: 36 Commonsense Ways to Reduce the Risk
In 2000, the World Allergy Organization (WAO) published a consensus definition of anaphylaxis as a severe, life-threatening generalized or systemic hypersensitivity reaction. The reaction is caused by the release of bioactive mediators from mast cells and basophils.
Key words: anaphylaxis,
In 2000, the World Allergy Organization (WAO) published a consensus definition of anaphylaxis as a severe, life-threatening generalized or systemic hypersensitivity reaction.1 The reaction is caused by the release of bioactive mediators from mast cells and basophils.2
The WAO recommends that if the reaction is immunologically mediated- involving IgE, IgG, or immune complex activation of the complement system-the term "allergic anaphylaxis" should be used (examples: peanuts, penicillin, bee venom, blood products, natural rubber latex). If nonimmunological reactions are involved, the organization recommends the term "nonallergic anaphylaxis" (examples: exercise, aspirin and NSAIDs, cold). Anaphylactoid, the older term for nonallergic anaphylaxis, is no longer recommended. Since the signs and symptoms of allergic and nonallergic anaphylaxis may be identical, the presence of 1 of 3 criteria for diagnosis has been suggested (Table 1).
Why one "shock organ" reacts preferentially over another is unknown. Fatalities have been most commonly associated with angioedema of the upper airway, followed by hypotension/
arrhythmias. Since the definition of anaphylaxis has varied from study to study, the prevalence is unknown. Possibly the best estimate is that about 1% of the population have been given an outpatient prescription for epinephrine.3 It is estimated that there are 7 to 10 nonfatal cases of anaphylaxis per 1000 parenteral doses of penicillin (1 fatal reaction per 50,000 doses) and 8 nonfatal cases per 1000 venomous stings from bees, wasps, hornets, and fire ants (40 to 50 deaths in the United States per year).4,5
Once a diagnosis of anaphylaxis is established by a temporal relationship (usually less than 1 hour) between an event (eg, administration of a medication or an x-ray dye, ingestion of a food, or a venomous sting) and the usual clinical manifestations, excellent treatment protocols are available.2
In this article, I suggest 36 ways to avert the largely preventable syndrome of anaphylaxis. An Wang, founder of Wang Laboratories, once said, "Success is more a function of consistent common sense than it is of genius." Most of the strategies suggested here are little more than that.
1. Always take a complete history of all adverse reactions to any diagnostic or therapeutic agent or to rubber or food.
A classic paper on fatal penicillin reactions states that in 50% of the deaths, no information about previous reactions was available in the medical records. It appears that no question about penicillin allergy was ever posed.4
The standard question "Do you have any drug allergies?" is too vague. Many patients do not consider over-the-counter medications "drugs" and may not be sure what an allergic reaction is. A better question would be "Have you ever had an allergic reaction or a bad reaction to a prescription medicine (such as penicillin), an over-the-counter medication (such as aspirin), a vaccination, an anesthetic, x-ray dye, rubber, blood product, or food?"
2. Don't bury vital written information about previous reactions.
Prominent display of adverse reactions is particularly important when one physician substituting for another is not as familiar with the patient's history. In addition to pasting stickers on chart fronts or if possible on the bed of inpatients, I recommend that each chart contain a standardized Adverse Reaction Form listing these facts:
Date or, if unknown, approximate year of reaction.
Provoking substance(s).
Nature of reaction.
Name of person who is entering the information.
Details such as mild upset stomach from an antibiotic need not be listed. However, when in doubt, record. A future standardized electronic medical record should keep vital information "unearthed."
3. Always believe the patient who tells you about having had an adverse reaction.
In one study, 70% of patients who died after a penicillin injection had previously received the drug; one-third of them had previously experienced sudden allergic reactions to it.4
In truth, a significant number of patients had told the physician they were allergic to penicillin-but were given it anyway!
4. When a patient tells you about an adverse reaction to a medication, always use an alternative unless a reliable, safe skin test is available to rule out allergy.
A substitute is almost always available for the medication the patient claims caused an adverse reaction. If the offending medication must be used, either seek allergy consultation or use a desensitization protocol (see No. 26). Although hypersensitivity may wane with time, the introduction of even micrograms may cause anaphylaxis in a sensitized patient.
Skin-testing protocols are available only for select IgE-mediated allergic reactions, such as those caused by penicillin. Experience has shown that careful pretesting with penicillin G and benzylpenicilloyl polylysine (PPL) can detect 90% to 95% of persons who have the potential for an anaphylactic reaction. To date, no fatalities have occurred among history-positive, skin test–negative patients who subsequently received penicillin.6 Unfortunately, commercial PPL testing material was removed from the market several years ago; currently, risk assessment by skin testing is available only in research facilities where the reagent can be prepared.
Skin testing with other antibiotics has not been evaluated in as many patients as penicillin has been. Risks associated with administration of other antibiotics to history-positive, skin test–negative patients are unknown.7 If you must use one of these because it is potentially lifesaving and the history suggests allergy, a desensitization protocol (oral route safer than parenteral route) in an ICU is recommended (see No. 26).
5. Know about potential cross-reaction between medications.
The risk of administering a first-generation cephalosporin to a patient with penicillin allergy is not negligible. For higher-generation cephalosporins, the risk is thought to be lower8; however, the package insert for every cephalosporin states caution in use, since "cross-hypersensitivity among β-lactam antibiotics has been clearly documented and may occur in up to 10% of patients with a history of penicillin allergy." If a cephalosporin is the treatment of choice over antibiotics that do not contain a β-lactam ring, the safest approach is a desensitization protocol (by the oral route if preparations are available). Use a protocol similar to that of penicillin, beginning with 0.05 mg for oral or 0.01 mg for intravenous administration.
NSAIDs pose a high risk in patients who have had an adverse reaction to aspirin, and vice versa. Reactions to aspirin or NSAIDs are not thought to be IgE-mediated; rather, they may be caused by blockade of the cyclooxygenase pathway, because these drugs inhibit prostaglandin synthetase.9 Consequently, there are no skin or in vitro tests to confirm the diagnosis, and giving a test dose is not recommended. Highly successful desensitization protocols are available for patients who have had asthmatic and/or sinusitis reactions to aspirin.10
In patients who are allergic to sulfa, it appears from the literature that using non-arylamine–containing sulfa medications (examples: oral hypoglycemics, diuretics, and NSAIDs such as celecoxib) is safe.8
6. Know how to handle previous adverse reactions to vaccines.
If a patient reports an "allergic" reaction to a vaccine, withhold and follow 1 of these 3 strategies:
For patients with a future vaccine need, skin test with the vaccine (this requires training and the use of proper skin testing controls) or give the vaccine in a graded-dose protocol and be prepared to treat anaphylaxis.2
For those with an uncertain need, check antibody levels to see if they are protective. If they are, withhold the vaccine; if not, proceed with the need strategy.
For those with no need of the vaccine in the future, document the reaction and withhold. Protocols are available for immunotherapy with tetanus toxoid on a need basis; however, these protocols take 10 to 20 weeks to complete.11
7. Know which vaccines contain egg residues and know which ones can be given to egg-allergic patients.
Vaccines against influenza are grown in chick extra-embryonic allantoic fluid; yellow fever in chick embryos; and single-virus rubella, mumps, rubeola, rubella/rubeola, rubella/mumps, rubella/rubeola/ mumps, and rabies in chick embryo fibroblasts.11 Measles-mumps-rubella (MMR) and purified chick embryo rabies vaccines can be given safely, even in egg-allergic patients; however, the safety of other vaccines has not been established.12,13
Before you give vaccines other than MMR or rabies, ask all patients whether they can eat eggs without any adverse reaction and withhold the vaccine if the reaction was anaphylactic. Use of influenza (killed and attenuated live) or yellow fever vaccines in patients with previous nonanaphylactic reactions to eggs is not recommended unless skin testing can be done to assess risk. Use of rabies vaccine in a patient with any previous significant adverse reaction to egg requires immediate allergy consultation. If consultation is not available, proceed with vaccination and be prepared to treat anaphylaxis.
8. Consider the oral rather than the parenteral route when giving antibiotics.
The statistics are frighteningly clear: between 400 and 800 patients per year die of antibiotic-provoked anaphylaxis, and 97% of these deaths are caused by β-lactams. Since penicillin has been in use, the vast majority of fatalities have resulted from parenteral administration.14
9. If you need to give an antibiotic parenterally, consider trying a preliminary oral dose.
The risk of provoking fatal anaphylaxis with oral penicillin is dramatically lower than with parenteral use (about 6 fatalities from orally administered penicillin have been reported). Consider giving the first dose orally and observing the patient for at least 30 minutes before you give the antibiotic parenterally.15
10. Always tell the patient which medication you plan to give just before injecting it.
Saying directly, "I am going to give you penicillin," can sometimes cause a few synapses to reconnect and previous problems recalled.
11. Give injections distally when possible.
If an anaphylactic reaction follows an injection, it may be helpful to place a tourniquet above the injection site. You can inject the site with a small amount of 1:1000 epinephrine. In truth, though, the advantages of tourniquets have not been proved.
12. Have patients wait 20 or 30 minutes after any injection.
Since most anaphylactic reactions occur within 30 minutes after an injection (antibiotics, vaccines, allergy shots, etc), tell patients who have been given anything by injection that a half-hour wait is office policy. The absence of a previous adverse reaction does not guarantee an anaphylactic reaction will not occur. If the patient cannot or will not wait, ask him or her to sign a form releasing you from medical responsibility.
13. Warn patients, particularly teenagers, not to withhold anaphylaxis treatment when it is indicated.
Patients may think "I'll see what happens" or "I can tough this out" or "I can make it through" and not use their epinephrine syringe when clearly needed. Teenagers are prone to this attitude and fatalities have resulted.16
14. Be extremely careful with patients who are allergic to natural rubber latex.
Anaphylactic reactions to natural rubber latex are becoming more common-especially among health care workers, rubber industry workers, and children with spina bifida or urogenital abnormalities. These children have had multiple exposures to latex for most of their lives because of examinations, surgical procedures, and fecal disimpactions.17
Skin contact with gloves, tourniquets for blood drawing, blood pressure cuffs, disposable draping, ECG pads, and adhesive bandages may cause anaphylaxis. Use vinyl or "synthetic" gloves. "Hypoallergenic" labeling is meaningless and has been removed from most medical products. Medical devices now should state whether they contain natural rubber latex. If there is any question about whether an older product such as a blood pressure cuff or tourniquet contains natural rubber latex, place a cloth towel underneath.
15. Urge patients to discard any unused drug or food they have reacted to.
If an outpatient medication is thought to have caused an anaphylactic reaction, check the contents against the label. Patients may put multiple medications in the same container or reuse older containers, making identification a challenge. Less likely, but still possible, is pharmacy mislabeling.
Many patients have an impaired memory and may inadvertently ingest the medication or food again if on hand-a frequent problem with aspirin and NSAIDs. Have the patient or a family member go through the medicine cabinet and drawers, food cabinets, and refrigerator to discard the offending food or medications.
16. Educate patients to avoid exposure to provoking agents.
Certain foods, such as peanuts, may be particularly difficult to avoid, since they may be disguised in cookies or other prepared foods. Another example is aspirin, an ingredient in many over-the-counter cold medications. Emphasize to patients that label reading is essential, and if there is any question about the safety of an item, they should not ingest it.
17. Warn patients not to become cavalier about known food allergies.
Patients may have the urge to try eating foods that previously caused allergic reactions, reasoning "I probably outgrew this" or "It won't happen to me" or "How could such a small amount hurt me?" Fatalities have been reported, principally among teenagers with a cavalier attitude about eating foods they knew to be risky.16
18. Remove a honey bee's stinging apparatus from the skin wound. The stinging apparatus ("stinger") is a muscular bag filled with venom that is connected to a hollow barbed apparatus.17 Remove the 1 to 2 mm wide bag by pinching it off, flicking it off with your finger, or breaking it off by scraping along the skin with a knife.
19. Refer all patients with anaphylactic reactions to Hymenoptera (wasp, bee, yellow jacket, hornet, fire ant) stings to an allergist.
Refer children younger than 16 years who have generalized reactions (cardiovascular and/or respiratory, not cutaneous only) and patients 16 years or older with generalized reactions (cutaneous, cardiovascular, and/or respiratory) to an allergist for venom skin testing and possible desensitization. Large local reactions are of no concern.18
An interesting study revealed physicians in the St Louis emergency departments were not appropriately referring such patients. There is no reason to believe other health care facilities are different.19
20. Prescribe an epinephrine syringe for patients at risk.
Epinephrine, not antihistamines or corticosteroids, is the initial medication of choice for treatment of anaphylaxis, and there are no known contraindications. It appears that the risk of not using it, even in older patients with cardiovascular disease, is greater than using it.2 When prescribed, it must be immediately available at all times in all places.
Patients at risk include those who have experienced anaphylactic reactions to:
Hymenoptera venom and have not yet been desensitized.
Food or food additives and cannot control their diets.
Natural rubber latex.
"Idiopathic anaphylaxis." Recommended adult dosing is 0.3 to 0.5 mL of 1:1000 solution (0.3 to 0.5 mg); for children, 0.01 mg/kg (maximum, 0.3 mg). Doses can be repeated 2 to 3 times at 5 to 15 minute intervals.2
Spring-loaded, temperature-stabilized epinephrine injectors can be prescribed, and they may be carried in a pocket, backpack, "fanny pack," or small bag. Temperature extremes in a car or glove compartment or the sun's heat outdoors may cause significant product deterioration.
Two devices are available in the US market: EpiPen and Twinject. The EpiPen delivers 0.3 mL of 1:1000 epinephrine for adults. For children who weigh 15 to 30 kg (33 to 66 lb), the EpiPen Jr is available; this device delivers 0.3 mL of 1:2000 epinephrine. A unit with 2 EpiPens is called the EpiPen 2 Pak.
The Twinject contains either 0.3 mg of epinephrine per dose for adults or 0.15 mg per dose for children who weigh 15 to 30 kg (33 to 66 lb) in the autoinjector device, combined with a separate similar dose of a self-injecting syringe (note that with Twinject 2 injection techniques are needed; see No. 21).
Epinephrine dosing in children who weigh less than 15 kg (33 lb) is discussed in an article by Sicherer and Simons.20
21. If you prescribe epinephrine, you are obligated to teach the patient how and when to use it.
Health care providers, especially those in emergency departments, often fail to instruct patients in the proper use of an epinephrine syringe. During an evolving anaphylactic reaction is hardly the time for the patient to read the package insert to learn how the device works. The EpiPen manufacturer will supply written information and practice trainers at no expense (www.epipen.com). The manufacturer of Twinject has an interactive Web site (www. twinjecttraining.com).
Injecting epinephrine into the lateral thigh is recommended because it has been shown to raise blood levels faster and higher than subcutaneous arm or intramuscular deltoid placement.1
After epinephrine is administered, the patient should preferably be transported by a second party to an emergency facility. If alone, the patient should call 911 for assistance. Transport patient in a supine position and elevate legs if light-headed or unconscious.
The patient should stay at the emergency facility for 4 to 6 hours. Provide patients with a written "action plan" that explains how and when to use the epinephrine syringes. Examples can be downloaded from the Web site of the American Academy of Allergy, Asthma, and Immunology (www.aaaai.org). Try to educate at least one family member, caregiver, or friend about epinephrine use in case the patient cannot self-administer.
22. Assess the need to use larger doses of epinephrine as the patient gets older, and check expiration dates.
For both autoinjector devices, review patient weight annually and increase the dose to the higher levels as recommended. Current recommendations are to use the adult-size EpiPen or Twinject 0.3 mg for weight greater than 30 kg, although some experts recommend it for weight greater than 25 kg.20
Use of outdated syringes is not recommended, but research has shown outdated syringes contain some epinephrine. In an emergency, they should be used if they are the only treatment available.21
23. Consider prescribing more than 1 epinephrine injection.
Although no consensus guidelines are available, most specialists prescribe 2 or more. Considerations for more than 1 injection include:
Previous anaphylactic reaction that required more than 1 injection.
Very obese child or adult.
Concerns about a "biphasic" anaphylactic reaction occurring 4 to 6 hours later (the incidence in published studies varies from 8% to 35%22) for patients who cannot get to an emergency facility.
Concerns about travel time to an emergency unit (the World Health Organization and Anaphylaxis Canada [www.anaphylaxis.org] recommend 1 dose per 10 to 20 minutes of travel time).
24. Recommend that all patients at risk for anaphylaxis wear identification jewelry, which can be purchased from most pharmacies, or jewelry that is registered (MedicAlert, 800-432-5378, www.medicalert.org), or carry a wallet card.
At-risk persons should consider wearing a bracelet or necklace or carry a wallet card with the proper information about the offending diagnostic or therapeutic agent, rubber, food, exercise, or other potential cause of anaphylaxis.
25. Do not premedicate patients who have had a previous IgE-mediated reaction and then challenge with medication.
Although pretreatment protocols have demonstrated protection in non–IgE-mediated reactions (eg, radiocontrast media23), there is no evidence that these protocols will protect against IgE-mediated anaphylaxis from penicillin, natural rubber latex, and other causes.
26. If a patient needs urgent treatment with an antibiotic known to have caused anaphylaxis, desensitize the person-preferably by the oral route.
The usual setting is a penicillin-allergic patient with a life-threatening infection (eg, meningitis or endocarditis) who is receiving a different antibiotic and dying of overwhelming infection. In this situation, giving penicillin is probably less life-threatening than withholding it. Desensitization is then recommended, rather than giving a "test dose." Detailed penicillin protocols have been published for the recommended safer oral approach and for the more risky parenteral approach.24 Protocols for sulfa are also available.24
27. If a patient needs a radiocontrast medium for an x-ray study and has had a previous anaphylactic reaction to it, use a pretreatment protocol.
The likelihood of a recurrent anaphylactic reaction to a radiocontrast medium can be dramatically reduced by using such protocols. Since the incidence of severe reactions (dyspnea, sudden hypotension, cardiac arrest, and/or loss of consciousness) is lower with low osmolar nonionic media,25 some authors strongly recommend the use of such media along with pretreatment protocols in patients who have had previous immediate reactions. Table 2 provides a pretreatment protocol recommended by Greenberger and colleagues.26
28. Warn patients with cold-induced urticaria/angioedema not to swim in cold water above their knees.
These patients usually present with localized swelling of the hands, mouth, and face after exposure to cold water, cold beverages, or cold air.27 Total immersion in cold water may cause anaphylaxis, with possible loss of consciousness and drowning.
29. Choose a different local anesthetic if patients report adverse reactions. Although most reactions to local anesthetics are vasovagal or caused by epinephrine, it is wise to perform a provocative testing protocol with the desired agent.23 Anesthetics have been arbitrarily divided into 2 groups:
Group 1 agents contain a cross-reacting para-aminophenol group (eg, procaine).
Group 2 agents do not contain this cross-reacting group (eg, lidocaine or mepivacaine).
If time does not permit a provocative testing protocol and the patient has had an adverse reaction to a group 1 anesthetic, then select an agent from group 2. If the patient has reacted to a group 2 anesthetic, then choose one in group 1 or a different group 2 agent.28
30. Use a desensitization protocol if the patient has had an anaphylactic reaction to human insulin.
Single-component insulins (ie, beef or pork) have been removed from the US market. If a patient has had an anaphylactic reaction to human insulin, skin testing and desensitization protocols are indicated.23
31. Use a pretransfusion protocol for all patients with previous significant transfusion reactions. Obtain a hematology or allergy consultation for patients who have had significant previous transfusion reactions. Pretransfusion protocols similar to those for radiocontrast media are recommended.29
32. Do not give heterologous serum (eg, horse-derived) to a patient who has had a significant previous reaction to horse protein.
A common scenario is the patient who may need horse serum antitoxin for a snakebite (antivenin) but has had a significant previous reaction to horse-derived antitoxin or to eating horse meat or is allergic to horses. Theoretically, skin testing and/or desensitization is advised; however, after a snakebite, the risk of withholding antivenin may be greater than giving it. In patients with possible allergy to horse protein, give the antivenin in an ICU and treat anaphylaxis early and vigorously if it occurs.
In some countries, horse serum–derived tetanus antitoxin is still available. Do not administer it to at-risk patients when a human-derived tetanus antitoxin is available.
33. Avoid giving -adrenergic blocking medications to patients at risk for anaphylaxis.
Patients who take β-blockers may not respond to epinephrine, which can result in fatal anaphylaxis. In patients at risk for anaphylaxis from foods, venom, natural rubber latex, or other causes, use alternatives to β-blockers for hypertension or arrhythmia. Allergy immunotherapy ("allergy shots") is contraindicated for patients receiving β-adrenergic blockers orally, parenterally, or topically (eg, eyedrops). 2 α-Adrenergic blockers may also decrease the effects of epinephrine. Angiotensin-converting enzyme inhibitors and, to a lesser degree, angiotensin-receptor blockers may interfere with the patient's own compensation to anaphylaxis. Sedating medications, alcohol, and recreational drugs may cloud a patient's judgment about the severity of a reaction or when to treat.
34. Warn patients with exercise anaphylaxis not to exercise alone.
Counsel such patients to always carry an epinephrine syringe if they wish to exercise. Instruct them to always work out with a partner who is familiar with use of the syringe.30
35. Withhold routine allergy immunotherapy (allergy shots) in patients at high risk for anaphylaxis.
There appears to be a dangerous synergistic effect between uncontrolled asthma and development of anaphylaxis after an allergy shot. Injections should also be withheld:
When the patient has just exercised vigorously.
If a fever or other illness has recently developed; a mild upper respiratory tract infection without fever is not a contraindication.
If the patient is receiving β-adrenergic blockers.
If the patient has severe symptoms of allergic rhinoconjunctivitis.
36. Always have the medications and equipment ready to treat an anaphylactic reaction.
Most reactions can be detected early and can be stopped quickly by properly used epinephrine and antihistamines. In any office where you give injections (eg, medication, vaccinations, or allergy shots), keep a variety of items for treatment of anaphylaxis on hand (Table 3).
Dr Steinberg wrote on the prevention of anaphylaxis for CONSULTANT in April 2000; he has expanded and updated his discussion here.
REFERENCES: 1. Sampson HA, Muñoz-Furlong A, Campbell RL, etal. Second symposium on the definition and managementof anaphylaxis: summary report-SecondNational Institute of Allergy and Infectious Disease/Food Allergy and Anaphylaxis Network symposium.J Allergy Clin Immunol. 2006;117:391-397.
2. Lieberman P. Anaphylaxis and anaphylactoid reactions. In: Adkinson NF, Bochner BS, Busse WW, et al, eds. Allergy: Principles and Practice. 7th ed. St Louis: CV Mosby Co; 2008.
3. Lieberman P, Camargo CA Jr, Bohlke LC, et al. Epidemiology of anaphylaxis: findings of the American College of Allergy, Asthma and Immunology Epidemiology of Anaphylaxis Working Group. Ann Allergy Asthma Immunol. 2006;97:596-602.
4. Idsoe O, Gruthe T, Willcox RR, de Weck AL. Nature and extent of penicillin side-reactions with particular reference to fatalities from anaphylactic shock. Bull World Health Organ. 1968;38:159-188.
5. Parrish HM. Deaths from bites and stings of venomous animals and insects in the United States. AMA Arch Intern Med. 1959;104:198-207.
6. Shepherd GM. Allergy to β-lactam antibiotics. Immunol Allergy Clin North Am.. 1991;11:611-633.
7. Wedner HJ. Drug allergy prevention and treatment. Immunol Allergy Clin North Am 1991;11:679-694.
8. Adkinson NF. Drug allergy. In: Adkinson NF, Bochner BS, Busse WW, et al, eds. Allergy: Principles and Practice. 7th ed. St Louis: CV Mosby Co; 2008.
9. Manning ME, Stevenson DD. Pseudoallergic drug reactions. Immunol Allergy Clin North Am. 1991;11: 659-678.
10. Stevenson DD, Pleskow WW, Simon RA, et al. Aspirin-sensitive rhinosinusitis asthma: a doubleblind crossover study of treatment with aspirin. J Allergy Clin Immunol. 1984;73:500-507.
11. Kelso JM. Adverse reactions to vaccines for infectious diseases. In: Adkinson NF, Bochner BS, Busse WW, et al, eds. Allergy: Principles and Practice. 7th ed. St Louis: CV Mosby Co; 2008.
12. James JM, Zeiger RS, Lester MR, et al. Safe administration of influenza vaccine to patients with egg allergy. J Pediatr. 1998;133:624-628.
13. James JM, Burks AW, Roberson OG, Sampson HA. Safe administration of the measles vaccine to children allergic to eggs. N Engl J Med. 1995;332: 1262-1266.
14. Sullivan TJ, Yecies LD, Shatz GS, et al. Desensitization of patients allergic to penicillin using orally administered beta-lactam antibiotics. J Allergy Clin Immunol. 1982;69:275-282.
15. Sullivan TJ. Advances in diagnosis and management of penicillin allergy. N Engl Reg Allergy Proc. 1985;6:160-165.
16. Yunginger JW, Sweeney KG, Sturner WQ, et al. Fatal food-induced anaphylaxis. JAMA. 1988;260: 1450-1452.
17. Slater JE. Latex allergy. J Allergy Clin Immunol. 1994;94:139-150.
18. Yunginger JW. Insect allergy. In: Middleton E, Reed CE, Ellis EF, et al, eds. Allergy: Principles and Practice. 5th ed. St Louis: CV Mosby Co; 1998.
19. Hutcheson PS, Slavin RG. Lack of preventive measures given to patients with stinging insect anaphylaxis in hospital emergency rooms. J Allergy Clin Immunol. 1988;81:201. Abstract.
20. Sicherer SH, Simons FE. Self-injectable epinephrine for first aid management of anaphylaxis. Pediatrics. 2007;119:638-646.
21. Simons FE, Gu X, Simons KJ. Outdated EpiPen and EpiPen Jr autoinjectors: past thei prime? J Allergy Clin Immunol. 2000;105:1025-1030.
22. Kelso JM. A second dose of epinephrine for anaphylaxis: how often needed and how to carry. J Allergy Clin Immunol. 2006;117:464-465.
23. Grammer LC, Greenberger PA. Drug Allergy and Protocols for Management of Drug Allergies. 3rd ed. Providence, RI: OceanSide Publications; 2003.
24. Gilbert DN, Moellering RC Jr, Eliopoulos GM, Sande ME. The Sanford Guide to Antimicrobial Therapy 2008. 38th ed. Sperryville, VA: Antimicrobial Therapy Inc; 2008.
25. Katayama H, Yamaguchi K, Kozuka T, et al. Adverse reactions to ionic and nonionic contrast media: a report from the Japanese Committee on the Safety of Contrast Media. Radiology. 1990;175: 621-628.
26. Greenberger PA, Halwig JM, Patterson R, Wallemark CB. Emergency administration of radiocontrast media in high-risk patients. J Allergy Clin Immunol. 1986;77:630-634.
27. Gorevic PD, Kaplan AP. The physical urticarias. Int J Dermatol. 1980;19:417-435.
28. deShazo RD, Nelson HS. An approach to the patient with a history of local anesthetic hypersensitivity: experience with 90 patients. J Allergy Clin Immunol. 1979;63:387-394.
29. Greenberger PA. Plasma anaphylaxis and immediate type reactions. In: Rossi EC, Simon TL, Moss GS, eds. Principles of Transfusion Medicine. Baltimore: Williams & Wilkins; 1991:635-639.
30. Sheffer AL, Soter NA, McFadden ER Jr, Austen KF. Exercise-induced anaphylaxis: a distinct form of physical allergy. J Allergy Clin Immunol. 1983;71:311-316.
Asthma | Atrial Fibrillation | Infection | Obesity | Vaccines