text:
\section{Introduction}
Quantum tunneling is a widespread phenomena, where a wavefunction leaking as an evanescent mode can be transmitted through a finite barrier. This simple description applies to many natural systems, accounting for instance for molecular conformation or radioactivity~\cite{Razavy2003}. In solid-state systems, nanoscale structures can use tunnelling effects in novel functionalities developed for CMOS electronics~\cite{Ionescu2011} as well as for quantum devices, where electrons can be confined and manipulated in quantum information schemes~\cite{Hanson2007,Hensgens2017,Fuechsle2012,He2019}.

For many-body quantum devices, the tunnel interaction $t$, which can couple the different sites, usually competes with the on-site interaction $U$ (also called the charging energy). This competition is core to the so-called Fermi-Hubbard model. For fermions, this model needs to be discussed together with the Pauli exclusion principle, which forbids to form a state with two parallel spins on the same orbital~\cite{Salfi2016,Mazurenko2017}. When the Coulomb interactions $U$ dominate over $t$, the system maps to the Heisenberg model with an exchange interaction which directly links to the tunnel coupling through the relationship $J=4t^2/U$. This Heisenberg limit is favourable for quantum simulations of magnetism~\cite{Hensgens2017, Dehollain2020} and for fast quantum computation schemes~\cite{Kane1998,Russ2016,He2019}. The mapping to the Heisenberg model breaks down when $t$ approaches $U$ and when the system is brought away from half-filling, to give rise to a rich phase diagram with links to exotic superconductivity and spin liquids~\cite{Georgescu2014,Balents2010,Gull2013,Salfi2016,Mazurenko2017}.

\begin{figure*}[htp]
\begin{center}
\includegraphics[width=18cm]{fig1_fin_LR.pdf}
\caption{\textbf{Direct measurement of coupled donors in silicon.} \textbf{a} Schematics of a 2D-array of single electron spins bound to phosphorus atoms in $\rm{^{28}Si}$, where two-qubit operations can occur between nearest neighbours, i.e. red/green spin pairs, using the Heisenberg exchange interaction. \textbf{b} (top) A donor's electron wavefunction oscillates at the valley wavevector $\bf{k_{\mu}}\sim\rm{0.81}\bf{k_0}$, with $k_0{=}2\pi/a_0$. Silicon presents a mass anisotropy which results in the donor orbital envelope to be anisotropic as well, as highlighted by their ovoidal shape in Fourier space. (bottom) Tunnel and exchange interactions result from the overlap between the two donor orbitals, represented by the yellow overlap area, which is sensitive to both envelope decay and valley interference between donors. \textbf{c} Experimental real-space map of the quasi-particle wave function of an exchange-coupled donor pair's two-electron neutral state. Sequential transport occurs vertically from a highly doped Si:As substrate, which acts as an electron reservoir, to a donor pair found in a low-doped phosphorus $\delta$-layer, and then to the STM tip above (not shown). The red and green dots represent the surface projections of the pinpointed lattice positions of the two donors. The two donors are separated by ${6.5a_0\sqrt{2}}$ along [110] (perpendicular to the Si dimers, ${a_0}$ is the silicon lattice constant), ${0.5a_0\sqrt{2}/2}$ (parallel to the Si dimers) along ${[1\bar{1}0]}$, and by ${1.25\,a_0}$ in depth. The grey dots represent the silicon atom positions of the $2 \times 1$ reconstructed surface. The black dashed contour indicates the experimentally measured area.}
\label{fig1}
\end{center}
\end{figure*}

Phosphorus donor-bound spins in silicon are highly suitable to explore and harness these different regimes. Donors can be placed at nanometer scale distances from each other in the silicon crystal~\cite{Dupont-Ferrier2013,Gonzalez-Zalba2014,Dehollain2014,Weber2014,Broome2018}, where direct tunneling interactions dominate over dipolar coupling. Notably, 2D donor arrays (see Fig.~\ref{fig1}a) can be fabricated using scanning tunneling lithography~\cite{Fuechsle2012,Weber2014}, where the atoms can be placed anywhere in a single atomic plane. These atomically precise devices can be engineered to achieve both the Heisenberg limit~\cite{He2019} or the non-perturbative tunneling interactions regime at short inter-dopant distances~\cite{Salfi2016}, with ratios $U/t$ possibly lower than 10.

The direct relationship between tunnel and exchange coupling can be understood conceptually as they are both based on wavefunction overlap. Hence, they are sensitive to the same physical effects, and these atomic-scale wavefunctions must be precisely investigated to warrant the development of applications which requires the exchange interaction to be well controlled. In contrast to atoms in the vacuum~\cite{Mazurenko2017}, donor-bound electrons in silicon acquire properties of the crystal band structure. In particular, silicon is an indirect band gap semiconductor~\cite{Gunawan2006,Randeria2018,Wang2018}, with the presence of an anisotropic mass and a valley degree of freedom~\cite{Kohn1955,Salfi2014}. More precisely, the finite valley momentum is aperiodic with the silicon lattice, a feature which can also be found in 2D material structures~\cite{Mudd2016,Gonzalez2016,Movva2018}. This aperiodicity causes interference between oscillating valley states from different donors (see Fig.~\ref{fig1}b). Consequently, the tunnel and exchange interactions can vary strongly with small lattice site variations in the donor positions, as they induce changes in both valley interference condition and envelope overlap. Such reduction of the exchange energy compared to hydrogenic systems has been observed in ensemble work~\cite{Cullis1970,Andres1981}, but a direct link to valley interference cannot be accessed from any ensemble measurement. Understanding the impact of valley interference at the atomic scale, i.e. at the wavefunction level, has become essential in the context of quantum computing~\cite{Kane1998,Koiller2001}, but the predicted valley-induced exchange variations range within 5 orders of magnitude~\cite{Kane1998,Koiller2001,Wellard2005,Testolin2007,Rahman2011,Saraiva2015,Gamble2015,Wang2016,Song2016}, which makes it challenging to design scalable donor qubit architectures with uniform couplings. The sensitivity of both tunnel and exchange interactions to the precise donor positions makes it essential to verify experimentally the presence and magnitude of valley interference. This is challenging to achieve in transport experiments~\cite{Dupont-Ferrier2013,Gonzalez-Zalba2014,Dehollain2014,Weber2014,Broome2018,He2019}, which are unable to discriminate between valley interference and envelope effects. Here, we instead implement a real-space probe into coupled donor wavefunctions. This experimental approach leads us to detail the precise role of envelope anisotropy, crystal symmetries, and dopant placement accuracy to reconcile the apparent disparity in the exchange variations predictions. In particular, we consider the dopant placement precision which can be ultimately achieved by scanning probe lithography~\cite{Fuechsle2012}. We find that exchange variations from pair to pair can be minimised to within an order of magnitude and investigate the potential of this strategy in view of quantum processing using exchange-based donor arrays.

\begin{figure*}[htp]
\begin{center}
\includegraphics[width=18cm]{fig2_fin_LR.pdf}
\caption{\textbf{Visualizing and quantifying valley interference between coupled donors. Pair \#1. a} 2D FFT of the STM image, centred on the first Brillouin zone (solid white lines). The white dots are located at $\{\pm k_0,\pm k_0\}$. The FFT shows a clear valley signal around ${k_{\mu}\sim0.81k_0}$ evidenced by the green ellipsoids.  The FFT also shows diagonal slices (blue dotted lines), cutting through the valley components of the FFT, which evidence the geometric interference between the two donors. \textbf{b} Real-space images of the valley interference, obtained after inverse Fourier transform of the FFT filtered around ${k_x\sim0.81k_0}$ for the $x$-valley interference (left) or ${k_y\sim0.81k_0}$ for the $y$-valley interference (right). The white crosses indicate the donor positions. The $x$-valleys look in-phase with the vertical stripes running continuously from one donor to the other. The $y$-valleys look out-of-phase with a clear discontinuity in the oscillatory valley pattern between the two donors. \textbf{c} 2D fits of the valley images, from which the position of the valley maxima and of the valley frequency, and hence the valley phase differences $\Delta\phi_x$ and $\Delta\phi_y$, can be obtained. The red dashed ellipsoids correspond to the donor envelope part of the fits, which highlights their anisotropy. \textbf{d} Line cuts taken through the ion-ion direction of both valley images (red lines) and their fit (black lines), for the $x$-valleys (left) and the $y$-valleys (right). The grey dashed lines represent the envelope part of the fits only. The $x$-valleys are in-phase, which results in the maxima of valley signal to always reach the envelop part. On the contrary, the $y$-valley are out-of-phase and the grey arrows in-between the two donors highlight the clear reduction of the valley signal compared to the envelope part as a result of the destructive interference.}
\label{fig2}
\end{center}
\end{figure*}

\section{Results}
\subsection{Valley interference and anisotropic envelope in exchange-coupled donors}

In order to directly probe valley interference between donors, we have designed and fabricated samples to host isolated donor pairs embedded beneath a silicon surface (see Methods). Spatially resolved transport is performed at 4\,K between a heavily doped reservoir and the tip of a scanning tunneling microscope (STM). An STM image of a donor pair is shown in Fig~\ref{fig1}c. It is taken at a tip-sample bias of $V_b=-0.95$\,V, close to the zero electric-field condition where the tip does not influence the two-electron neutral molecular state~\cite{Salfi2016,Salfi2018}. More specifically, the spatially resolved tunneling current to the tip represents a quasi-particle wavefunction (QPWF), corresponding to the sum of the transitions from the two-electron ground state to energetically available one-electron states. Hence, the STM image contains two-electron wavefunction information including interference between the two donor wavefunctions~\cite{Rontani2005,Salfi2016,Salfi2018}. Moreover, the exact site positions of the two donor ions ($P_1$ and $P_2$, respectively green and red dot) are determined out of different possible position configurations using a comprehensive image symmetry recognition protocol~\cite{Usman2016,Brazdova2017}, which notably include the tip orbital, as the oscillating pattern observed for each donor qualitatively varies depending on their position in the silicon lattice. In particular, donor $P_1$ is located in the $z{=}5.5\,a_0$ atomic plane, in-between two dimer rows, and presents a minima at the surface projection of the ion location. The image corresponding to donor $P_1$ presents two rows of $2{\times}3$ local maxima running along the $[1\bar{1}0]$ crystallographic axis, on each side of the ion location. On the contrary, donor $P_2$ is found to be in the $z{=}6.75\,a_0$ atomic plane, and sits directly underneath the middle of a dimer row of the $2{\times}1$ reconstructed surface. Donor $P_2$ presents a maximum (instead of a minimum for $P_1$) at this location, part of a row of three local maxima running along this dimer.

\begin{figure}[htp]
\includegraphics[width=8.8cm]{fig3_fin_LR.pdf}
\caption{\textbf{Theoretical two-electron STM image and valley interference.} \textbf{a} Theoretical STM image computed using the pinpointed locations of the two donors and FCI calculations performed to determine the two-electron wavefunctions based on tight-binding one-electron states. \textbf{b} 2D Fourier transform of the STM image focussed on the first Brillouin zone. The valley components at 0.81$k_0$ and the diagonal slices highlighting the interference are clearly visible. \textbf{c} Real-space image of the $x$-valley obtained by filtering the FFT around ${k_x\sim0.81k_0}$. \textbf{d} Corresponding fitted image, using the same fitting procedure as for the experimental data, and from which $\Delta\phi_x$ and the ratio $b/a$ for each donor (red dashed ellipsoids) can be extracted. As for the experiment, the $x$-valleys are found to be in-phase. \textbf{e,f} Same for the $y$-valleys, which like for the experiment are out-of-phase.}
\label{fig2bis}
\end{figure}

\begin{figure}[htp!]
\begin{center}
\includegraphics[width=8.8cm]{fig4_fin_LR.pdf}
\caption{\textbf{Valley interference for pair \#2.} \textbf{a} Experimental STM image of pair \#2. The red crosses indicate the ion locations. \textbf{b} FFT of the STM image, centred on the first Brillouin zone. As for pair\#1, the FFT shows a valley signal at 0.81$k_0$ (green ellipsoids) and diagonal slices that indicate the interference, whose separation and slope is linked  to the inter-donor distance and orientation. \textbf{c} Real-space image of the $x$-valley obtained by filtering the FFT around ${k_x\sim0.81k_0}$, same procedure as for pair \#1. Same scale as the STM image shown in \textbf{a}. The observed distortions in the $x$-valley image, notably on the right-hand side of $P_1$, are attributed to an instability of the tunneling tip during the measurement. \textbf{d} Corresponding fitted image, using the same fitting procedure as for pair \#1, and from which $\Delta\phi_x$ and the ratio $b/a$ for each donor (red dotted ellipsoids) can be extracted. \textbf{e,f} Same for the $y$-valleys.}
\label{fig2bis2}
\end{center}
\end{figure}

\begin{figure}[htp!]
\begin{center}
\includegraphics[width=8.8cm]{fig5_fin_LR.pdf}
\caption{\textbf{Table summarising the valley phase differences obtained for the two pairs.} The $x$ and $y$-valley phase difference for each pair obtained from fitting the 2D valley images can be compared to the geometrical phase differences obtained from the pinpointed lattice separation between the two donors along [110] and $[1\bar{1}0]$ and assuming a valley momentum at $0.81k_0$.}
\label{fig2sum}
\end{center}
\end{figure}

The reduced symmetries of the STM image compared to a spherical $1s$-orbital for atoms in the vacuum, and the alignment of its local maxima with the dimer rows at the silicon surface clearly indicate the presence of both lattice and valley frequencies in the donor wavefunctions. These frequencies can be probed in more detail in Fourier space~\cite{Saraiva2016}. A contour mask was first applied around the two donors to avoid the presence of spurious frequencies in the fast Fourier transform (FFT) from the image boundaries. The first Brillouin zone of the resulting Fourier transform is shown in Fig.~\ref{fig2}a. The different Fourier components which can be observed correspond to scattering processes between valley and lattice wavevectors~\cite{Saraiva2016}. In particular, the frequencies of the silicon $2\times1$ surface reconstruction can be identified at $(k_x,k_y)=\{\pm1,\pm1\}k_0$ (with $k_0{=}2\pi/a_0$), corresponding to the $a_0\sqrt{2}$ periodicity between the dimer rows, i.e. along $[110]$, as well $(k_x,k_y)=\pm(0.5,0.5)k_0$ corresponding to the $a_0\sqrt{2}/2$ periodicity along [110] between each pair of silicon atoms forming a dimer. The components of interest for the valley interference analysis are found around $\pm(0.81,0)k_0$ and $\pm(0,0.81)k_0$. They relate to valley scattering processes, respectively between the $\pm x$ and $\pm z$-valleys, and the $\pm y$ and $\pm z$-valleys. It is important to note that these valley processes can be completely dissociated from any lattice frequency-associated process, since they rely on the valley momentum only. Moreover, the Fourier transform presents clear diagonal slices (blue dashed lines), which match the geometric destructive interference condition between the two donors. Their position with respect to the valley signal gives a hint to whether the valley states are in or out-of-phase, if their corresponding signal in the FFT falls in-between or on one these diagonal stripes, respectively (See Supplementary Note 1). In order to focus on these valley interference processes, a Gaussian filter was applied to the FFT around the valley signal (see green ellipsoids in Fig.~\ref{fig2}a) and transformed back to real space. The left image in Fig.~\ref{fig2}b shows the $x$-component result of this filtering: a set of vertical stripes, corresponding to the valley oscillations in the $x$-direction can be observed for each donor, with the valley phase pinned at each donor site. For this particular inter-donor distance, the $x$-valleys look in-phase as the vertical stripes run continuously from one donor to the other. The same filtering procedure was performed for the $y$-valley real-space image. In contrast to the $x$-valley, the $y$-valleys look out of phase with a clear break in the continuity of the horizontal stripes in-between the donors and a succession of phase slips. In order to be more quantitative, these valley images can be fitted to the sum of two 2D envelopes oscillating at the same frequency. The fitted 2D images are shown in Fig~\ref{fig2}c. They give the same visual impression of the fits as that of the experimental images. Furthermore, the valley phase differences can be extracted from the fits, yielding $k_x=(0.8077\pm0.0001)^*k_0$, $k_y=(0.8039\pm0.0001)^*k_0$, $\Delta\phi_x=(0.050\pm0.001)^*2\pi$ and $\Delta\phi_y=(0.434\pm0.001)^*2\pi$, which confirms that the $x$-valleys are in-phase and that the $y$-valleys are out-of-phase. We show in Fig.~\ref{fig2}d line cuts through the two ions of each valley image, experimental ones and their respective fit, to notably highlight the clear reduction of the $y$-valley signal in-between the two donors compared to the sum of the envelopes of the two donors due to the destructive interference.

The procedure developed here establishes the existence of a geometric valley phase interference between donors, which depends on their relative position. This phase interference is by construction included in the Heitler-London regime of vanishing tunnel coupling, as the two electrons fully localise on the donors~\cite{Salfi2016}. In this regime, the STM image becomes equivalent to the sum of the charge distributions of two independent single donors (see Fig.~\ref{fig2}d and Supplementary Note 1). However, in our case the inter-donor distance is around 5\,nm, at which some deviation from the Heitler-London regime is expected~\cite{Rahman2011,Saraiva2015}, as highlighted by the finite overlap between the donor envelopes in Fig.~\ref{fig2}b and d. To verify the deviation from the Heitler-London limit and whether the phase is robust is this regime where the electrons start to delocalise between the two donors, we have computed the STM image based on a calculated two-electron wavefunction which includes electron interactions. This theoretical image, shown in Fig.~\ref{fig2bis}a, is computed using state-of-the-art atomistic modelling capabilities summarised here and detailed in the Methods section. First, starting from the donor pinpointed positions, the one-electron states are obtained by atomistic tight-binding (TB) modelling using a multi-million atom grid. The two-electron states are then obtained using a full configuration interaction method (FCI)~\cite{Tankasala2018, Wang2016} based on $1e$-molecular orbitals. Interface, reservoir and electric field effects are taken into account throughout this modelling framework to ensure an accurate description of the coupled donors spectrum. We found a two electron ground state composed at 67\% of the bonding $A_1{-}A_1$ ground state with an exchange energy of 1.5\,meV (see Supplementary Note 1). As a reference, the Heitler-London limit results in an equal 50\% contribution of both $A_1{-}A_1$ bonding and anti-bonding molecular orbitals since the tunnel coupling vanishes. The theoretical STM image is then obtained by computing the QPWF including STM transport and tip orbital effect~\cite{Usman2016} and is shown in Fig.~\ref{fig2bis}a. We have applied the same filtering procedure to obtain the FFT of this image, shown in Fig.~\ref{fig2bis}b. It shows very similar features compared to the experimental FFT, with notably the presence of valley components at $\pm0.81k_0$ and the diagonal slices which indicate the interference. The resulting $x$ and $y$-valley images are shown in Fig.~\ref{fig2bis}c and d respectively. The valley phases are also pinned to the donor ions and the valley phase differences can be obtained using an identical fitting procedure, giving $\Delta\phi^{FCI}_x=(0.025\pm0.001)^*2\pi$ and $\Delta\phi^{FCI}_y=(0.430\pm0.001)^*2\pi$, in good agreement with the experimental data as the fitted images in Fig.~\ref{fig2bis}e and f show.

We present in Fig.~\ref{fig2bis2}a the results obtained using the same protocol performed on another pair. The two donors are separated by $13a_0\sqrt{2}/2$ along $[110]$ and $9.25a_0\sqrt{2}$ along $[1\bar{1}0]$, i.e. a larger inter-donor distance and a different orientation than the first pair. Its FFT (Fig.~\ref{fig2bis2}b) presents the same characteristics as for pair \#1, with a clear valleys signal around $0.81k_0$ and the presence of diagonal stripes highlighting the geometric interference between the donors. The real-space images resulting from Fourier filtering around the valley signals and their respective fit are shown in Fig.~\ref{fig2bis2}c-f. We note the presence of phase distortions in the $x$-valley image which are different from a succession of phase slips expected for a destructive valley interference pattern. These isolated features are attributed to an instability of the tunnelling tip during the measurement (See Supplementary Note 1), and, importantly, they do not perturb the region of interest for the valley interference and the exchange interaction, i.e. the central region between the two donors. A theoretical STM image was also obtained and analysed, based on a Heitler-London calculation of the two-electron wavefunction as this pair shown an inter-donor distance greater than 7\,nm and therefore falls in this regime. We summarise the phase differences obtained for each pair in Fig.~\ref{fig2sum}, both experimental and theoretical, to notably highlight the matching of the fitted valley phases to the geometrical phase difference expected from the exact lattice pinpointing of each donor atom. Full details on the filtering procedure, as well as on the robustness of the extracted valley phase differences against the dimension of the Fourier space filter can be found in the Supplementary Note 1.

\begin{figure}[htp]
\begin{center}
\includegraphics[width=8.8cm]{fig6_fin_LR.pdf}
\caption{ \textbf{Donor envelope overlap and exchange interaction.} \textbf{a} Two donors placed in the same $xy$-plane at a target distance ${d_{tar}}$ and angle $\rm{\theta_{tar}}$ defined from [100]. The exchange interaction can be considered as a sum of valley interfering envelope overlaps $j_{\mu\nu}$ between the $\pm x$ (orange), $\pm y$ (purple) and $\pm z$-valleys (brown). The mass anisotropy results in each envelope orbital, $F_x$, $F_y$ or $F_z$, to be constricted along its own direction. For instance $F_x$ has a small envelope radius $b$ along $x$, and a large envelope radius $a$ along $y$ and $z$. \textbf{b} Normalised envelope weights $j_{\mu\nu}$ plotted vs. $\theta_{tar}$ for $d_{tar}{=}12$\,nm, using $b/a{=}0.52$ and $a{=}2.8$\,nm. Because of orbital anisotropy, the $j_{yy}$,  $j_{yz}$, and $j_{zz}$ terms (respectively $j_{xx}$,  $j_{xz}$, and $j_{zz}$ terms) are degenerate around [100] (respectively [010], red spots), while $j_{zz}$ dominates around [110] and $\rm{[-110]}$ (blue spots).}
\label{fig4a}
\end{center}
\end{figure}

The fitting procedure we have developed here also allows to investigate the envelope part of the donor valley states, whose characteristic extent are represented by the red dashed lines in Fig.2-4, for each donor and each valley. Contrarily to a simple $1s$-orbital with a spherical symmetry, the envelopes are here clearly ellipsoidal. This feature originates from the silicon mass anisotropy, which results in each valley orbital to present a small envelop radius $b$ along their longitudinal direction and a large radius $a$ along the two transverse directions~\cite{Kohn1955, Saraiva2016} (see Fig.~\ref{fig4a}a). The values $b/a$ obtained across all experimental and theoretical image fits average to 0.52 which is in good agreement with single donors measurements~\cite{Saraiva2016} (see Supplementary Note 1) and with other predictions~\cite{Koiller2001,Pica2014,Gamble2015}. Our experimental results demonstrate the existence of a valley interference effect between donor pairs which present a finite overlap between their wavefunctions. It is noteworthy that the tunnel current probes the extent of the wavefunction at the silicon/vacuum interface. In our case, this means that the tunneling tip probes the overlap between the tails of sub-surface donor wavefunctions, which is precisely the essence of what the tunnel and exchange interactions rely upon.

\subsection{Exchange variations analysis for atomically precise donor qubit devices}
Valley interference between neighbouring donors impact the exchange interaction in a non-trivial manner. To detail this effect we have developed a model based on an effective mass Heitler-London formalism~\cite{Koiller2001}. Importantly, this phenomenological effective mass model (P-EM) strongly relates to the valley phase differences $\Delta\phi_{\mu}$ and to the ratio $b/a$ of the donor envelope which have been experimentally investigated above. The P-EM model decomposes the exchange interaction into a sum of oscillating terms, weighted according to 6 possible envelope terms $j_{\mu\nu}$, as follows (see Supplementary Note 3):

\begin{equation}
J(\vec{R})=\sum_{\substack{\mu,\nu= \\ \pm \{x, y, z\}}} j_{\mu\nu}(\vec{R},a,b)\cos(\Delta\phi_{\mu}(\vec{R})\pm \Delta\phi_{\nu}(\vec{R}))
\label{exc}
\end{equation}

\noindent where $\mu$ (respectively $\nu$) denotes the valley in which the first (respectively second) electron is exchanged between the two donors. Qualitatively, each weight $j_{\mu\nu}$ is a four term-product, between two envelope orbitals $F_{\mu}$ separated by $\vec{R}$, and two envelope orbitals $F_{\nu}$, likewise also separated by $\vec{R}$. The $1s$-like nature of the donor orbitals causes these envelope terms $j_{\mu\nu}$ to vary exponentially with the inter-donor distance, with a characteristic length scale related to the major envelope radius $a$. As $k_\mu$ is close to $k_0$, the valley phase differences evolve rapidly with site to site changes in the lattice position of the donors, which can strongly modulate the exchange. Both envelope and valley dependencies hence suggest that the exchange coupling will change significantly by the displacements of dopants, hence requiring atomic scale dopant placement accuracy~\cite{Koiller2001,Song2016} for stability. To date the most precise dopant placement technique is obtained using STM lithography~\cite{Fuechsle2012}, with the fabrication of in-plane atomic devices where donors can be placed within $\pm 1$ lattice site precision. In the following, we investigate the exchange variations which can be expected using this unique device fabrication capability.

\begin{figure*}[htp]
\begin{center}
\includegraphics[width=18cm]{fig7_fin_LR.pdf}
\caption{ \textbf{Limited exchange in-plane variations for STM placed donors.} \textbf{a} Single donors can be incorporated in a patch of 3 desorbed hydrogen dimers on the silicon surface, giving 6 possible positions for each donor. \textbf{b} There are 12 non-equivalent position configurations for $P_2$ for a target along [100], taking the convention to fix $P_1$ at the origin. A target along [110] results in 10 possible configurations. \textbf{c} Left: plot of the 12 possible exchange values along [100], normalised over the target one, plotted vs the distance difference $\Delta d=d-d_{tar}$ with $d_{tar}=12$\,nm, for both the P-EM (black crosses, the large one denotes the target) and TB-HL (orange balls) models. The configurations along the red dashed line (same as \textbf{b}) result in destructive $j_{yz}$ terms and their exchange values are reduced by more than two orders of magnitude compared to the configurations perfectly aligned with [100] (blue dashed lines). Right: the exchange variations for a target along [110] are limited to less than a factor of 10 as $j_{zz}$ dominates, making the exchange interaction insensitive to in-plane valley interference. \textbf{d} Ratios $J_{min}/J_{max}$ vs $d_{tar}$ between 5 and 25\,nm for both [100] (orange) and [110] (blue). The impact of in-plane valley interference vanishes for target distances beyond 12\,nm along [110], to bound exchange variations to the envelope limit. Destructive $y$-valley positions, and the degeneracy between $j_{yz}$, $j_{yy}$ and $j_{zz}$, are always present along [100] independently of the target distance, resulting in large exchange variations. The light blue lines show the exchange variations if the two donors are in different atomic $z$-planes, resulting in a finite $z$-valley phase difference.}
\label{fig4b}
\end{center}
\end{figure*}

The relative weights of the 6 different envelope terms $j_{\mu\nu}$ are plotted in Fig.~\ref{fig4a}b for a target distance $d_{tar}$ of 12\,nm as a function of the in-plane angle $\theta_{tar}$ defined with respect to [100]. To parametrise the P-EM model, the valley momentum and anisotropy ratio are set to the experimentally obtained average values, i.e. $k_{\mu}{=}0.81k_0$ and $b/a{=}0.52$. The large envelope radius $a$ is set to 2.8\,nm obtained from fitting Heitler-London calculations along [110] (See Supplementary Note 3). The weights ($j_{xx}$, $j_{xy}$, $j_{xz}$, $j_{yy}$, $j_{yz}$ and $j_{zz}$) evolve smoothly with $\theta_{tar}$ (and $d_{tar}$), since they do not contain any valley interference, but their ratios are not constant and vary by several orders of magnitude. This is a direct consequence of the anisotropic and exponential nature of the donor envelope. Along [100], at $\theta_{tar}=0^\circ$, the $j_{yz}$ terms are degenerate with $j_{zz}$ and $j_{yy}$, and largely dominate over any term where an electron is exchanged in a $x$-valley. This can be understood as mass anisotropy results in $F_{x}$ to have a minor envelope radius $b$ along ${x}$, hence the product between two $F_{x}$ orbitals separated along [100] is smaller than its $F_{y}$  and $F_{z}$-orbital counterparts, as they both have a major envelope radius $a$ along $x$ instead. The degeneracy between $j_{yz}$, $j_{zz}$ and $j_{yy}$ arises from symmetry as the products between $y$ and $z$ orbitals are equal along [100].

The envelope weight anisotropy influences the way valley interference impact the exchange coupling. In order to get further insight on its role, we must consider the precise placement scheme provided by STM lithography. Each donor is stochastically incorporated within $\pm 1$ lattice site precision in a patch of 3 desorbed hydrogen dimers (see Fig.~\ref{fig4b}a). This placement precision results along [100] in 12 non-equivalent configurations for the donors separation shown in Fig.~\ref{fig4b}b, taking the convention to fix $\rm{P_1}$ at the origin, (see Supplementary Note 3). From pair to pair, different configurations will be stochastically obtained, resulting in the phase terms $\Delta\phi_x$ and $\Delta\phi_y$ to vary accordingly, and to potentially become destructive. Along [100], the degeneracy and dominance of the $j_{yy}$, $j_{zz}$ and $j_{yz}$ terms implies that the sum expressed in Eq.~\ref{exc} can be reduced to these terms, which only involve $\Delta\phi_y$ and $\Delta\phi_z$. Hence, $\Delta\phi_x$ does not influence the exchange and can be ignored along [100]. Furthermore, $\Delta\phi_z{=}0$ since the $z$-valleys are constructive anywhere in the $xy$-plane, and only $\Delta\phi_y$ matters along [100]. The 12 values of exchange obtained from these configurations are plotted in Fig.~\ref{fig4b}c for a target distance of 12\,nm. Assigning each of them to their respective position configuration allows to understand the observed spread. The values can be separated in 4 different groups according to their respective $\Delta\phi_y$ since it is the only phase term of interest in this case. Among each group, the exchange values evolve monotonically since their valley phase terms are the same, leaving only an envelope dependence. The configurations perfectly aligned with [100] (blue dashed line in Fig.~\ref{fig4b}b-c) lead to constructive $y$-valleys, i.e. $\Delta\phi_y=0$ and a maximised exchange coupling. The fast damping of exchange oscillations purely along [100] was already pointed out in previous work~\cite{Koiller2001,Pica2014,Gamble2015}, which can result in favouring [100] as the target axis if dopant placement accuracy is not appropriately considered. In fact, the configurations misaligned with [100] result in finite $\Delta\phi_y$ and hence to a reduced exchange energy. In particular, in-plane positions off the [100] axis by $a_0/2$, i.e. the closest positions to [100] (red dashed line in Fig.~\ref{fig4b}b-c), result in destructive $y$-valley interference and hence negative $j_{yz}$ contributions to the exchange. These negative contributions almost perfectly cancel out the constructive $j_{yy}$ and $j_{zz}$ terms in the exchange equation, and the exchange energy is reduced by more than two orders of magnitude for these specific positions~\cite{Koiller2001}. It is important to note that these destructive configurations are common to any previous theoretical work, although they had different conclusions because of different approaches in dopant placement accuracy (see Supplementary Note 3). Moreover, they are always present for any inter-donor distance since they result from the envelope weight degeneracy between $j_{yy}$, $j_{yz}$ and $j_{zz}$ inherent to the [100] axis. These two arguments are crucial to definitely rule out [100] as a favourable placement axis.

Considering placement accuracy is essential when looking to fully understand the role of valley interference and envelope anisotropy on the exchange interaction. Some approaches have considered random dopant placement around a target~\cite{Koiller2001,Testolin2007,Gamble2015,Song2016}, but the actual in-plane placement accuracy at any in-plane angle $\theta_{tar}$ that STM lithography can ultimately offer has been overlooked. Away from [100] at finite $\theta_{tar}$, the envelope anisotropy breaks the degeneracy between the $j_{yy}$, $j_{zz}$ and $j_{yz}$ terms (see Fig.~\ref{fig4a}b). The $j_{zz}$ term becomes dominant over any term involving an electron exchanged in a $F_x$ or $F_y$ orbital, as the $F_z$ orbitals are the only ones to face each other across their major envelope radius $a$ independently of $\theta_{tar}$ (as their minor envelope radius is out of the plane). The prevalence of $j_{zz}$ is maximised at $\theta_{tar}=45^\circ$, i.e. for donors separated along [110]. There, a different symmetry condition is reached with a degeneracy occurring between the $F_{x}$  and $F_{y}$  orbital products since $x{=}y$ along this direction. The following order is hence obtained, with the $j_{zz}$ terms dominating over the degenerate $j_{xz}$ and $j_{yz}$ terms, themselves dominating over the $j_{xx}$, $j_{xy}$ and $j_{yy}$ terms, which are also degenerate by symmetry. Placing donors along the [110] orientation results in finite $\Delta\phi_x$ or $\Delta\phi_y$, which can vary according to the configuration specifically obtained from pair to pair, and hence to destructive $j_{xz}$ or $j_{yz}$ terms. However, they both have a negligible impact on the value of exchange since $j_{zz}$ dominates. As a result, the possible exchange values obtained for two donors aimed along the [110] axis are much more constrained and vary by less than an order of magnitude as shown in Fig.~\ref{fig4b}c. To summarise these results we plot in Fig.~\ref{fig4b}d the ratio $J_{min}/J_{max}$ defined for each target distance and orientation. Along [100], the exchange energy presents large variations independent of target distance as the degeneracy between $j_{yy}$, $j_{yz}$ and $j_{zz}$ remains. However, along [110] the in-plane valley interference $\Delta\phi_x$ or $\Delta\phi_y$ do not impact the exchange coupling for target distances beyond 12\,nm as the variations reach an asymptotic limit set by envelope considerations only (see Supplementary Note 3). As for the [100] case, this result is in agreement with previous work~\cite{Koiller2001,Pica2014,Gamble2015} (See supplementary Note 3). It is revealed here through an atomic-scale understanding of the interplay between envelope anisotropy, degeneracies, valley interference and dopant placement accuracy. Furthermore, the dominance of the $j_{zz}$ envelope terms along [110] results in $\Delta\phi_z$ to be the only relevant valley phase difference, and thus to the exchange variations to be arranged as a function of the depth difference, i.e. atomic planes, between the donors. The resulting variations with respect to the maximum in-plane exchange value are shown in Fig.~\ref{fig4b}d for depth variations included within $\pm$1\,$a_0$. Only the ${a_0/4}$ and $1a_0$ planes show a significant reduction of the exchange interaction. Moreover, for target distances beyond 10\,nm none of these planes lead to exchange variations as large as for the in-plane exchange variations obtained around the [100] direction, which are the largest within $\pm$1\,$a_0$ variation in $z$-placement for this direction (See Supplementary Note 3).

We also compared the variations obtained from our P-EM model to Heitler-London calculations based on the tight-binding wavefunctions (TB-HL), for which we already demonstrated in Fig~\ref{fig2} an excellent agreement with the experiment at the wavefunction level. The TB-HL exchange calculations shown in Fig.~\ref{fig4b}c confirm two orders of magnitude of exchange variations for donors placed along the [100] direction because of the presence of destructive $y$-valleys configurations. They also confirm that exchange variations can be reduced to less than an order of magnitude along [110]. A more detailed level of comparison between TB and P-EM models is discussed in the Supplementary Note 3. Hence, TB formalism accurately models the donor wavefunction's details and can be further used to predict the properties of advanced donor-based quantum devices which notably include electric fields. Finally, our understanding of the interplay between valley interference, envelope anisotropy and atomic placement on the exchange interaction which we developed from our P-EM model can be tied back to the original pair which has been experimentally measured. In order to obtain a normalisation constant for the exchange energies, we have fitted the exchange energy obtained from tight-binding calculations in the Heitler-London limit along [110] for the bulk case (See Supplementary Note 3). We notably obtain excellent agreement on the value of the valley momentum $k_{\mu}$ and on the anisotropy $b/a$ with the experimental ones. Equipped with this calibration, we can predict an effective mass exchange value for pair \#1, which we found to be 1.50\,meV, in excellent agreement with the FCI value calculated and mentioned above. Furthermore, we have also computed a nearby case of pair \#1, where donor $P_1$ was brought from the $z{=}5.5a_0$ to the $z{=}6.5a_0$ atomic plane. This shift results for these two donors to have the same $x$ and $y$ coordinates but to be separated by $\Delta z{=}0.25a_0$, which is a very destructive plane difference for the $z$-valleys as seen in Fig.~\ref{fig4b}d for such pair in the neighbourhood of [110]. Indeed, the P-EM model yields an exchange of 0.133\,meV and the FCI calculations 0.108\,meV, again in excellent agreement with each other. We note that for such inter-donor distance the $z$-arrangement of the exchange values along [110] is not fully formed yet, i.e. $\Delta\phi_x$ and $\Delta\phi_y$ are non-negligible for these two cases, nevertheless this quantitative agreement clearly demonstrates the influence of the valley interference on the exchange interaction, as both values for pair \#1 and its nearby cases are much lower than the maximum exchange values of the order of 10\,meV that can be obtained in this neighbourhood.

 \section{Discussion}

The direct measurement and quantification of valley interference between donor states at the atomic-scale using STM which was realised here provides a detailed level of understanding of their impact on exchange variations~\cite{Koiller2001,Gamble2015,Song2016}. Importantly, we found that the exchange interaction along the [110] direction is dominated by the $j_{zz}$ term and hence insensitive to in-plane valley interference $\Delta\phi_x$ and $\Delta\phi_y$. The agreement between atomistic calculations and the P-EM model which relies upon parameters which we have here assessed experimentally, further establishes the importance of the envelope radius anisotropy and of valley interference to fully understand the behaviour of the exchange interaction at the atomic scale. Using the current state of the art STM lithography~\cite{Fuechsle2012, Weber2014, Koch2019} with $\pm$\,1 lattice site precision, the preferential crystallographic placement along [110] can be leveraged together with an in-plane placement resulting in $\Delta\phi_z=0$. As a result, STM lithography enables to engineer donor devices where the exchange can be totally immune to valley interference, hence achieving a true semiconductor vacuum where complex degeneracies of the band structure can be ignored for coupled donors. The exchange variations are minimised to a factor of less than 10 between configurations where dopants are moved by $\pm$1 lattice site. This factor is only due to change in the envelope overlap between the wavefunctions as it is the case for vacuum systems. Importantly, by symmetry, and as confirmed by our results in Fig.~\ref{fig4a}b, the exchange coupling along the [-110] direction (perpendicular to [110]) is also dominated by $j_{zz}$ and therefore also protected from in-plane valley interference. As such it is possible to place donors using STM lithography along both the [110] and [-110] directions to create 1D and 2D arrays with reduced exchange coupling variations between nearest neighbours. In our work, the donors were found at different atomic planes which we attribute to an annealing step at $600\,^{\circ}$C performed during sample fabrication in order to flatten the surface for tunneling spectroscopy purposes. Experimental progress has been made to minimise the segregation of highly doped phosphorus monolayers~\cite{Keizer2015,Wang2018a}, which should be further reduced for single donors as segregation and diffusion constants strongly depends on dopant concentration~\cite{Hu1983}. Single donor segregation mechanisms are predicted to activate from $250\,^{\circ}$C~\cite{Bennett2009}, which bulk donor qubit device fabrication can withstand~\cite{He2019}. These results motivate our scheme to keep the donors in the same plane around the [110] axis to maximise the exchange interaction uniformity.

Controllable exchange coupling between atom qubits is a key requirement for two-qubits gates, which must be performed with high fidelities and high speed in views of fault-tolerant quantum computing architectures~\cite{Fowler2012, Hill2015}. Exchange variations from pair-to-pair can create rotation errors as the CNOT gate length is calibrated to a particular target value, which can impair the operation of a quantum processor. To avoid these errors, a composite CNOT gate can be performed with a so-called BB1 sequence instead of a single pulse~\cite{Hill2005,Testolin2007}. This composite CNOT gate can be decomposed in a set of single and two-qubit rotations, with the advantage to maintain a high-fidelity above 99.9\%, i.e. above quantum error correction thresholds, for any qubit pair despite a 10\% error in the characterisation of the exchange coupling. For donors separated by 12\,nm along the [110] direction, our TB-HL calculations give exchange values ranging from 11 to 93\,MHz. These values can be used together with known single qubit gate times (340\,ns~\cite{Pla2012}) to obtain CNOT gate times varying by less than 1\% across an array (See Supplementary Note 4), with an average value of $1.2\mu s$, for fully characterised exchange values. This average CNOT gate time is dominated by the single qubit rotation time for this target distance, and the spread could be overcome by tuning the exchange values with each other electrically~\cite{Wang2016}. Such tuning would be impossible for donors placed along [100] because of too large exchange variations. The operation time expected for the out-of-plane configurations within one monolayer do not exceed $1.34\mu s$. For exchange values characterised to 90\%, adding the correcting sequence to maintain the fidelity would result in CNOT operation times average to $2.3\mu s$ with a spread limited to 4\% for the in-plane configurations, and a maximum time of $3.7\mu s$ for out-of-plane configurations with only 6 out of 82 total configurations exceeding $3\mu s$. Whilst these operation times are slower compared to other spin-based CNOT gates~\cite{Veldhorst2015, Watson2018, Zajac2017}, they are well below donor coherence times which can approach seconds using dynamical decoupling sequences~\cite{Tyryshkin2011}.\\

As already mentioned, exchange and tunnel interactions are closely related since they both rely on wavefunction overlap considerations. From our exchange analysis, we obtain tunnel coupling values varying by less than a factor 5 for inter-donor distances down along [110] to 5\,nm (see Supplementary Note 3). This distance is the lower bound at which the Heitler-London description is valid, as tunnel coupling values are there predicted to exceed 10\,meV, i.e. becoming a substantial fraction of the 47\,meV charging energy. Expected tunnel coupling values~\cite{Gamble2015} up to target distances of 12\,nm along [110] remain above 200$\mu$eV for in-plane configurations, and above 60$\mu$eV for out-of-plane ones, all much larger than the achievable electronic temperature of about 50\,mK (i.e. about 5$\mu$eV). This opens the way to the study of Fermi-Hubbard problems robust to this level of disorder, as for the case of dimerised chains~\cite{Su1979,Le2019}, with the competition between topological gaps originating from the tight-binding picture~\cite{Slot2017, Drost2017, Ni2019} and on-site interactions. The prospect to extend studies to the regime of strong tunneling interactions and to 2D systems makes donors in silicon a standout platform for quantum simulation of the Fermi-Hubbard model.\\

In summary, starting from direct real-space measurements of donor wavefunctions, we have been able to unambiguously quantify valley interference between donor atoms in silicon in real space and validate the predictions of existing theories. Driven by this experimental approach, we consider the dopant placement precision offered by STM lithography for a detailed understanding of the interplay between valley interference, envelope anisotropy on the exchange interaction. In full agreement with previous theoretical work, our results identify the [110] crystallographic direction as optimal for building 2D donor arrays where we predict less than an order of magnitude variation in exchange and tunnel couplings. We envision this fabrication strategy, in conjunction with quantum control schemes~\cite{Testolin2007} and exchange tuning mechanisms~\cite{Wang2016}, to be a key component in leveraging the exceptional coherence of donor qubits in silicon towards scalable quantum simulators and quantum processors.

\section*{Methods}
\subsection{Sample preparation}

Samples were prepared in ultrahigh vacuum (UHV) with a pressure lower than $10^{-10}$\,mbar, starting from a commercial n-type As doped wafer with a resistivity of $\rm{0.001-0.003\,\Omega.cm}$. Samples are first flash annealed three times around $\rm{1150\,^{\circ}C}$ for a total of 30\,s. After the final flash anneal, the temperature was rapidly quenched to $\rm{800\,^{\circ}C}$, followed by slow ($\rm{1\,^{\circ}C/s}$) cooling to obtain a flat $\rm{2\times1}$ surface reconstruction. Under these conditions, a layer of $\rm{\sim15\,nm}$ from the Si surface is depleted from As dopants. P dopants are incorporated at this stage in Si by submonolayer phosphine ($\rm{PH_3}$) dosing with a sheet density of $\rm{5\cdot10^{11}\,cm^{-2}}$. This low-dose P $\rm{\delta}$-layer was overgrown epitaxially by $\rm{\sim2.5\,nm}$ of Si. Growth parameters such as temperature and flux were chosen to achieve minimal segregation and diffusion whilst preserving a flat surface for STM imaging and spectroscopy purposes. Notably, the first nanometer is a lock-in layer grown at room temperature~\cite{Keizer2015}. Subsequent growth alternates between $\rm{250\,^{\circ}C}$ and $\rm{450\,^{\circ}C}$ with a duration ratio of 3/1. A $\rm{600\,^{\circ}C}$ flash follows for 10\,s to flatten the surface. The surface is finally hydrogen passivated at $\rm{340\,^{\circ}C}$ for 10\,min under a flux of atomic H produced by a thermal cracker, in a chamber with a $\rm{10^{-7}\,mbar}$ pressure of molecular hydrogen. STM measurements are taken in the single-electron transport regime described in ref.~\cite{Salfi2014, Voisin2015}.

\subsection{Measurement techniques}

The electrical measurements were carried out at 4.2\,K in a scanning tunnelling microscope (Omicron LT-STM). Both sample fabrication and measurements are done in ultrahigh vacuum with a pressure lower than $10^{-10}$\,mbar. The tunnel current $I$ was measured as a function of the bias voltage $U$ using ultralow noise electronics including a transimpedance amplifier. The differential conductance d$I$/d$U$ shown in Supplementary Note 2 was obtained by numerical differentiation. Spatially resolved measurements of donor pairs quantum state were acquired using the multi-line scan technique, where the topography is recorded at ${U= -1.45\,V}$ during the first pass, and played during the second pass in open-loop mode with the current $I$ recorded at the bias mentioned in the caption of the corresponding figures. The sample fabrication described above results in the donor pairs to be measured in the sequential transport regime, with a first tunnel barrier with tunnel rate $\rm{\Gamma_{in}}$ occurring from the highly doped substrate annealing, and the second tunnel barrier with tunnel rate $\rm{\Gamma_{out}}$ being a combination of the Si overgrowth after P deposition and the vacuum barrier, mainly dominated by the latter and tip-sample distance. Additional information regarding STM images and spectroscopy analysis can be found in the Supplementary Note 1.

\subsection{Atomistic simulations}

Single-particle energies and wave functions for P donor in silicon are computed by solving a $sp^3d^5s^*$ tight-binding Hamiltonian~\cite{Boykin2004a}, where the P atom is represented by central-cell corrections including donor potential screened by non-static dielectric function~\cite{Usman2015}, and the P-Si nearest-neighbour bond-lengths are modified in accordance with the published DFT prediction~\cite{Overhof2004}. The size of simulation domain (Si box) consists of roughly four million atoms with closed boundary conditions in all three spatial directions. The effect of surface strain due to $\rm{2\times1}$ surface reconstruction is included in the tight-binding Hamiltonian by properly displacing surface Si atoms and by modifying the inter-atomic interaction energies in the tight-binding Hamiltonian~\cite{Usman2016}. The calculation of STM images of donor wave functions follows the published methodology~\cite{Usman2016}, where tight-binding wave function is coupled with Bardeen's tunneling theory~\cite{Bardeen1961} and derivative rule of Chen~\cite{Chen1990}. In our STM measurements, dominant contribution is from $d_{z^2}$ orbital in STM tip. For two-particle STM images, two-electron wave functions are computed from full configuration interaction approach~\cite{Tankasala2018}. The STM image represents a quasi-particle wave function resulting from 2e to 1e transition~\cite{Rontani2005}. The resulting quasi-particle state is used to compute tunnelling matrix element described in the Supplementary Note 1. The exchange calculations shown in Fig.~\ref{fig4b} are computed either from the corresponding atomistic tight-binding single-particle wave functions~\cite{Wellard2003}, or from a phenomenological effective mass model detailed in the Supplementary Note 3, both based on Heitler-London formalism.

\section{Acknowledgements}
We thank J. Keizer for advice on sample fabrication, C.Hill, M.J. Calderon and S.N. Coppersmith for valuable discussions, and J.K. Gamble \textit{et al.} for publishing a complete data set of tunnel coupling calculations~\cite{Gamble2015}. We acknowledge support from the ARC Centre of Excellence for Quantum Computation and Communication Technology (CE170100012), Silicon Quantum Computing Pty Ltd., and from the U.S. Army Research Office (W911NF-08-1-0527). J.S. acknowledges support from an ARC DECRA fellowship (DE160101490). The authors acknowledge the use of computational resources from NanoHUB, the Network for Computational Nanotechnology at Purdue University, and from the Australian Government through the Pawsey Supercomputing Centre under the National Computational Merit Allocation Scheme (NCMAS). This work used the Extreme Science and Engineering Discovery Environment (XSEDE) ECS150001, which is supported by National Science Foundation Grant No. ACI-1548562~\cite{Towns2014}.

\section{Author contributions}

S.R. designed the project. J.B. and  B.V. conducted the STM experiments and carried out the STM image analysis, with J.S., M.Y.S. and S.R. providing input. M.U., B.V., A.T., J.S. and J.B. pinpointed the dopant positions. M.U., A.T. and R.R. performed the single donor tight-binding calculations. A.T. and R.R. performed the two-electron FCI exchange calculations and computed QPWFs, with J.S. providing input. M.U. calculated the theoretical STM images and computed Heitler-London exchange calculations using tight-binding wavefunctions, with L.C.L.H. and R.R. providing input. B.V. formulated the phenomenological effective mass model and carried out the exchange variation analysis. All authors contributed to data analysis and conclusions. B.V., J.S., M.Y.S., L.C.L.H. and S.R. wrote the manuscript, with input from all authors.

\section{Data availability}
Any data and code used for the purpose of this article is available upon reasonable request.

\section{Competing interests}
M.Y.S. is a director of the company Silicon Quantum Computing Pty Ltd.
B.V, J.S. and S.R. have submitted a patent application that describes the use of a stabilised exchange coupling for quantum computing with donors in silicon. Other authors declare no competing interests.

\bibliographystyle{aipnum4-1.bst}

redpajama_set_name: RedPajamaArXiv


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Fantastic Four (2015) Movie Review
21 Comments	/ By tiffanyyongwt / Movie Review
Fantastic Four (2015) Movie Review | by tiffanyyong.com
Recommended Audience: Fans of Miles Teller, Michael B. Jordan, Kate Mara, Jamie Bell, Toby Kebbell and Marvel movie fans
Fantastic Four Movie Synopsis
FANTASTIC FOUR, a contemporary re-imagining of Marvel's original and longest-running superhero team, centers on four young outsiders who teleport to an alternate and dangerous universe, which alters their physical form in shocking ways. Their lives irrevocably upended, the team must learn to harness their new abilities and work together to save Earth from a former friend turned enemy.
Fantastic Four Viewer Rating: 3.5/5 ***
Fantastic Four Movie Review:
There had been quite a lot of negative reviews when the film was out. I wanted to watch it myself and see how 'bad' it was. To be truthful, I thought the negative criticism was mainly because Fantastic Four is a Marvel film and the critics had wanted a Marvel-ous result.
This would most probably have received better reviews if it hadn't been a Marvel story. I like the focus on the scientific development, the initial character development of the friendship between Richard Reeds (Miles Teller) and Ben Grimm (Jamie Bell), and the subtle love-triangle between Richard Reeds, Sue Storm (Kate Mara) and Victor Von Doom (Toby Kebbell). It was difficult imagining Miles Teller to be the nerdy geek after his memorable performance in Insurgent and That Awkward Moment, but well, he was kinda getting it. Not exactly there, but still pretty believable.
While I have little complains for Kate Mara's portrayal of Sue Storm as a genius instead of a hot babe, her nose was really distracting!
Jamie Bell is "The Thing" with the least lines (and screen time), but yet, I thought he was the one with the most potential. Too bad, his role was underdeveloped and the focus was leaning heavily toward Richard Reeds.
While the whole world is complaining about Johnny Storm being a black guy, I thought the use of child adoption to weave the siblings together was not a bad idea. The one BIG problem with this film was how it was the climatic fight scene was too short and Doctor Doom died way too easily. While I love the time-lapse clip on how the machine was built, the time spent on the individual four when they received their powers were dreadfully short.
The finale resembles a Captain Planet cartoon or even Mighty Morphin Power Rangers episode where the "leader" shouts out how they should work together to fight thy enemy. It would have been great, if I was watching this 10 years, no, 20 years ago. Indeed, it is Fantastic For kids.
Stan Lee has no cameo in this movie and there is no post-credit scenes.
Michael B. Jordan ran into Chris Evans, who initially played Johnny Storm in Fantastic Four (2005) and its sequel, at an industry event. According to Jordan, they ended up talking about the role and Evans told him, "Man, I can't give you anything. You're great, you're awesome. Just do your thing. And enjoy it. It's gonna be fun."
Saoirse Ronan, Allison Williams, Emmy Rossum and Margot Robbie auditioned for the role of Susan Storm/The Invisible Woman before Kate Mara was cast.
Kit Harington, Anton Yelchin, Richard Madden and Jack O'Connell auditioned for the role of Reed Richards/Mister Fantastic before Miles Teller was cast.
A teacher jokes about young Reed building a flying car. In the comics, Reed Richards constructed the Fantasticar, a flying car that served as the Fantastic Four's personal vehicle.
Miles Teller is the first American actor to portray Reed Richards/Mister Fantastic; his predecessors, Alex Hyde-White and Ioan Gruffudd, were British. In contrast, Jamie Bell is the first British actor to play Ben Grimm/The Thing; his predecessors, Michael Bailey Smith and Michael Chiklis, were American.
This is the second time Michael B. Jordan has portrayed a superhero, after voicing Cyborg in Justice League: The Flashpoint Paradox (2013)
Miles Teller (Reed Richards/Mr. Fantastic) and Michael B. Jordan (Johnny Storm/The Human Torch) previously starred together in That Awkward Moment (2014).
Check out Fantastic Four official website and Facebook Page!
Fantastic Four is out in cinemas on 6 August 2015.
*Disclosure: No monetary compensation was received for the movie review.
21 thoughts on "Fantastic Four (2015) Movie Review"
melisasource
I've heard so much about this film! My boys want to go see it, so I may take them soon!
Gilliannong.com
I watched this.. lol . I think it was a pretty alright movie but it was so dull!
Haha… Oh wel… Let's just say it's a very "Scientific" movie!
I watched it almost feel asleep in the cinema. The movie is long and draggy with lots of conversation and slow motion part. Quite boring.
3xhcch
I actually like "That Awkward Moment" more than this film. Haha! Only the last part was exciting, then it was over, just like that. The whole buildup was very very disappointing. – Fred
Every time a new superhero movie comes along, I clap like a child along with the whole world. It's sad that this movie got negative reviews, so I will do as you did and watch it myself to see what the fuss is about.
sinyees
This is a really disappointing Marvel movie… The thrilling part only last for 15 minutes… hmmmm…
I'm going to watch this in the future but I was so surprised at how many people hated it! I was actually surprised by your rating! 😀
You are actually one of those raters who gave good grades to this movie. I've read a lot of bad reviews with Fantastic Four so we didn't watch it in the movie house. I guess i'll just wait for my sister to get a downloaded version of this and watch it at home to see if it really sucked or not. :p
I agree people may have already set the bar high in the first place. The cast though is not as star-studded as the previous one. I'll probably check it out when it comes out on DVD.
Frankly speaking I have heard not so good reviews about this movie.so not sure whether going to watch.
Sorry if I judged it even before watching it but honestly… when i first saw the trailer, I kind of didn't like it already. It would have been better if they just used the same actors like the previous one. I somehow sensed the movie will be focused to the Reed's character. I guess I made the right choice not to watch it.
phyliciamarie
Finally, a review that's not too scathing. It's too bad that people judged it waaay too much because it is a Marvel movie. I like how you offered different explanations as to why people were so against the movie.
Honestly, this is a very bad film. I've wasted a portion of my hard earned bucks watching this one.
Hahaha… You are not the first nor the last to think that way!
I think I'll just sit and wait for a bluray release. I've had it with remakes this year, there's so many of them!
I've read some very bad reviews since this movie came out. The cast of A-listers was a hard act to follow, which seems to be a factor as to why this movie was a flop at the box office. I myself wasn't that enthusiastic to see it, I still prefer Jesicca Alba I guess.
Debra Lord Daigle
Im sorry but I did not like it. It was campy and predictable. The acting could have been better if the characters were a bit older and experienced. I would give it a 2 on a 5 scale and thats being generous. Im a huge Marvel fan.
I am eagerly waiting for its release in Thailand. The waiting is actually killing me.
So high your rating… or is it rating for kids? 😀
7/10 is pretty watchable. Don't think it's very high. 6/10 is too low for that movie~

redpajama_set_name: RedPajamaCommonCrawl


THE "OLD FIRST" VIRGINIA AT GETTYSBURG.
And the Part the Old First Virginia Regiment Played In It.
Much has been written about this historic event and chiefly by those who are writers, but get their information from all kinds of publications, while those who were actors in the bloody drama have had but little to say, and they are fast passing on to answer the roll call of their comrades gone before.
The story of Pickett's charge will ever be remembered and generations yet to come will point to it as one of the grandest acts of heroism in American history.
The Old First Virginia formed part of Kemper's brigade. It held the centre position in the brigade line. The 3d of July, 1863, was extremely hot, and the brigade had to endure the sweltering sun, lying in rear of Seminary Ridge in open field, while to its left were the brigades of Garnett and Armistead partly sheltered in the woods.
The distance from the position of Kemper's brigade to the angle of the stone wall, the point of attack, was just one mile across an open hilly plain, crossed by the Emmettsburg road, thus the enemy from their position on Roundtop Hill could see and count every man we had when we advanced to the charge. Moreover, on these hills the enemy placed their batteries, which fired with fatal effort on our men as they charged.
Just before our artillery opened, there was a detail of fifteen men from each regiment made to act as skirmishers. These moved at once forward in rear of the batteries near which Wilson's brigade was in position. At 1 o'clock our artillery opened the battle and a few minutes afterward the Federal guns joined in, and the very ground shook. It was simply awful, the bursting of the shells, the smoke, and the hot sun combined made things almost unendurable for our men lying in long rows in rear of the ridge.
Many of our men were wounded by the shelling, and it was a relief when finally the artillery ceased its terrible work and orders came for Pickett's men to charge. The skirmish line (to which the writer was attached) moved forward towards the enemy's skirmish line. Some two hundred yards in the rear came the line of battle, Richard B. Garnett's brigade on the left and Kemper's brigade on the right, while Armistead's came close in the rear.
It was a splendid exhibition, the alignment was nearly perfect. After advancing some three hundred yards the enemy's artillery opened on the columns and shells came screaming through the ranks of Pickett's men. As the men fell the ranks closed, and forward went the line, leaving the dead and wounded in its track.
The move was made in a left oblique direction to reach the point of attack, which was the angle of a stone wall or fence on the ridge of Seminary Hill. When the line reached this point it became irregular. Many of the officers fell before this point was gained. Colonel Joseph Mayo, of the Third, ordered the brigade to face to the right just as the wall was reached.
There were heavy columns of the enemy coming from that direction, while Garnett's men came in contact with the enemy behind the wall; then Armistead's men rushed across the wall and pursued the enemy, who abandoned the battery some 300 feet in rear of the wall. Then came a short lull in the battle, but firing was kept up and men fell to rise no more.
About 150 Federa-s were captured at the angle and taken off the field. It was at this time that General Lewis A. Armistead was killed, having his left hand on one of the guns of Cushing's battery, and in his right hand he held his sword on which he had placed his hat. Thus a hero meets a hero's death.
The line around the angle was being fast thinned out, and now was the time for reinforcements to push on the victory within our grasp, but none were there to aid Pickett's men in their struggle to hold the position for which they had fought so hard.
The supporting line on Pickett's left struck the enemy's line further to our left, reaching there long before Pickett, their line being nearly one-half shorter, and as Pickett's men advanced the line our left was seen to be in full retreat, having suffered heavily. The men of Pickett's division--that is, about one-tenth of what was left--retraced their steps, falling back in small groups, firing as they retreated.
General Pickett was seen in the midst of his survivors when the battle was over, but at the close Wilcox's brigade came rushing down. It came about half way when it met the concentrated fire of the enemy and fell back faster than it came, adding only to the losses and accomplishing naught.
Sergeant Major J. R. Polak states that he was ordered by Colonel Williams to bring up the ambulance corps, as men were falling right and left and needed attention. He went off on "Nelly" (Colonel Williams's horse) to execute the orders given him, and on his return the regiment, with the rest of the division, were all charging, and all he could do was to return Colonel Williams's horse and take his place in the ranks. Colonel Williams at once mounted and wheeled in front of the regiment and was almost immediately struck down. Then Major Langley took command; he was soon disabled. Then Captain Norton took command with the same result. Then Captain Davis jumped in front of the line and was bowled over almost immediately. Then I remember we pushed up to the wall, and could almost see the Yankee gunners leaving their places and running in our lines for safety. Whilst we were waiting with our line for reinforcements, I had a short talk with Lieutenant Cabell about the massing of the Yankees in our front, and the next thing I saw was Colonel Patton of the Seventh Virginia, struck, and when I asked him if he was hurt he tried to answer, but the blood gushed out of his mouth, and made it impossible.
The next thing that I remember was that no reinforcements came and that the Yankees came over the works and we "got," at least I did. I was slightly wounded in the face and in the arm, and found it somewhat difficult to jump what looked to me a ten rail fence, but I managed this all the same. When I got my breath about a quarter of a mile from the field, I saw General Lee riding unattended, and after a few minutes of observation he rode back and returned with General Longstreet, and then established a point for the returning men to fall back on.
The account given of Lieutenant William M. Lawson, who was the color bearer of the regiment is as, follows : "When the order was given to forward the color bearer and guard consisting of Color Bearer William M. Lawson, Sergeants Pat Woods, Theodore R. Martin, Corporal John Q. Figg, and Private Willie Mitchell moved four paces to the front of the line and kept in their position until one after the other was shot down. About half way Willie Mitchell was wounded, but he declined to go back and kept on. About one hundred yards further he was killed. Pat Woods, Theodore R. Martin and John Q. Figg were shot down and the line came close to the stone fence. The color bearer had his right arm shattered by a bullet, and the colors fell from his hand among the dead and dying. J. R. Polak attempted to raise and secure the colors, but was also wounded. Those that were able now fell back and the colors remained where they fell near the angle of the stone wall.
Sergeant Pat Woods was shot through the body and remained in prison for some time. He was a most reckless, daring Irishman. There were no better men than Sergeant Theodore R. Martin and John Q. Figg. Both of these were severely wounded. Sergeant John Q. Figg was afterwards promoted to color bearer and made a splendid record for himself in the battles that followed in 1864 and 1865 until the close of the war.
In straggling groups the survivors of that charge gathered in rear of Seminary Ridge, near the point from which they set out to do or die. It was a sad sight. Most of them were bleeding; numbers of them were bathing their wounds in a little creek which ran along the valley, making its clear water run red, which others used to quench their burning thirst. Some 300 or 400 men were there. General George E. Pickett was mounted, and was talking to the men here and there. Only two of the regiments had retained their colors, one of which was the 24th Virginia, and the color bearer, a tall mountaineer, named Charles Belcher, was waving it, crying: "General, let us go at them again!" just about then General James L. Kemper was carried into the crowd, and the latter came to a halt. Then General Lee was seen to ride up, and we, as was usual, wanted to know what he had to say, crowded around him.
General Pickett broke out into tears, while General Lee rode up to him, and they shook hands. General Lee spoke to General Pickett in a slow and distinct manner. Anyone could see that he, too, felt the repulse and slaughter of the division, whose remains he viewed.
Of the remarks made to General Pickett, by General. Lee, we distinctly heard him say: "General Pickett, your men have done all that men could do; the fault is entirely my own." These words will never be forgotten.
Just then, he turned to General Kemper and remarked: "General Kemper, I hope you are not seriously hurt, can I do anything for you?" General Kemper looked up and replied: "General Lee, you can do nothing for me; I am mortally wounded, but see to it that full justice is done my men who made this charge." General Lee said: "I will," and rode off.
General Pickett turned to us, saying: "You can go back to the wagons and rest until you are wanted." The men then left for their wagon trains.
There was little or no organization among them. Night was coming on and the writer and several of his company slept in a mill, about half way to the wagon train, getting back with those of the survivors of the Old First on the morning of the 4th. The whole command numbered hardly thirty men, rank and file, and Captain B. F. Howard had charge of the squad.
About 10 o'clock the drum beat to fall in, and, as we took our places in rank, J. R. Polak came out with a set of colors, which he got from an ordinance wagon (the same had been left in our hands by Holcomb's Legion at Second Manassas) and, waiving it, though he had his hand in a sling, and his nose was all bloody from the charge, but we declined to play color guard, and the flag was returned to the wagon.
Then the order from General Lee, constituting Pickett's division the provost guard for the army was read, and was but little relished by the men, most of them considering it as almost a disgrace to act as provost guard; however, orders must be obeyed, and, after an hour or two of waiting, we were marched up on both sides of the road and the Federal prisoners filed in between us, and Pickett's division saw them safely turned over to Imboden's command on the 9th. At the Potomac river, on the 10th, the 1st, 3rd and 24th Virginia regiments reached again the green fields of Virginia.
The 1st Virginia Infantry numbered about 175, rank and file, at Gettysburg, July 3, 1863.
The officers present, as far as can be remembered, were: Lewis B. Williams, Colonel; Frank H. Langley, Major; Company B--Captain T. Herbert Davis, Lieutenant Logan S. Robins, Lieutenant J. A. Payne and about twenty-five men; Company C--Captain James Hallihan, Lieutenant John E. Dooley and about twenty men; Company D--Captain George F. Norton, Lieutenants E. P. Reeve, W. H. Keiningham, Adolphus Blair and about forty men; Company G--Captain Eldridge Morris, Lieutenants W. T. Woody, L. R. Shell and about thirty men; Company H--Captain A. J. Watkins, Lieutenants E. W. Martin, P. C. Cabell and about thirty men; Company I--Captain B. F. Howard, Lieutenants W. A. Caho, H. C. Ballow and about twenty-five men.
As far as we could we have made out a list of the killed, wounded and missing which is, however, not complete, as many recruits had been recently added to the regiment, and it was, therefore, impossible to give all the names in the long list of casualties. This refers especially to Company C, which was at that time mostly filled up with recruits.
OFFICERS KILLED AND DIED FROM WOUNDS.
Colonel Lewis B. Williams, Captain James Hallihan, Company C; Lieutenant W. A. Caho, Company I.
Company B--Fendall Franklin; Company C--James Thomas; Company D--D. S. Edwards, Willie Mitchell, J. W. Freeman, M. J. Wingfield; Company G--W. F. Miller; Company L--Corporal L.0. Ellett, E. J. Griffin, Edward Taliaferro, H. McLaughlin.; Company H-- Sergeant C. P. Hansford, Corporal Richard Chaddick, W. J. Vaughan, Flowers, Nuckols, St. Clair, John Paine, M. Brestrahan, W. S. Waddill.--Total, twenty-three.
WOUNDED-Those marked * were left in enemy's hands : Field and Staff--Major F. H. Langley, Sergeant-Major J. R. Polak, Color-Sergeant William Lawson.* Company B--Captain T. Herbert Davis,* Lieutenant J. A. Payne, Corporal W. J. Carter,* Corporal John Q. Figg,* Privates George R. Heath,* James Stagg,* Joseph Daniel,* H. L. Specard, R. H. Street, W. J. Mallory; prisoner, E. Goetze. Company C--Lieutenant John E. Dooley, Sergeant Pat Woods. Company D--Captain G. F. Norton, Lieutenant E. P. Reeve, Lieutenant William H. Keiningham,* Lieutenant A. Blair, Sergeant J. M. Finn,* Corporal G. E. Craig, Corporal C. T. Loehr Privates James B. Angle, William J. Armstrong, 1. F. Wheely, George W. Johnson,* Joseph C. Keiningham,* T. S. Morton,* E. Priddy,* L. R. Wingfield,* S. L. Wingfield, C. M. Sublett; prisoners, Sergeant J. H. Kepler, Private N. W. Bowe. Company G--Captain E. Morris, Lieutenant W. T. Woody, Sergeant Thomas W. Hay,* Corporal John Allen, Sergeant Thomas H. Durham,* Privates James Farrar, H. C. Fergusson* C. W. Gentry, B. H. Hord, W. T. Kendrick, C. A. Redford, T. S. Rogers, A. Jeff Vaughan, Robert R. Walthall, William H. Martin, Sergeant William H. Dean:, prisoners, Sergeant George W. Ball, Privates J. Rosser Atkisson, B. F. Ashby and A. Haskins. Company H--Captain A. J. Watkins, Lieutenant E. W. Martin, P. C. Cabell, Sergeant T. R. Martin, Corporal R. N. Dunn, W. H. Duerson, Privates W. B. Mosby,* J. H. Daniel, W. N. Anderson,* Sol. Banks,* R. E. Dignun,* F. Faison,* E. Fizer,* W. R. Kilby,* Thomas Maring, J. J. Sinnott, S. Smith, W. C. Hite;* prisoners, Privates Mat. Lloyd and Robert Lloyd. Company I--Sergeant W. F. Terry, Corporal C. L. Parker,* Corporal J. T. Ayres,* Corporal T. E. Traylor, Privates R. 0. Meredith,* G. W. Shumaker,* S. S. Neal,* C. A. Wilkes* and C. H. Chappell,* Sergeants John T. Crew, E. C. Goodson, and W. T. White, and Privates S. Clarke and W. C. Taliaferro.
Killed and died of wounds, twenty-three; wounded and prisoners, eighty-seven; prisoners and wounded left with enemy, marked *forty seven.
From all information obtainable it may be stated that the First Virginia Regiment lost in killed, wounded and prisoners, not less than 125 men out of about 160 that went into the charge.
Pickett's men could have gone into battle on the previous evening, when they reached Gettysburg. They were in fine condition. The march from Chambersburg did not fatigue them at all. Anyone who will visit Gettysburg battlefield will see the truth of these views. The writer calls to memory that just before the artillery opened he filled his canteen from a well near which one of our batteries was posted. In talking with the men of the contemplated charge, and, having the position pointed out to him, he remarked on his return to the line, "He would not give twenty-five cents for his life if the charge was made."
He further recalls that one of the comrades, M. J. Wingfield, called "Monk," turned to him when about half way across the field, saying, "Where are our reinforcements?" On looking around nothing was in sight, except the three brigades of Pickett about 300 yards in rear of our skirmish line and now subject to a storm of shells, tearing great gaps into the lines. The writer then replied, "Monk, I don't see any," on which he replied, "We are going to be whipped, see if we don't." Alas, for the poor fellow, these were his last words, for a bullet ended his life only a few minutes afterward.
The story here told is but a record of the excellence of all of the fifteen regiments of Pickett's division that charged on that historic day.


Walking disgrace Aaron Schlossberg unleashed his racist poison on the world recently, publicly whiplashing and threatening employees of a Manhattan eatery for speaking Spanish. Today, the world received an important reminder that karma is real, with Schlossberg suffering for his actions in every possible way. Professionally, personally, seriously, public opinion and it may cost him legally… it's coming from all directions, it will continue and he deserves it.
A mariachi band has performed songs including "La Cucaracha" (the roach) during a protest in front of the apartment of racist lawyer Aaron Schlossberg, caught on video ranting against Spanish-speaking workers.
The band stood shoulder-to-shoulder facing the Upper West Side condo. They were joined by a group of close to 1,000 people who collectively sang along with the mariachis and sounded off against the hate filled lawyer. It was the ultimate act of trolling, and his neighbors did not seem to mind a bit.
Chased down the street by the tabloids and he cowered under an umbrella to cover his face, while he dialed someone for help, his first words were; "help"! , a very different tone form his bravado hate filled video.
Thousands of one-star reviews materialized on his Manhattan law firm's Yelp page.
His landlord terminated his lease and he was evicted from his office.
He skipped out on a Friday court session with a client rather than face the media.


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About The Same: No More Marching on Memorial Day?
No More Marching on Memorial Day?
Memorial Day has long been my favorite U.S. holiday. Sure, the 4th of July has more flash to it (literally and figuratively), and yes, it's our nation's birthday, so there's that. Back in my school days, Labor Day was always fun because it was the last hurrah before the school year started, and these days it kind of kicks off the countdown to the winter holidays. But Memorial Day is its own level of special, not least of which is because it's intended to honor those veterans who have served our country, which is why I'm devastated at the absolute lack of Memorial Day parades here in the land of the A.T.L.
Let's talk about some of the great aspects of Memorial Day. First, whether or not you acknowledge its raison d'être, Memorial Day kicks off summer. You have to admit that no matter the weather after Memorial Day, and no matter the true date that summer begins (June 21 this year, for those of you who are blissfully unaware of this), your mindset changes after Memorial Day to a more carefree, if-I'm-not-currently-on-vacation-at-least-I'll-take-more-time-to-daydream-about-vacation setting.
Also, Memorial Day affects fashion. We are allowed to wear white pants after Memorial Day as well as white shoes without being fashion heathens. I dig the white pants and admit that I wear them outside of the ascribed "appropriate time frame." I am not, however, a fan of the white shoes unless they're sneakers; perhaps they should be banned altogether.
Memorial Day encourages exercise and togetherness. Think about it. Most pools and beaches open on Memorial Day weekend. Therefore, Memorial Day weekend opens up more opportunities for kids and families to get outside into the fresh air and to play around and to spend time together. It's a time for kids to learn to swim and then to practice and practice and practice even though they think they're just playing and playing and playing.
Finally, and most importantly, Memorial Day is a time to remember those who fought for and continue to fight for our country. Whatever your politics, it's a day to put those aside and simply to honor the men and women who felt and feel it their duty to put their lives on the line in support of our nation, our government and, well, us.
And this is why I'm so disturbed by the fact that I can't find a single Memorial Day parade within a decent radius of my home (there's one in Dacula, but that's a hike and a half from my town). I grew up in the beautiful New England town of Fairfield, Connecticut, where on Memorial Day we held THE parade of the year. The middle school and high school bands marched, as did groups like Girl Scout and Boy Scout troops, the Rotary Club, Little League Teams and, of course, the American Legion. There were walking groups and clowns and floats and fire trucks.* The parade was festive and joyous, a time for the whole town (and it's not a small town) to come together and celebrate. The parade still happens there every year – in fact, they just passed an ordinance requiring people to stop reserving spots along the route (which people apparently did as much as a week in advance) – and it's one of the things I miss the most about my home town. This parade was what initiated my love of a day that has grown in my heart as I've aged and have learned to appreciate the day's origin and meaning.
The fact that a Memorial Day parade celebrates the day is perhaps what's driving this move away from parades. Maybe people believe that unless a Memorial Day ceremony is solemn, serious and entirely focused on gravity, it can't possibly honor the veterans appropriately. I guess I can respect that. But I can't get behind it. I liked Fairfield's Memorial Day parade because it allowed all of us – young and old – to take part and honor our veterans in our own way and at our own level. Let's face it, most kids just don't have the capacity to consider the meaning of Memorial Day quite the way we adults do. But if we give them a way to participate that's meaningful to them, which often means incorporating fun and joy, there's more of a chance they'll continue to anticipate Memorial Day with eager awe each year. Their understanding of the seriousness will grow and evolve as they do, don't worry.
And then there's my own crazy perspective: I want to celebrate (there's that word again) the lives and contributions of these men and women, not just mourn them and the challenges they endured and continue to endure. I want to smile and dance and rejoice in the fact that people like these exist who bring such honor to our country and who look out for all of us. Do I mourn their sacrifices and struggles? Yes, I do. Do I think every Memorial Day event should include a period of serious and somber remembrance? Absolutely. But does celebration distract from the honor and meaning of the day? To that, I heartily disagree.


text:
Derogatoriness of Being a Republican at Latin
Blaike Young Staff Writer Now more than ever, and maybe just because I'm finally old enough to really understand what's going on this election year, I really feel election buzz and debate in the air. In the 5 minute passing periods and in conversations in classrooms before the clock has hit starting time, there is always some mention of politics, of Romney and Obama, and whose policies are better or worse. Even the service fair this year had people debating, and sometimes judging, on who went in what room. Intentional or not, they put Republicans for Victory on the right side, and Obama for the Win on the left side of the 2 rooms next door to each other. Just waiting outside for the next 10-minute session to start caused quite a stir about personal political beliefs. While the room on the right side often pulled in a large crowd, overwhelming belief at Latin tends to lean to the left. Before this year I had some sort of concept of where I fell on the spectrum of belief. I knew which policies, I believed in and which I didn't, and often my beliefs didn't fall in just one side, but both. I believed some things from the Democratic side and some things from the Republican side, and so I was a self proclaimed Independent. This was part of the reason I signed up to take Honors Politics 2012. Not only did I really want to hone in on what I specifically believe, but also I wanted to educate myself about politics, and about an election that for the first time, will probably affect me. One of the first things Mr. Greer assigned the class to do was to take a typology quiz online. This short quiz, offering very black and white answers, was surprisingly spot on with my beliefs. I got Libertarian. This group is somewhere in the middle, but leans to the right. Most of the other people in my class were given typology groups that either leaned to the left, or were as far left as you could get. There were only 2 or 3 others in my class who associated themselves largely with the Republican side. I realized as I continued on with the class that my standpoint on the economy was strongly Republican. I still held some beliefs that were on the left side, but they weren't my priority views. This election really is about priorities. Truth is, no candidate will ever be perfect and no candidate will truly represent every single thing you believe as an individual. So you are forced to choose a side where the beliefs you hold most important, line up with the candidate's. This is where it gets a little controversial. My priority this election is the economy. I could talk all day about why, but that's a separate topic. However, when talking to a group of people at Latin, I often find that as a female, me saying my priority isn't women's issues can create confusion, and sometimes even anger. Obviously as a female, I do not want to go back to the days of severe inequality, where I would have no opportunities to vote and no opportunities at all in the workplace. I think the media has taken conservative view and pushed way farther than reality. Do I think that if Romney gets elected that women will be taken back to the place they stood 50 years ago? No, I do not. First of all, the amount of uprising that will occur if such legislation is presented is enough alone to prevent us from going back in time. Second of all, do I believe Romney is in any way against women? No, I do not. I once again can go on a tangent about how campaign finance is really driving party polarization, and that's why Romney is forced to say things sometimes with an anti-woman connotation, but I think if you really thought about it, you could figure it out on your own. The reality is, is that candidates say a bunch of things they don't really believe because they have to do so to even make it through the primary. This is the nature of American politics. Latin has an extremely educated group of people, but sometimes I find that many don't do enough research. Looking at one side of an argument is not enough to educate you about the opposite side. It's easy to be stubborn, to decide that you have your beliefs, and you don't want to change them because you already know everything that you could possibly know. It's totally fine to have strong beliefs, and it's a good thing to have them, but I ask you to be open to others as well. I do often meet derogatory looks when I say that I would probably associate myself more with the Republican side than the Democratic side. I often get looks from my female classmates who don't understand my priorities this election or how I could side with someone the media portrays as anti-women. Taking the politics class has solidified my ideas, but that was after learning significantly about both sides. Being a Republican does not mean that you are totally against everything Democratic. Being a Democrat does not mean that you can't agree occasionally with Republicans. Just because the parties have polarized, does not mean we have to.]]>
efinch • Sep 18, 2012 at 8:43 pm
Awesome article Blaike. You can tell you really have a passion for politics
https://readtheforum.org/1877/op/derogatoriness-of-being-a-republican-at-latin/#comment-459


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