text:
Sticky Notes is a desktop notes application included in Windows 7, Windows 8, and Windows 10. The app loads quickly and enables users to quickly take notes using post-it note–like windows on their desktop.

Sticky Notes originated in Windows XP Tablet Edition in 2002 and was included with Windows Vista as a gadget for the Windows Sidebar. According to Microsoft, there were eight million monthly Sticky Notes users as of April 2016. It's built in Outlook.com and Microsoft Teams.

Development
The original Sticky Notes was a gadget included with Windows Vista. Gadgets were continued in Windows 7, though Sticky Notes itself became a standalone app built on the Win32 platform, that could still open at startup. This version did not directly support pen input. The default color is yellow, but five other colors are offered. Sticky Notes have jumplists and a taskbar preview, which shows the notes in a stack. Sticky Notes are automatically saved. This version was reused in Windows 8 and the initial releases of Windows 10.

In the Windows 10 Anniversary Update, released in 2016, a new version of Sticky Notes built on the Universal Windows Platform was introduced. It can be launched as a standalone app or part of the Windows Ink workspace. The latter method causes the space behind the notes to become blurred. The new version directly accepts pen input and can recognize words and letters in handwritten text, basic text formatting, pictures. It is designed to be stick to the desktop or move around. The new Sticky Notes provides stock information when a ticker is typed or written, and it provides flight info when a flight number is typed or written. It has Cortana integration and can create reminders from notes that include a date. Unlike the Windows 7 version, this version's taskbar preview shows a stock image rather than the notes a user has created. It originally did not have a jump list, but that was added back in version 1.6.2 on February 6, 2017.

System Requirements (UWP app)

Cross-platform
Sticky Notes can sync notes across multiple devices, not just to Windows 10 devices, but also to iOS and Android devices running Microsoft OneNote and Outlook for Windows. A web client to edit sticky notes is also available on the OneNote website, at the obscure onenote.com/stickynotes location.

On Android devices, Microsoft Launcher can show sticky notes synced with a local instance of the OneNote app.

References

External links
 Microsoft Sticky Notes on Windows Store

Universal Windows Platform apps
Windows 7
Windows 10
Windows components


text:
The Ksp 58 (Swedish: Kulspruta 58) is a Swedish variant of the Belgian FN MAG general purpose machine gun that is currently being manufactured by the Swedish company Carl Gustafs Stads Gevärsfaktori and was adopted by the Swedish Armed Forces in 1958.

History
After 1945, many countries were trying to produce their own machine guns based on the MG 42 design. In the early 1950s, Belgian arms manufacturer FN Herstal succeeded in developing a general-purpose machine gun called the MAG. The initial Ksp 58A version used by Sweden was chambered for 6.5×55mm, while the B and later models were chambered for 7.62×51mm NATO.

Users
: Used by the Swedish Armed Forces since 1958 to the present.

 : Ksp 58B version in use. Was first received from Sweden in 1990's as military aid.

 : Ksp 58B version in use. Was first received from Sweden in 1990's as military aid.

 : Ksp 58B version in use. Was first received from Sweden in 1990's as military aid.

 :Ksp 58B version in use. Received as military aid

References

Machine guns of Sweden

redpajama_set_name: RedPajamaWikipedia


Image Title: Duvet Covers Bedding Ll Bean Comforter Most With Comfortable Cover Idea 17. Post Title: Most Comfortable Duvet Cover. Filename: duvet-covers-bedding-ll-bean-comforter-most-with-comfortable-cover-idea-17.jpg. Image Dimension: 728 x 728 pixels. Images Format: jpg/jpeg. Publisher/Author: Tremaine Kiehn. Uploaded Date: Saturday - June 23rd. 2018 16:15:31 PM. Category: Architecture. Image Source: freshome.com. Comforter Cover Duvet Ding S Remodel With Most Comfortable Idea Feather Decorations Bean 19. Prepare Covers Within Sheets 14. 17. Bedding Grey The Ll Medium Decor Throughout Duvets Linen Regarding Ems Regard Inspirations Sets 2. Material To And Best Pillows Peachy Size Designs 12. 6. Ideas 10. Discount 7. Insert Men Luxury Choosing In Inside 11. Usa 0.


text:
Q: Advice Required response from EMV card? I am trying to communicate with a SAM which apparently is implemented according to EMV specifications. The developer does only refer me to EMV books whenever I ask them a question. After limping through the EMV card and terminal specifications, I finally managed to send commands one after the other, and get to  the GENERATE CRYPTOGRAM command with CDOL 1. My command looks like this (CDOL1):
80AE40001D0000000000010000000000000364000000000003640B300E001234567800

And here's the card's response:
802B08003280DBD8B5E81B4AF5065B0E038420000000000000000000000F000000000000000000000000000000

Now, am I correctly reading it? ADVICE REQUIRED bit to 1, correct? If that is the case, what happens now? This SAM is supposed to work off-line with only a PIN number and no online connectivity requirements.

A: Your gen ac command having p1 = 40 , here  terminal is requesting an Transaction Certificate (offline transaction)
Your response is showing , card is returning with using format 1 - premitive data object with tag equal to 80.
Here response containing :-
1 - Cryptogram Information Data ( 1 byte)
08
2 - Application transaction counter ( 2 byte)
0032
3 - Application cryptogram ( 8 byte)
80DBD8B5E81B4AF5
4 - Issuer Application data ( 32 byte)
065B0E038420000000000000000000000F000000000000000000000000000000
the CID byte indicate which type of cryptogram is returned by the card and here value is 08 - Transaction  declined
Actually The CID reveal what kind of Application Cryptogram is returned. It can optionally contain an advice message if the transaction will rejected.
for more about advice message , how it process between card and terminal, look EMV book 2 and 3 (6.3.7 -card action analysis)
this is what your command response is indicating. hope it helps, if you have any other query , please share.

redpajama_set_name: RedPajamaStackExchange


text:
""" ESC/POS Exceptions classes """

import os

class Error(Exception):
    """ Base class for ESC/POS errors """
    def __init__(self, msg, status=None):
        Exception.__init__(self)
        self.msg = msg
        self.resultcode = 1
        if status is not None:
            self.resultcode = status

    def __str__(self):
        return self.msg

# Result/Exit codes
# 0  = success
# 10 = No Barcode type defined
# 20 = Barcode size values are out of range
# 30 = Barcode text not supplied
# 40 = Image height is too large
# 50 = No string supplied to be printed
# 60 = Invalid pin to send Cash Drawer pulse
# 70 = Invalid number of tab positions
# 80 = Invalid char code

class BarcodeTypeError(Error):
    def __init__(self, msg=""):
        Error.__init__(self, msg)
        self.msg = msg
        self.resultcode = 10

    def __str__(self):
        return "No Barcode type is defined"

class BarcodeSizeError(Error):
    def __init__(self, msg=""):
        Error.__init__(self, msg)
        self.msg = msg
        self.resultcode = 20

    def __str__(self):
        return "Barcode size is out of range"

class BarcodeCodeError(Error):
    def __init__(self, msg=""):
        Error.__init__(self, msg)
        self.msg = msg
        self.resultcode = 30

    def __str__(self):
        return "Code was not supplied"

class ImageSizeError(Error):
    def __init__(self, msg=""):
        Error.__init__(self, msg)
        self.msg = msg
        self.resultcode = 40

    def __str__(self):
        return "Image height is longer than 255px and can't be printed"

class TextError(Error):
    def __init__(self, msg=""):
        Error.__init__(self, msg)
        self.msg = msg
        self.resultcode = 50

    def __str__(self):
        return "Text string must be supplied to the text() method"

class CashDrawerError(Error):
    def __init__(self, msg=""):
        Error.__init__(self, msg)
        self.msg = msg
        self.resultcode = 60

    def __str__(self):
        return "Valid pin must be set to send pulse"

class TabError(Error):
    def __init__(self, msg=""):
        Error.__init__(self, msg)
        self.msg = msg
        self.resultcode = 70

    def __str__(self):
        return "Valid tab positions must be in the range 0 to 16"

class CharCodeError(Error):
    def __init__(self, msg=""):
        Error.__init__(self, msg)
        self.msg = msg
        self.resultcode = 70

    def __str__(self):
        return "Valid char code must be set"

redpajama_set_name: RedPajamaGithub


text:
Q: Is there alternative to array in field in MYSQL? I have 2 tables namely userinfo and newsinfo. Each user can add/remove any news feed as they wish. So at any time, news will only be delivered to those who subscribed to each news providers only. Users in table userinfo and news providers in table newsinfo will be added or removed as time goes by. I'm using php as the front-end.
Table: userinfo
+---------------+-----------------+--------------------+
|    index      |      name       |    channel_list    |
+---------------+-----------------+--------------------+
|      0        |       aaaa      |     0,1            |
|      1        |       bbbb      |     0,1,2,3        |
|      2        |       cccc      |     3,4            |
+---------------+-----------------+--------------------+

Table: newsinfo
+---------------+-----------------+
|    channel    |     provider    |
+---------------+-----------------+
|      0        |        cnn      |
|      1        |        bbc      |
|      2        |        fox      |
|      3        |        rtl      |
+---------------+-----------------+

Currently what I did was to use array in userinfo.channel_list to store subscribed news channel.
Is there any better way to achieve this without using array in field?

A: create a many-to-many relation with the following additional table (userinfo_newsinfo):
+-------+------+  +---------+-------------+  +-------------------+
| index | name |  | channel | provider    |  | userinfo_newsinfo |
+-------+------+  +---------+-------------+  +--------+----------+
|   0   | aaaa |  |   0     |    cnn      |  | index  |  channel |
|   1   | bbbb |  |   1     |    bbc      |  +--------+----------+
|   2   | cccc |  |   2     |    fox      |  |  0     |    0     |
+-------+------+  |   3     |    rtl      |  |  0     |    1     |
                  +---------+-------------+  |  1     |    0     |
                                             |  1     |    1     |
                                             |  1     |    2     |
                                             |  1     |    3     |
                                             |  2     |    3     |
                                             |  2     |    4     |
                                             +--------+----------+

Now you can remove the column channel_list on table userinfo and translate it to the new table.

Note: A column like channel_list should not be used! Use normalization to check and improve your database structure. The new table userinfo_newsinfo improves the database structure by considering the normalization.

To create this new table you can use the following SQL:
CREATE TABLE userinfo_newsinfo (
    `index` INT NOT NULL,
    `channel` INT NOT NULL,
    FOREIGN KEY (`index`) REFERENCES userinfo(`index`),
    FOREIGN KEY (`channel`) REFERENCES newsinfo(`channel`)
);

To select all channels of a user you can do the following query:
SELECT newsinfo.provider
FROM userinfo u
    INNER JOIN userinfo_newsinfo un ON u.index = un.index
    INNER JOIN newsinfo n ON n.channel = un.channel
WHERE u.index = 0


Opening game for Ireland at 2015 Homeless World Cup. Ireland V Ukraine.
The Republic of Ireland had a famous movie star supporter on pitch one this afternoon for their first game of the Homeless World Cup against Ukraine. Hollywood actor Colin Farrell joined the Irish team on the field for their national anthem and was pitch side cheering them on throughout.
Ukraine opened the scoring but the Irish quickly equalised. Captain Joseph Thompson finished a well-worked move making the score 1-1. Ukraine scored a second on six minutes, and got their third just before the break with seconds left. At halftime, the score was 3-1.
Ireland continued to press but could not get back in the game. The Ukraine team managed to take advantage of their chances and at the final whistle, the game was won 6-1 by the men in yellow.


text:
\section{Introduction.}

Excitons play a prominent role in the optical properties of atomically thin transition metal dichalcogenide (TMDC) semiconductors due to electron-hole Coulomb interaction
being strongly enhanced by carrier confinement and reduced dielectric screening.
This suggests an interpretation of experimental results as well as theoretical prediction
in terms of excitons rather than unbound
electrons and holes. \cite{zhang_absorption_2014,berghauser_analytical_2014,sun_observation_2014,schmidt_ultrafast_2016,selig_excitonic_2016} On the other hand, it is well-known that at a certain
excitation density of electron-hole pairs the Mott transition is observed. \cite{shah_investigation_1977,manzke_mott_2012,chernikov_electrical_2015}
Here a phase where excitons and unbound carriers can coexist evolves into a fully ionized electron-hole plasma, which shows the significance of plasma effects to the
physics of excited semiconductors.

Since excitons are more or less neutral compound particles, many-particle renormalization and screening effects in an exciton gas are very different from those in a plasma of
unbound electrons and holes, which we refer to in the following as quasi-free carriers. For this reason it is highly desirable to quantify the relative importance of excitonic
and plasma effects over a wide range of electron-hole excitation densities and for various material and externally controllable parameters.
It has already been suggested to tune
exciton binding energies by electrical doping \cite{chernikov_electrical_2015} and some effort has been devoted to study the influence of dielectric screening
on excitons in TMDC semiconductors. \cite{lin_dielectric_2014,ugeda_giant_2014,latini_excitons_2015,trolle_model_2017}

In the past, a very powerful scheme has been developed to theoretically describe the so-called ionization equilibrium between the formation of bound particles and
their dissociation into quasi-free particles \cite{kremp_equation_1984,kremp_ladder_1984,zimmermann_mass_1985,kremp_quantum_1993, kremp_quantum_2005, semkat_ionization_2009},
with applications to atomic plasmas and highly excited semiconductors.
In general, a dominance of free-carrier plasma over excitons is expected at very low excitation density due to entropy ionization of excitons \cite{mock_entropy_1978} and above the so-called Mott density due to
pressure ionization of excitons. The fraction of excitons reaches a maximum at elevated densities still below the Mott transition and can assume values of practically $100\%$ in TMDCs, though being sensitive to
various externally controllable parameters.
The scheme relies on the assumption of a quasi-equilibrium between plasma and excitons being established before electron-hole recombination sets in.
Ultrafast equilibration is facilitated by efficient carrier-carrier \cite{steinhoff_nonequilibrium_2016} and carrier-phonon interaction \cite{selig_excitonic_2016}
as well as exciton formation \cite{ceballos_exciton_2016,steinleitner_direct_2017} after optical excitation, see Ref.~\citenum{koch_semiconductor_2006} for a review.

Experimental verification of the ionization equilibrium has been achieved in GaAs quantum wells using THz spectroscopy to probe transitions between 1s- and 2p-exciton states. \cite{kaindl_ultrafast_2003,koch_semiconductor_2006}
A similar technique in the mid-infrared range has been applied recently to monolayer WSe$_2$. \cite{steinleitner_direct_2017}
Alternatively, the fractions of excitons and plasma can be determined from their contributions to photoluminescence (PL) spectra \cite{chatterjee_excitonic_2004}
in combination with additional PL simulations.
As we suggest below, other ways to quantify the degree of exciton formation are angular-resolved photoemission spectroscopy (ARPES) and
scanning tunneling spectroscopy (STS).

In this paper, we combine calculations of material-realistic band structures and Coulomb matrix elements of the monolayer TMDC materials MX$_2$ (M$=$W,Mo and X$=$S,Se) with the state-of-the-art theory of ionization equilibrium, which we briefly introduce in the following section before discussing the results in detail. The theory is based on GW- and T-matrix self-energies describing the excited carriers and the effect of frequency-dependent screening. We also include excitonic screening that we find to be relevant and that is usually not taken into account. On these grounds, we study the influence of experimental and device-relevant parameters like dielectric screening, temperature and carrier doping on the ionization equilibrium and the Mott density.

\section{Spectral Functions and Exciton Satellites.}

To examine the equilibrium properties of excited carriers in TMDCs, we follow the approach developed in
Refs.~\citenum{kremp_equation_1984,kremp_ladder_1984,zimmermann_mass_1985,kremp_quantum_1993} and reviewed in Ref.~\citenum{semkat_ionization_2009}.
We use the quantum-statistical expression for the carrier density $n_a$ of the species $a$, which can be electrons or holes, as a function of temperature $T$
and chemical potential $\mu_a$ as a starting point:
\begin{equation}
  n_a(\mu_a,T)=\frac{i\hbar}{\mathcal{A}}\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\sum_{\mathbf{k}\sigma}f^a(\omega)A_{\mathbf{k}\sigma}^a(\omega)
     ~.
    \label{eq:carr_dens}
\end{equation}
$f^a(\omega)$ denotes the Fermi distribution function depending on $\mu_a$ and $T$, $\mathcal{A}$ is the crystal area and
$A_{\mathbf{k}\sigma}^a(\omega)=2i\textrm{Im}G^{\textrm{ret},a}_{\mathbf{k}\sigma}(\omega)$ is the spectral function of the single-particle
state $\ket{\mathbf{k}\sigma a}$ related to the retarded single-particle Green's function
\begin{equation}
  G^{\textrm{ret},a}_{\mathbf{k}\sigma}(\omega)=\frac{1}{\hbar\omega-\varepsilon_{\mathbf{k}\sigma}^a-\Sigma_{\mathbf{k}\sigma}^{\textrm{ret},a}(\omega)}
     ~.
    \label{eq:G_ret}
\end{equation}
The self-energy $\Sigma_{\mathbf{k}\sigma}^{\textrm{ret},a}(\omega)$ accounts for many-particle effects giving rise to renormalizations of
the single-particle band structure $\varepsilon_{\mathbf{k}\sigma}^a$ as well as contributions of bound states. For a given self-energy,
the inversion of Eq.~(\ref{eq:carr_dens}) yields the chemical potential $\mu_a(n_a,T)$ for each species and therefore any thermodynamic property
of the system in the grand canonical description.
\begin{figure}[h!t]
\begin{center}
\includegraphics[width=1.\columnwidth]{./figure_1_new2.eps}
\caption{
\textbf{Spectral properties of excited carriers in monolayer WS$_2$.}
\textbf{(a)} Band structure of freestanding WS$_2$ as obtained
from a G$_0$W$_0$ calculation at zero excitation density.
\textbf{(b)} Bound-state spectrum for WS$_2$ on SiO$_2$ substrate relative to the quasi-particle gap at zero excitation density
over the modulus of total exciton momentum $Q$ as obtained from a Bethe-Salpeter equation, see Eq.~(\ref{eq:bse}) in the Methods section.
Excitons involving the $\Gamma$, $K'$ and $\Sigma'$ valleys are included but not marked explicitely.
\textbf{(c)} Electron spectral function in extended quasi-particle approximation at $T=300$ K and excitation density
$n_a=3.2\times10^{12}$~cm$^{-2}$ showing resonances from bound and quasi-free particles
in momentum-resolved representation on a logarithmic scale and as normalized local density of states (LDOS).
Energies are measured relative to the quasi-particle band gap at zero excitation density.
A phenomenological Gaussian broadening of $10$ meV (HWHM) is applied.
\textbf{(d)} Hole spectral function in extended quasi-particle approximation.
\textbf{(e)} Electron spectral function as in (c) for spin-down electrons at the $K$-point.
The vertical line marks the electron chemical potential.
\textbf{(f)} Hole spectral function as in (d) for spin-up holes at the $K$-point.
}
\label{fig:spectralf}
\end{center}
\end{figure}
\begin{figure*}[h!t]
\begin{center}
\includegraphics[width=\textwidth]{./figure_4.eps}
\caption{\textbf{Degree of ionization as a function of excitation density} $n_a=n_{\textrm{free}}^{a}+n_X$, where $a$ denotes electrons or holes. In general, a fully ionized
plasma ($\alpha_a=1$) is found above the Mott density, excitons dominate ($\alpha_a\ll1$) below the Mott density and ionization appears again at low densities.
\textbf{(a)} Comparison of different TMDC materials on SiO$_2$ substrate.
\textbf{(b)} Comparison of WS$_2$ in different dielectric environments with dielectric constant $\varepsilon$ of bottom/top environment.
\textbf{(c)} Comparison of WS$_2$ on SiO$_2$ substrate for different temperatures.
\textbf{(d)} Comparison of MoS$_2$ with different lattice constants on SiO$_2$ substrate. The unstrained layer corresponds to $a=3.18$~\AA\,
while tensile biaxial strain is simulated by $a=3.20$~\AA\,.
\textbf{(e)} Fraction of ionized electrons for different levels of hole doping in WS$_2$ on SiO$_2$ substrate.
\textbf{(f)} Fraction of ionized holes for different levels of hole doping in WS$_2$ on SiO$_2$ substrate.}
\label{fig:ionization}
\end{center}
\end{figure*}
As we describe in detail in the Methods section, by using a T-matrix self-energy in screened ladder approximation and assuming small quasi-particle damping,
we obtain a spectral function $A^a(\omega)$ in the so-called extended quasi-particle approximation. It exhibits poles for quasi-free and bound carriers
as shown in Fig.~\ref{fig:spectralf}.
From the multiple valleys in the single-particle band structure of electrons and holes (Fig.~\ref{fig:spectralf}(a)), a rich spectrum of bound states emerges (Fig.~\ref{fig:spectralf}(b)),
that contains a variety of dark excitons with large total momentum $Q$ besides the bright $K$-valley excitons commonly referred to as A and B. The dark excitons, though playing a minor role in optical
experiments, are essential to the description of the ionization equilibrium.
Various bound states are reflected in the low-energy satellites of the single-particle spectral function.
This shows that excitonic contributions are expected to be observed in experiments that are sensitive to these spectral properties.
In ARPES \cite{damascelli_angle-resolved_2003},
momentum-resolved images of the electron spectral function comparable to Fig.~\ref{fig:spectralf}(c) are
obtained, weighted with Fermi distribution functions that are defined by the chemical potential $\mu_e$ and temperature $T$. For a fixed quasi-momentum state as shown in
Fig.~\ref{fig:spectralf}(e), this is typically referred to as energy distribution curve.
On the other hand, STS \cite{fischer_scanning_2007} probes the local density of states (LDOS) and thus momentum-averaged spectral functions of electrons and holes, which are
displayed in Figs.~\ref{fig:spectralf}(c) and (d).
We therefore propose to use these experimental techniques to spectrally distinguish between excitons and quasi-free carriers. This opens the possibility to
quantify the degree of exciton ionization and verify the results we present in this paper.

\section{Degree of Ionization and Mott Transition.}

According to Eq.~(\ref{eq:carr_dens}), the spectral function can be used to separate the total electron and hole density ($a=e,h$),
\begin{equation}
\begin{split}
  n_a=n_{\textrm{free}}^a+n_X
     \,,
    \label{eq:density_final_short}
\end{split}
\end{equation}
into contributions from quasi-free carriers and from carriers bound as excitons, where the excitons are approximately treated as bosons.
Hence the properties of the excited semiconductor at a given temperature and excitation density are defined by the density of electrons $n_e$,
the density of holes $n_h$ and the density of excitons $n_X$.
A certain degree of ionization of the excited carriers
\begin{equation}
\alpha_a=\frac{n_{\textrm{free}}^{a}}{n_a}
    \label{eq:ionization}
\end{equation}
will be established that is determined by the ionization equilibrium between electrons, holes and excitons. While for optical excitation, equal densities
of electrons and holes are generated, we distinguish here between electron and hole ionization
to also include the effect of carrier doping where electron and hole densities are different.

Using single-particle band structures and bound-state spectra, which are determined as discussed in the Methods section, we solve Eq.~(\ref{eq:density_final_short}) numerically
to obtain the degree of ionization $\alpha_a$ in various TMDC materials under different experimental conditions.
The results are collected in Fig.~\ref{fig:ionization} and exhibit the behaviour of ionization degree as a function of excitation density.
There are different regimes of ionization to be observed. At high excitation densities between
$3\times10^{12}$~cm$^{-2}$ and $1\times10^{13}$~cm$^{-2}$, depending on experimental parameters, efficient screening and
many-particle renormalizations lead to a full ionization of excited carriers, which is known as Mott effect. At lower densities around $n_a=1\times10^{12}$~cm$^{-2}$,
excitons dominate the physical properties of TMDCs for the parameters studied here due to the large exciton binding energies and density of states that
is mostly given by dark excitons. Bright excitons with very small momenta that are optically active make up only a tiny fraction of the total exciton density.
As Fig.~\ref{fig:ionization}(b) shows, an efficient tuning knob for the degree of ionization is the
dielectric screening by the environment, which can change over a wide range depending on the experimental situation or device realization in which the TMDC monolayer is the active material.
The reason is the strong impact of dielectric screening on the exciton binding energies.
Typical examples for substrates are Borofloat~($\varepsilon=2$), SiO$_2$~($\varepsilon=3.9$) and sapphire~($\varepsilon=10$).
The dielectric constant of the environment on top of the monolayer is often given by the vacuum value. On the other hand, in devices the TMDC
monolayer is fully encapsulated by dielectric material. As an example we consider a full dielectric environment with $\varepsilon=10$, which might be either sapphire or additional layers of TMDC material
in a vertical heterostructure whose main influence on the excitons is the dielectric screening. \cite{andersen_dielectric_2015} We find that the minimal degree of ionization can be tuned from below $0.1\%$
($99.9\%$ excitons) at weak dielectric screening to about $30\%$ at strong screening, while the Mott density is lowered at the same time by roughly a factor of $3$.
The second important parameter that is relevant to applications of TMDC monolayers is the doping with additional carriers which might be either intrinsic or induced by external electric fields in a capacitor
structure. Here the fractions of ionized electrons and holes, $\alpha_e$ and $\alpha_h$, are discussed separately as the densities of the species are not equal anymore. We consider hole
doping of WS$_2$, but similar results are expected in case of electron doping. Looking at Figs.~\ref{fig:ionization} (e) and (f), we find that even at weak doping the minority
carriers are practically all bound as excitons below the Mott transition. On the other hand, at higher doping levels an increasing fraction of majority carriers exists as quasi-free plasma due to
missing partners for exciton formation.
As a function of minority-carrier density the Mott transition is lowered by roughly the density of doped excess carriers.
From this we conclude that at doping levels above
$10^{13}$~cm$^{-2}$ neither dark nor bright excitons will exist in any case. This is supported by the experimental estimate for doping-induced
ionization at several $10^{13}$~cm$^{-2}$. \cite{chernikov_electrical_2015}
Another crucial parameter is the temperature, see Fig.~\ref{fig:ionization}(c), which can vary in experiments or devices due to heating of the active material under strong optical or electrical pumping. This
effect has been taken into account to explain the observed exciton-to-plasma ratio in monolayer WSe$_2$ in Ref.~\citenum{steinleitner_direct_2017}.
At room temperature and even at elevated temperatures up to $700$ K excitons clearly dominate below the
Mott transition. At the same time, the Mott density slightly increases with temperature due to weaker renormalizations of the quasi-particle gap. It turns out that strain
is no efficient tuning knob as both bright and dark excitons contribute to the ionization equilibrium, although bright excitons are preferred in moderately tensile-strained TMDCs, see the discussion in the Methods
section.
A comparison of different TMDC materials shows that excitons are slightly more important in molybdenum- than in tungsten-based TMDCs due to the larger binding energies, which leads to larger Mott densities.
\begin{figure*}[h!t]
\begin{center}
\includegraphics[width=\textwidth]{./figure_6.eps}
\caption{\textbf{Excitation-density dependence of spectral functions.}
Shown are spectral functions in extended quasi-particle approximation for spin-down electrons \textbf{(a)} and spin-up holes \textbf{(b)} at the $K$-point in WS$_2$ on SiO$_2$ substrate at $T=300$ K.
A phenomenological Gaussian broadening of $10$ meV (HWHM) is applied. Electron energies are measured relative to the quasi-particle band gap at zero excitation density. Hole energies are shown as valence-band energies
to match Fig.~\ref{fig:spectralf}(f).}
\label{fig:spectralf_density}
\end{center}
\end{figure*}

When approaching the Mott density from the low-density side, many-particle renormalizations become increasingly important, cf. Eq.~(\ref{eq:GW_energy}) in the Methods section.
Exchange interaction and efficient screening due to free carriers as well as excitons reduce the quasi-particle band gap and the exciton binding energies.
More and more excitons are ionized, which leads to an increase of efficient free-carrier screening and thereby to a self-amplification of the ionization effect until
all excitons are dissociated into an electron-hole plasma and the degree of ionization becomes $\alpha_a=1$.
Note that $\alpha_a$ includes not only bright but also dark excitons with large total momentum for example between $K$ and $\Sigma$ valleys.
They may have larger binding energies and be slightly more stable against ionization than bright excitons visible in an optical experiment.
Fig.~\ref{fig:spectralf_density} shows an illustration of the Mott effect in terms of the spectral functions in extended quasi-particle approximation, which
contain both exciton and quasi-free-particle signatures. At low excitation densities, the only spectral contribution stems from quasi-free carriers at the band edge.
With increasing density, the quasi-particle peak is shifted to lower energies due to many-particle renormalizations. At the same time, spectral weight is transferred from the quasi-particle to the
bound-state peaks as exciton populations increase, see the explicit expression of the spectral function in Eq.~(\ref{eq:spectral_fct_extended_T_matrix}).
The appearence of several exciton satellites in the hole spectral function is due to different bound states involving electrons either in the $K$- or $\Sigma$-valleys, see Fig.~\ref{fig:spectralf}~(b).
The spectral position of a bound-state peak in the spectral function of carrier $a$
is given by the difference of the corresponding exciton energy $E^{ab}$ and the energy of the second carrier $b$ involved in the bound state.
The bound resonance might therefore be interpreted as an effective ionization energy of the actual carrier $a$ with respect to its energy in the quasi-particle band structure.
This underlines the fact that excitonic signatures are observable in experiments that are sensitive to the single-particle spectral function, such as ARPES and STS. Note that while the amplitudes of
bound-state resonances in the spectral functions are relatively small, observables like the carrier density (\ref{eq:carr_dens}) and the photoemission intensity
involve weighting with a Fermi function that strongly favors the low-energy
resonances over the quasi-free contribution. With increasing excitation density, quasi-particle and excitonic resonances approach until above the Mott density all excitons are ionized and only a quasi-particle peak remains.
Fig.~\ref{fig:E_Gap} shows the reduction of the quasi-particle gap until the Mott transition appears around $n_a=8\times10^{12}$~cm$^{-2}$.
\begin{figure}[h!t]
\begin{center}
\includegraphics[width=1.\columnwidth]{./figure_5_ink.eps}
\caption{\textbf{Ionization equilibrium and quasi-particle band-gap renormalization.} Shown is the band-gap renormalization $\Delta E_{\textrm{Gap}}$ for spin-up carriers at the $K$-point
in WS$_2$ on SiO$_2$ substrate at $T=300$ K as function of excitation density.
The vertical black line marks the Mott transition. The inset shows a schematic of the ionization equilibrium introducing the quasi-particle band gap at zero excitation density $E^0_{\textrm{Gap}}$,
which is conventionally set to zero energy. All quantities including the bound-state energies $E_{\nu}$ and the sum of electron and hole chemical potentials are measured relative to $E^0_{\textrm{Gap}}$.}
\label{fig:E_Gap}
\end{center}
\end{figure}

An alternative picture of the interacting electrons and holes, that is consistent with the extended quasi-particle approximation, is the so-called \textit{chemical picture}
in which excitons are considered as a new particle species besides electrons and holes. \cite{kremp_quantum_2005,semkat_ionization_2009} They are characterized
by a chemical potential
\begin{equation}
\mu_{X,\nu}=\mu_e+\mu_h-E_{\nu}\,,
    \label{eq:gen_MAL}
\end{equation}
with bound-state energies $E_{\nu}$ that are given by the relative motion of electron and hole, and an ideal Bose distribution function.
In the chemical picture, solving Eq.~(\ref{eq:density_final_short}) corresponds to an adaption of the chemical potentials of the different particle species,
namely electrons, holes and excitons, as in a chemical reaction.
These considerations are consistent with the theory based on spectral functions, that
we use to obtain all numerical results presented in this paper. Only for the purpose of illustration, we simplify the theory considering
the nondegenerate case ($f^a(E^a_{\mathbf{k}\sigma})\ll 1$) and a single band-structure valley for electrons and holes each.
Then a Saha equation can be formulated that determines the degree of ionization:
\begin{equation}
\frac{n_X}{n_e n_h}\propto e^{\beta I_{\nu}^{\textrm{eff}}} \,.
    \label{eq:saha}
\end{equation}
In analogy to the usual mass action law, $I_{\nu}^{\textrm{eff}}=\Delta E_{\textrm{Gap}}-E_{\nu}$
can be interpreted as an effective ionization potential of excitons that corresponds to the exciton binding energy, see also the inset in Fig.~\ref{fig:E_Gap}.
It is obvious from Saha's equation, that a large exciton binding energy and low temperature favor the formation of excitons versus the dissociation into an unbound electron-hole plasma.
The ionization potential depends on excitation density as a consequence of the excitation-induced
lowering of the band continuum edge given by $\Delta E_{\textrm{Gap}}$ and the shift of the bound-state energy $E_{\nu}$.
The bound-state shift on the other hand is a net result of band-gap shrinkage, screening of exciton binding energy and Pauli blocking \cite{steinhoff_influence_2014} and is much weaker than
the band-gap shift due to compensation effects.
In the end, the ionization potential is lowered with increasing excitation density until at $I_{\nu}^{\textrm{eff}}=0$
the bound state vanishes and merges with the continuum edge, which is the Mott effect.

A striking observation in Fig.~\ref{fig:ionization} is the degree of ionization approaching unity at low excitation densities, which is somewhat counter-intuitive but can be
understood from a thermodynamical point of view. The potential
that is minimized by the many-particle system is the free energy $F=U-TS$. At low densities and fixed temperature, the entropy $S$ gained by a dissociation of an exciton into two separate particles
overcompensates the reduction of internal energy $U$ by the exciton binding energy $E_B$. Hence the so-called entropy ionization already discussed by Mock et al.~\cite{mock_entropy_1978} is connected
to the huge phase space available for quasi-free carriers in the low-density limit.
We may clarify this using the entropy of an ideal gas with $N$ particles in a volume $V$ as given by the Sackur-Tetrode equation:
\begin{equation}
\begin{split}
  S=N k_B\left[\textrm{ln}\left(\frac{V}{N} c(T)\right) +\frac{5}{2}\right]
     \,,
    \label{eq:entropy_ideal_gas}
\end{split}
\end{equation}
where $c(T)$ is a temperature-dependent parameter. Obviously, the dissociation of an exciton gas ($N$ particles) into a free electron-hole plasma ($2N$ particles) yields the entropy
$\Delta S=N k_B \textrm{ln}\left(n^{-1}\right)$ with $n=N/V$ up to some additive constant. It follows that the critical density $n_{\textrm{crit}}$ below which the free energy is dominated by entropy essentially
scales as $\textrm{exp}\left(-E_B/k_B T\right) $ with temperature.

Although the extended quasi-particle approximation and the chemical picture are very descriptive, we have to be aware of their limitations.
The approach relies on the assumption of a quasi-equilibrium of both types of carriers,
which tends to overestimate the fraction of bound carriers as exciton formation takes a certain time after excitation of electron-hole pairs.
Nevertheless, we expect the approach to give a reasonable quantitative description of the ionization equilibrium, particularly of the trends that can be expected under variation of external
experimental parameters.
A rather fundamental discussion is concerned with the Mott transition as a first-order phase transition between an exciton gas and a fully ionized electron-hole plasma. \cite{kremp_quantum_2005, semkat_ionization_2009}
The phase transition would be connected to an instability of thermodynamic functions that manifests itself in an ambiguity of $\alpha_a$ in a certain region below the Mott density.
Due to excitation-induced broadening of the two-particle states, which is assumed small in our approach, and the shrinkage of the ionization potential towards the Mott transition,
quasi-free and bound carriers cannot really be separated in this density regime.
We avoid this regime as
a more sophisticated theory including full spectral
functions and exciton-exciton interaction would be required. Also, screening in a correlated many-particle system near the Mott transition is an intricate problem \cite{kraeft_quantum_1986}.
However, we observe that taking into account excitonic screening is necessary to obtain meaningful results around the minima of $\alpha_a$ in the exciton-dominated regime.
Otherwise, coming from the low-density side of the ionization curves in Fig.~\ref{fig:ionization}, there would be no mechanism to efficiently break up the excitonic binding
and trigger the transition to an ionized plasma. We discuss the contribution of excitons to screening in the following section.

Another prominent feature of TMDC semiconductors is the formation of trions, which could in principle be included as additional particle species in the spirit of the chemical picture. \cite{kremp_quantum_1993}
In practice, obtaining bound-trion spectra on the same footing as excitons is a very challenging task of its own that is beyond the scope of this paper. Due to the relatively small trion binding energies, we
assume that their influence on our results are negligible.

\section{Excitonic Screening.}

In the spirit of the extended quasi-particle approximation to the spectral function, there are two types of contributions to excited-carrier screening of the Coulomb interaction,
the metal-like free-carrier screening and dipolar screening due to bound excitons.
\begin{figure}[h!t]
\begin{center}
\includegraphics[width=\columnwidth]{./figure_2.eps}
\caption{\textbf{Characterization of excited-carrier screening.}
Shown is the plasmon spectral function given by the imaginary part of the inverse dielectric function including the 2-d-Coulomb singularity $\varepsilon^{-1,\textrm{ret}}_{\mathbf{q}}(\omega)/|\mathbf{q}|$ for momenta
along the contour $\Gamma$-$K$ in WS$_2$ on SiO$_2$ substrate at $T=300$ K. A quasi-particle broadening of $10$ meV is used. The carrier densities are
 \textbf{(a)} $n_{\textrm{free}}=2.7\times10^{10}$ cm$^{-2}$, $n_X=3.1\times10^{12}$ cm$^{-2}$ and \textbf{(b)} $n_{\textrm{free}}=1.8\times10^{13}$ cm$^{-2}$, $n_X=0$ corresponding to
points on the ionization equilibrium curve in Fig.~\ref{fig:ionization} in the exciton-dominated and the plasma-dominated regime, respectively.}
\label{fig:plasmon}
\end{center}
\end{figure}
The screening can be characterized by the plasmon spectral function, see Eq.~(\ref{eq:W_spec}), that contains excitations in the interacting electron-hole plasma as poles in the
$q$-$\omega$-plane, see Fig.~\ref{fig:plasmon}. In the exciton-dominated regime shown in Fig.~\ref{fig:plasmon}(a), besides the usual 2-d free-carrier contribution at small energies and small momenta
a broad resonance above $150$ meV appears. It stems from transitions between 1s- and 2s-like exciton states, see Fig.~\ref{fig:spectralf}(b),
and also from comparable transitions between exciton states with large momenta.
There are contributions at smaller energies as well that can not be as easily distinguished from free-carrier screening.
At large densities beyond the Mott transition the plasmon spectral function shows a pronounced peak structure with a square-root-like behaviour at small momenta
which has been discussed for TMDCs in Ref.~\citenum{groenewald_valley_2016} and which is typical for a two-dimensional electron gas. \cite{haug_quantum_1993}
Although excitons are expected to be much less polarizable than a free electron-hole plasma and hence contribute less to screening, at elevated excitation densities with a large
fraction of carriers bound as excitons, their contribution can be essential. From the many-particle renormalization caused by free-carrier and excitonic screening,
we deduce that in monolayer TMDC semiconductors excitonic screening is less efficient by two to three orders of magnitude for comparable excitation
densities. Nevertheless, in a regime where more than $99\%$ of carriers are bound as excitons, excitonic screening still yields a significant contribution.
As the plasmon spectral function is directly observable by electron energy loss spectroscopy (EELS) \cite{kogar_exciton_2016}, we suggest to use this technique to explore exciton signatures in the dielectric function
eperimentally.

\section{Conclusion.}

The exciton ionization equilibrium in monolayer TMDC semiconductors has been studied for various material as well as experimentally and device-relevant external parameters
on the basis of an ab initio description of the electronic band structure and Coulomb interaction. We observe entropy ionization of excitons at
low excitation densities
and a Mott transition to a fully ionized plasma at high densities between $3\times10^{12}$~cm$^{-2}$ and $1\times10^{13}$~cm$^{-2}$ depending on
experimental parameters. Below the Mott transition, excitons become dominant in all cases with maximal fractions of excitons between $70\%$ and more than $99.9\%$. The most efficient tuning knobs are dielectric screening of the Coulomb interaction via the choice of dielectric environment and carrier doping that can induce complete ionization above a level of $10^{13}$~cm$^{-2}$. We suggest that fingerprints of excitonic contributions
can be observed in ARPES and STS experiments, which are sensitive to the single-particle spectral functions. Moreover, we find that excitonic screening, although two to
three orders of magnitude less efficient than free-carrier screening at comparable excitation densities, plays an important role in the description of ionization equilibrium. Exciton signatures in the
dielectric function suggest EELS as another way to study the ionization equilibrium in excited semiconductors.

\section{Methods.}

\subsection{Theory of Ionization Equilibrium.}

We start from the general expression for the carrier density (\ref{eq:carr_dens}) and the spectral function
\begin{equation}
  A_{\mathbf{k}\sigma}^a(\omega)=2i\textrm{Im}\,\frac{1}{\hbar\omega-\varepsilon_{\mathbf{k}\sigma}^a-\Sigma_{\mathbf{k}\sigma}^{\textrm{ret},a}(\omega)}
     ~.
    \label{eq:G_spec}
\end{equation}
In the limit of small quasi-particle damping $\textrm{Im}\,\Sigma^{\textrm{ret},a}\ll\textrm{Re}\,\Sigma^{\textrm{ret},a}$, the spectral function can
be expanded in linear order of $\textrm{Im}\,\Sigma^{\textrm{ret},a}$ yielding the carrier density in so-called extended quasi-particle approximation
\begin{equation}
\begin{split}
  &n_a(\mu_a,T)\\ & =\frac{1}{\mathcal{A}}\sum_{\mathbf{k}\sigma}f^a(E^a_{\mathbf{k}\sigma}) \\ & -\frac{1}{\mathcal{A}}\sum_{\mathbf{k}\sigma}\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}
  \frac{2}{\hbar}\textrm{Im}\,\Sigma_{\mathbf{k}\sigma}^{\textrm{ret},a}(\omega)\left[f^a(E^a_{\mathbf{k}\sigma})-f^a(\omega)\right]\\
  &\frac{d}{d\omega}\frac{\mathcal{P}}{\omega-E^a_{\mathbf{k}\sigma}/\hbar}\\
  &=n_a^{\textrm{QP}}+n_a^{\textrm{corr}}
  ~,
    \label{eq:n_ext_qp_approx}
\end{split}
\end{equation}
where the quasi-particle energy $E^a_{\mathbf{k}\sigma}$ is given by $E^a_{\mathbf{k}\sigma}=\varepsilon_{\mathbf{k}\sigma}^a+\textrm{Re}\,\Sigma_{\mathbf{k}\sigma}^{\textrm{ret},a}(E^a_{\mathbf{k}\sigma})$
and $\mathcal{P}$ denotes the Cauchy principal value. \cite{kremp_equation_1984,semkat_ionization_2009} The total density is divided into
contributions from quasi-free particles and correlated particles, the latter being either in bound or scattering many-particle states.

The spectral function in extended quasi-particle approximation corresponding to this separation into free and correlated carriers is given by
\begin{equation}
\begin{split}
  A_{\mathbf{k}\sigma}^a(\omega) = &-2\pi i\delta(\hbar\omega-E^a_{\mathbf{k}\sigma})(1-Z_{\mathbf{k}\sigma}^a) \\
  &- 2\pi i \Gamma_{\mathbf{k}\sigma}^a(\omega)
  ~,
    \label{eq:spectral_fct_extended}
\end{split}
\end{equation}
with $ \Gamma_{\mathbf{k}\sigma}^a(\omega) = \textrm{Im}\Sigma_{\mathbf{k}\sigma}^{\textrm{ret},a}(\omega)\frac{1}{\pi}\frac{d}{d\hbar\omega}\frac{\mathcal{P}}{\hbar\omega-E^a_{\mathbf{k}\sigma}} $ and
the renormalization factor $Z_{\mathbf{k}\sigma}^a = \int d\hbar\omega \Gamma_{\mathbf{k}\sigma}^a(\omega)$. The first term describes quasi-free particles at renormalized energies. Their spectral weight
is reduced according to the renormalization factor to account for correlated carriers, which are spectrally described by the second term.

To evaluate the expressions (\ref{eq:n_ext_qp_approx}) and (\ref{eq:spectral_fct_extended}), we have to choose an approximation for the self-energy
$\Sigma^{\textrm{ret},a}(\omega)$. The real and imaginary parts of $\Sigma$ determine the quasi-particle energies and the correlated part of the carrier density,
respectively. An appropriate choice is the screened ladder approximation \cite{stolz_correlated_1979,kremp_equation_1984,kremp_quantum_1993}
$\Sigma(\omega)=\Sigma^{\textrm{H}}+\Sigma^{\textrm{GW}}(\omega)+\Sigma^{\textrm{T}}(\omega)$ that takes into account screening
of Coulomb interaction due to excited carriers as well as the formation of bound two-particle states and consists of Hartree, GW and T-matrix contributions.
We assume that renormalizations due to the Hartree self-energy are small compared to exchange and correlation effects.
In the T-matrix contribution, we neglect exchange terms and assume static screening so that the T-matrix depends only on one instead of three frequency arguments.
Thus we obtain for the imaginary part of the self-energy using the generalized Kadanoff-Baym ansatz \cite{kremp_quantum_2005}:
\begin{equation}
\begin{split}
  &\textrm{Im}\,\Sigma_{\mathbf{k}\sigma}^{\textrm{ret},a}(\omega) \\
  &=\frac{1}{\mathcal{A}}\sum_{\mathbf{k} b}V^{ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}\textrm{Im}\,\varepsilon^{-1,\textrm{ret}}_{\mathbf{k}-\mathbf{k}'}(\omega-E^b_{\mathbf{k}'\sigma}/\hbar)\\
  &\left[f^b(E^b_{\mathbf{k}'\sigma})-n^B(E^b_{\mathbf{k}'\sigma}-\hbar\omega)\right]\\
  &+\frac{1}{\mathcal{A}}\sum_{\mathbf{k} b\sigma'}\textrm{Im}\,T''^{,\textrm{ret},ab}_{\mathbf{k}\bk'\sigma\sigma'}(\omega+E^b_{\mathbf{k}'\sigma'}/\hbar)\\
  &\left[f^b(E^b_{\mathbf{k}'\sigma'})+n^B_{ab}(\hbar\omega+E^b_{\mathbf{k}'\sigma'})\right]
     ~.
    \label{eq:im_self_en_screened_ladder}
\end{split}
\end{equation}
Here we applied thermal equilibrium relations for the screened Coulomb interaction \cite{kremp_quantum_2005}:
\begin{equation}
\begin{split}
  & V^{\textrm{S},<,ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}(\omega)=n^B(\omega)V^{ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}2i\textrm{Im}\,\varepsilon^{-1,\textrm{ret}}_{\mathbf{k}-\mathbf{k}'}(\omega), \\
  & V^{\textrm{S},>,ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}(\omega)=(1+n^B(\omega))V^{ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}2i\textrm{Im}\,\varepsilon^{-1,\textrm{ret}}_{\mathbf{k}-\mathbf{k}'}(\omega)\,.
    \label{eq:thermal_plasmon_prop}
\end{split}
\end{equation}
$\varepsilon^{-1,\textrm{ret}}_{\mathbf{q}}(\omega)$ is the longitudinal dielectric function describing screening due to excited carriers and $n^B(\omega)$ is the Bose distribution function
of the elementary plasma excitations called plasmons. $V^{ab}$ denotes Coulomb matrix elements between species $a$ and $b$ which contain dielectric screening due to carriers in the ground state and due to
the environment but no screening due to excited carriers. $T''$ denotes the T-matrix with the two lowest-order terms subtracted from the ladder expansion and is discussed in the following subsection.

\subsection{T-matrix and Bound Carriers.}

The T-matrix in statically screened ladder approximation describing bound and scattering two-particle states between carrier species $a$ and $b$ obeys a Lippmann-Schwinger equation (LSE)
\begin{equation}
  T^{\textrm{ret},ab}(\omega)=V^{\textrm{S},\textrm{ret},ab}+i\hbar V^{\textrm{S},\textrm{ret},ab}\,\mathcal{G}^{\textrm{ret},ab}(\omega)\, T^{\textrm{ret},ab}(\omega)
     \,,
    \label{eq:LSE}
\end{equation}
where $\mathcal{G}^{\textrm{ret},ab}(\omega)$ is the free two-particle Green's function in the particle-particle channel. The corresponding interacting
two-particle Green's function $G^{\textrm{ret},ab}_2(\omega)$ fulfills a Bethe-Salpeter equation, that has been discussed in detail in \cite{kraeft_quantum_1986,bornath_two-particle_1999}
and is equivalent to the LSE. We will exploit this fact later when solving the LSE and evaluating the T-matrix self-energy.
In its homogeneous form, the BSE in static ladder approximation is given by
\begin{equation}
\begin{split}
&0=(E_{\mathbf{k}\sigma}^a+E_{\mathbf{k}+\mathbf{Q}\sigma'}^b)G^{\textrm{ret},ab}_{2,\mathbf{k},\mathbf{k}+\mathbf{Q}\sigma\sigma'}  \\
  -&(1-f_{\mathbf{k}\sigma}^a-f_{\mathbf{k}+\mathbf{Q}\sigma'}^b)\frac{1}{\mathcal{A}}\sum_{\mathbf{k}'}V^{\textrm{S},ab}_{\mathbf{k}+\mathbf{Q},\mathbf{k}',\mathbf{k},\mathbf{k}'+\mathbf{Q}}G^{\textrm{ret},ab}_{2,\mathbf{k}',\mathbf{k}'+\mathbf{Q}\sigma\sigma'}
  \,.
    \label{eq:bse}
    \end{split}
\end{equation}
Diagonalization yields bound states $\ket{\nu\sigma\sigma'\mathbf{Q}}$ and eigenenergies $E^{\sigma\sigma'}_{\nu\mathbf{Q}}$. We drop the indices $a$ and $b$ here, assuming that only two-particle states between
different carrier species are involved. Due to the translational invariance of the crystal, the bound states can be classified by
the total exciton momentum $\mathbf{Q}$ as discussed in \cite{qiu_nonanalyticity_2015}. Here we neglect the effect of electron-hole exchange interaction that leads to a fine-structure
splitting of excitons and trions \cite{qiu_nonanalyticity_2015,jones_excitonic_2016,plechinger_trion_2016} in the meV range, which is small compared to the exciton binding energies of several hundred meV.
As a consequence, electron and hole spins,
which are already good quantum numbers in monolayer TMDC materials due to crystal symmetry, also classify the bound states. For each total momentum and spin combination a series
of excitons exists, which is labeled here by $\nu$, analogue to the angular momentum states of Hydrogen-like Wannier excitons. Due to the two-dimensional nature of monolayer TMDCs and the related strong
momentum dependence of dielectric screening, nontrivial exciton series deviating from a Hydrogen-like
spectrum are observed. \cite{qiu_optical_2013,chernikov_exciton_2014,berghauser_analytical_2014} The eigenenergies decompose into a part from the relative motion of
electron and hole and a kinetic part depending on the total momentum: $E^{\sigma\sigma'}_{\nu\mathbf{Q}}=E^{\sigma\sigma'}_{\textrm{rel},\nu}+E^{\sigma\sigma'}_{\textrm{kin},\mathbf{Q}}$.
We can use Bloch basis functions to find a representation of the bound states corresponding to exciton wave functions
\begin{equation}
\begin{split}
& \psi^{\sigma\sigma'}_{\nu\mathbf{Q}}(\mathbf{k})= \big< \mathbf{k}\bk'\sigma\sigma'ab \big| \nu\sigma\sigma'\mathbf{Q} \big> \delta_{\mathbf{k}',\mathbf{k}+\mathbf{Q}}\,,
    \label{eq:wave_functions}
    \end{split}
\end{equation}
where $\mathbf{k}$ conventionally denotes the hole momentum, while the electron momentum is fixed via the total momentum.

An explicit expression for the T-matrix can be obtained by writing the LSE (\ref{eq:LSE}) in the basis of two-particle eigenstates $\ket{\nu\sigma\sigma'\mathbf{Q}}$ as shown in detail
in Ref.~\citenum{kremp_quantum_2005}. Since the BSE represents a generalized eigenvalue problem, the eigenstates form a biorthogonal basis. The procedure yields a spectral representation
of the T-matrix in operator form that is referred to as \textit{bilinear expansion}:
\begin{equation}
\begin{split}
&T^{\textrm{ret},ab}(\omega)= \\
&\sum_{\nu\sigma\sigma'\mathbf{Q}}N_{ab}^{-1}(E_{\textrm{kin}}-\hbar\omega)\frac{\ket{\nu\sigma\sigma'\mathbf{Q}}\bra{\nu\widetilde{\sigma\sigma'}\mathbf{Q}}}{\hbar\omega - E^{\sigma\sigma'}_{\nu\mathbf{Q}}}(E_{\textrm{kin}}-E^{\sigma\sigma'}_{\nu\mathbf{Q}})
    \label{eq:bilinear}
    \end{split}
\end{equation}
with the Pauli blocking factor $N_{ab}=1-f^a-f^b$, the operator of kinetic energy $E_{\textrm{kin}}$ and the eigenstate of the adjoint BSE $\bra{\nu\widetilde{\sigma\sigma'}\mathbf{Q}}$.
The bilinear expansion is used in the following to evaluate the imaginary part of the self-energy (\ref{eq:im_self_en_screened_ladder}) and thereby the contribution of correlated carriers.

\subsection{Separation of Bound and Quasi-Free Carriers.}

Inserting Eq.~(\ref{eq:im_self_en_screened_ladder}) into Eq.~(\ref{eq:n_ext_qp_approx}) and noting that neither the GW self-energy nor the two lowest
T-matrix terms contribute to the carrier density \cite{stolz_correlated_1979}, we obtain \cite{kremp_quantum_1993,semkat_ionization_2009}
\begin{equation}
\begin{split}
  n_a(\mu_a,T)&=\frac{1}{\mathcal{A}}\sum_{\mathbf{k}\sigma}f^a(E^a_{\mathbf{k}\sigma})\\
  &+\frac{1}{\mathcal{A}^2}\sum_{\mathbf{k}\bk' b\sigma'}\int_{-\infty}^{E_{\textrm{Gap}}}\frac{d\omega}{\pi}n^B_{ab}(\omega)\\
  &\textrm{Im}
  \,T^{\textrm{ret},ab}_{\mathbf{k}\bk'\sigma\sigma'}(\omega)\frac{d}{d\omega}i\hbar\mathcal{G}^{\textrm{ret},ab}_{\mathbf{k}\bk'\sigma\sigma'}(\omega)\\
  &+n_{\textrm{scatt}}
     \,.
    \label{eq:density_full}
\end{split}
\end{equation}
$n^B_{ab}(\omega)=\big[\textrm{exp}(\beta(\hbar\omega-\mu_a-\mu_b))-1\big]^{-1}$ is the Bose distribution function depending on the chemical potentials of both carrier species.
Eq.~(\ref{eq:density_full}) contains contributions of both bound two-particle states
(below the single-particle gap $E_{\textrm{Gap}}$) and scattering two-particle states, the latter being explicitely given in Refs.~\citenum{kremp_ladder_1984,zimmermann_mass_1985,kremp_quantum_1993}.
The renormalization factor $Z_{\mathbf{k}\sigma}^a$ of the quasi-particle resonance in the spectral function (\ref{eq:spectral_fct_extended})
enters the contribution of correlated carriers as Pauli-blocking factor and as correction to the two-particle scattering spectrum.
To simplify the following discussion, we neglect the contribution $n_{\textrm{scatt}}$ of scattering states beyond the quasi-free carriers and consider only the bound-state contribution
given by the real-frequency poles of the T-matrix \cite{kremp_ladder_1984}:
\begin{equation}
\begin{split}
  &\frac{1}{\mathcal{A}^2}\sum_{\mathbf{k}\bk' b\sigma'}\textrm{Im}
  \,T^{\textrm{ret},ab}_{\mathbf{k}\bk'\sigma\sigma'}(\omega)\frac{d}{d\omega}i\hbar\mathcal{G}^{\textrm{ret},ab}_{\mathbf{k}\bk'\sigma\sigma'}(\omega)\Big|_{\textrm{bound}} \\
   &=\pi\frac{1}{\mathcal{A}}\sum_{\nu\sigma'\mathbf{Q}}\delta(\hbar\omega - E^{\sigma\sigma'}_{\nu\mathbf{Q}})\,.
    \label{eq:dens_bound}
\end{split}
\end{equation}
Using Eq.~(\ref{eq:dens_bound}), we arrive at the final expression for the carrier density:
\begin{equation}
\begin{split}
  n_a(\mu_a,T)&=\frac{1}{\mathcal{A}}\sum_{\mathbf{k}\sigma}f^a(E^a_{\mathbf{k}\sigma})\\
  &+\frac{1}{\mathcal{A}}\sum_{b\neq a}\sum_{\sigma\sigma'}\sum_{\nu\mathbf{Q}}n^B_{ab}(E^{\sigma\sigma'}_{\nu\mathbf{Q}})\\
  &=n_{\textrm{free}}^{\textrm{GW},a}+n_X
     \,.
    \label{eq:density_final}
\end{split}
\end{equation}
The total carrier density separates into contributions from quasi-free carriers and from carriers bound as excitons according to the two poles in the spectral
function $A^a(\omega)$. For a specific material, the ionization equilibrium has to be computed numerically.
The electron and hole chemical potentials are determined by adapting the Fermi functions $f^a(E^a_{\mathbf{k}\sigma})$ of electrons and holes to a given density of
quasi-free carriers at the quasi-particle energies $E^a_{\mathbf{k}\sigma}$. As the chemical potentials also enter the bound-carrier density via the Bose function $n^B_{ab}$,
Eq.~(\ref{eq:density_final}) represents an implicit equation for the fraction of
quasi-free carriers $\alpha_a=n_{\textrm{free}}^{a}/n_a$, that has to be solved self-consistently with the quasi-particle
energies in GW approximation, see Eq.~(\ref{eq:GW_energy}), and the bound-state energies $E^{\sigma\sigma'}_{\nu\mathbf{Q}}$.
To simplify the procedure, we exploit the fact that shifts of excitonic resonances are naturally much smaller than band-gap shifts, which is due to compensation effects between
gap shrinkage and binding-energy reduction. \cite{bornath_two-particle_1999,steinhoff_influence_2014} Hence we assume that the exciton spectrum depends only weakly on the
excitation density so that we can limit ourselves to the BSE (\ref{eq:bse}) in the limit of zero excitation density.

Consistent with the imaginary part of the self-energy (\ref{eq:im_self_en_screened_ladder}), the quasi-particle energies $E^a_{\mathbf{k}\sigma}$ contain GW- and T-matrix contributions:
\begin{equation}
\begin{split}
  E^a_{\mathbf{k}\sigma}&=\varepsilon_{\mathbf{k}\sigma}^a+\textrm{Re}\,\Sigma_{\mathbf{k}\sigma}^{\textrm{GW},\textrm{ret},a}(E^a_{\mathbf{k}\sigma})+\textrm{Re}\,\Sigma_{\mathbf{k}\sigma}^{\textrm{T},\textrm{ret},a}(E^a_{\mathbf{k}\sigma})
     \,.
    \label{eq:GW_energy_full}
\end{split}
\end{equation}
The GW self-energy is separated into the Fock term and the so-called Montroll-Ward term containing all contributions beyond bare exchange interaction. The T-matrix contribution is explicitely given in
Ref.~\citenum{stolz_correlated_1979} and leads to a blue shift of single-particle energies that is in the nondegenerate case ($f^a(E^a_{\mathbf{k}\sigma})\ll 1$) caused by the bound-carrier population.
At the same time, the Fock self-energy contains exchange interaction with both quasi-free and bound carriers via the extended spectral functions that leads to a lowering
of single-particle energies.
This can be seen by using the T-matrix self-energy in Eq.~(\ref{eq:im_self_en_screened_ladder}) to obtain an excitonic contribution to the spectral function (\ref{eq:spectral_fct_extended}) given by
\begin{equation}
\begin{split}
  &\Gamma_{\mathbf{k}\sigma}^a(\omega)= \frac{1}{\mathcal{A}}\sum_{b\neq a} \sum_{\nu\sigma'\mathbf{Q}}\sum_{\mathbf{k}'}\\
  &(|\psi^{\sigma\sigma'}_{\nu\mathbf{Q}}(\mathbf{k}) |^2\delta_{a,h}\delta_{\mathbf{k}',\mathbf{k}+\mathbf{Q}} + |\psi^{\sigma\sigma'}_{\nu\mathbf{Q}}(\mathbf{k}-\mathbf{Q}) |^2\delta_{a,e}\delta_{\mathbf{k}',\mathbf{k}-\mathbf{Q}}) \\
   &\delta(\hbar\omega+E^b_{\mathbf{k}'\sigma'}-E^{\sigma\sigma'}_{\nu\mathbf{Q}})[n^B_{ab}(E^{\sigma\sigma'}_{\nu\mathbf{Q}})+f^{b}(E^b_{\mathbf{k}'\sigma'})]
  ~.
    \label{eq:spectral_fct_extended_T_matrix}
\end{split}
\end{equation}
It yields a sharp resonance for each bound state weighted by its Bose population function and the exciton wave functions at the corresponding position in k-space.
Note that the spectral positions of the resonances are not given by the bound-state energies $E^{\sigma\sigma'}_{\nu\mathbf{Q}}$, which are two-particle quantities,
but by an effective binding energy of the carrier in state $\ket{\mathbf{k}\sigma a}$, as $\Gamma$ represents a single-particle spectral function.
The Fock self-energy \cite{kremp_quantum_2005} can then be expressed in terms
of the spectral function using the Kubo-Martin-Schwinger relation for the propagators $G^{<}(\omega)$ in thermal equilibrium:
\begin{equation}
\begin{split}
    \Sigma_{\mathbf{k}\sigma}^{\textrm{F},a}=&i\hbar\frac{1}{\mathcal{A}}\sum_{\mathbf{k}'}V^{aa}_{\mathbf{k}\bk'\mathbf{k}\bk'}G^{<,a}_{\mathbf{k}'\sigma}\\
    =-&i\hbar\frac{1}{\mathcal{A}}\sum_{\mathbf{k}'}V^{aa}_{\mathbf{k}\bk'\mathbf{k}\bk'}\int\frac{d\omega}{2\pi}f^a(\omega)A_{\mathbf{k}'\sigma}^a(\omega)  \\
    =-&\frac{1}{\mathcal{A}}\sum_{\mathbf{k}'}V^{aa}_{\mathbf{k}\bk'\mathbf{k}\bk'}\Big(f^a(E^a_{\mathbf{k}'\sigma})+f^{a,\textrm{bound}}_{\mathbf{k}'\sigma}\Big)\,~.
    \label{eq:HF_self_energy}
\end{split}
\end{equation}
The first contribution to the Fock self-energy scales, besides the Coulomb matrix elements, with the free-carrier density while the second contribution scales with the density
of bound carriers. It turns out that similar to exchange interaction with free carriers, bound-carrier exchange leads to k-dependent renormalizations according to the exciton wave functions and populations
that are contained in the population factor $f^{a,\textrm{bound}}_{\mathbf{k}'\sigma}$. As a conclusion, the real part of the self-energy (\ref{eq:GW_energy_full}) contains quasi-particle renormalizations
due to exciton populations via the T-matrix in two different places that act in opposite directions.
We assume that these renormalizations cancel to a large degree and focus on the free-carrier contributions in accordance with Refs.~\citenum{kremp_quantum_1993,semkat_ionization_2009}.
Then we obtain for the quasi-particle energies:
\begin{equation}
\begin{split}
  E^a_{\mathbf{k}\sigma}&\approx\varepsilon_{\mathbf{k}\sigma}^a+\textrm{Re}\,\Sigma_{\mathbf{k}\sigma}^{\textrm{GW},\textrm{ret},a}(E^a_{\mathbf{k}\sigma})\Big|_{\textrm{free}}\\
            &=\varepsilon_{\mathbf{k}\sigma}^a+\Sigma_{\mathbf{k}\sigma}^{\textrm{F},a}\Big|_{\textrm{free}}+i\hbar\int_{-\infty}^{\infty}\frac{d\omega'}{2\pi}\\
            \sum_{\mathbf{q}}&\frac{(1-f^a(E^a_{\mathbf{q},\sigma}))V^{\textrm{S},>,aa}_{\mathbf{k}\mathbf{q}\mathbf{k}\mathbf{q}}(\omega')+
            f^a(E^a_{\mathbf{q},\sigma})V^{\textrm{S},<,aa}_{\mathbf{k}\mathbf{q}\mathbf{k}\mathbf{q}}(\omega')}{E^a_{\mathbf{k}\sigma}-E^a_{\mathbf{q},\sigma}-\hbar\omega'}
     \,.
    \label{eq:GW_energy}
\end{split}
\end{equation}
In a similar manner as for the Fock self-energy, the full spectral functions could be used to evaluate the Montroll-Ward self-energy in Eq.~(\ref{eq:GW_energy}).
Due to the spectral structure of the self-energy, however, renormalizations of the single-particle band structure caused by bound carriers involve a denominator of the order of the exciton
binding energy, which is very off-resonant. Therefore the Montroll-Ward term is evaluated using spectral functions for quasi-free carriers.

\subsection{Screening due to Excited Carriers.}

In the spirit of the extended quasi-particle approximation, screening of the Coulomb interaction due to both free carriers
and bound excitons is taken into account. The free-carrier screening is treated in RPA with a Lindhard dielectric function \cite{steinhoff_influence_2014},
while the excitonic polarizibilities are calculated as described in \cite{ropke_influence_1979,ropke_greens_1981}:
\begin{equation}
\begin{split}
  &\varepsilon^{\textrm{ret}}_{\mathbf{q}}(\omega)=\varepsilon^{\textrm{ret},\textrm{RPA}}_{\mathbf{q}}(\omega)\\
  &-V_{\mathbf{q}}\frac{1}{\mathcal{A}}\sum_{\nu\nu'\sigma\sigma'\mathbf{Q}}\left|M^{\sigma\sigma'}_{\nu\nu'\mathbf{Q}}(\mathbf{q})\right|^2\frac{n^B_{ab}(E^{\sigma\sigma'}_{\nu\mathbf{Q}})-n^B_{ab}(E^{\sigma\sigma'}_{\nu'\mathbf{Q}-\mathbf{q}})}
  {E^{\sigma\sigma'}_{\nu\mathbf{Q}}-E^{\sigma\sigma'}_{\nu'\mathbf{Q}-\mathbf{q}}-\hbar\omega-i\gamma}
    \label{eq:screening}
\end{split}
\end{equation}
with matrix elements
\begin{equation}
\begin{split}
&M^{\sigma\sigma'}_{\nu\nu'\mathbf{Q}}(\mathbf{q})=\\
&\frac{1}{\mathcal{A}}\sum_{\mathbf{p}}\psi^{\sigma\sigma'}_{\nu\mathbf{Q}}(\mathbf{p})\Big[(\psi^{\sigma\sigma'}_{\nu'\mathbf{Q}-\mathbf{q}}(\mathbf{p}+\mathbf{q}))^*-(\psi^{\sigma\sigma'}_{\nu'\mathbf{Q}-\mathbf{q}}(\mathbf{p}))^*\Big]
    \label{eq:screening_ME}
\end{split}
\end{equation}
and exciton wave functions $\psi^{\sigma\sigma'}_{\nu\mathbf{Q}}(\mathbf{p})$ as defined above. The momentum and frequency dependence of screening is characterized
by the plasmon spectral function
\begin{equation}
\begin{split}
\hat{V}^{\textrm{S},ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}(\omega)&=V^{\textrm{S},>,ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}(\omega)-V^{\textrm{S},<,ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}(\omega) \\
&=V^{ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}2i\textrm{Im}\,\varepsilon^{-1,\textrm{ret}}_{\mathbf{k}-\mathbf{k}'}(\omega)\,.
    \label{eq:W_spec}
\end{split}
\end{equation}

\subsection{Ab initio Single- and Two-Particle Properties.}

\begin{figure*}[h!t]
\begin{center}
\includegraphics[width=\textwidth]{./figure_3.eps}
\caption{\textbf{Bound-state spectra at zero excitation density.} The spectra are measured relative to the quasi-particle band gap and shown
over the modulus of total exciton momentum $Q$.
\textbf{(a)} Comparison of different TMDC materials on SiO$_2$ substrate. \textbf{(b)} Comparison of WS$_2$ in different dielectric environments with dielectric constant $\varepsilon$ of
bottom/top environment. Only 1s-excitons are shown. The lines serve as guide to the eye.
\textbf{(c)} Comparison of MoS$_2$ with different lattice constants $a$ on SiO$_2$ substrate. The unstrained layer corresponds to $a=3.18$~\AA\,
while tensile biaxial strain is simulated by $a=3.20$~\AA\,.}
\label{fig:bound_states}
\end{center}
\end{figure*}
For a material-realistic description of the strong Coulomb interaction in atomically thin systems, we use band structures $\varepsilon^{a}$ and Coulomb matrix elements $V^{ab}$
from material-realistic G$_0$W$_0$ calculations for freestanding slabs of various monolayer TMDCs as a basis, see the Supporting Information and Ref.~\citenum{steinhoff_influence_2014}.
The matrix elements already take into account dielectric screening due to charge carriers in the ground state of the system.
Furthermore, we account for additional screening provided by a possible dielectric environment, like a substrate, as described in the Supporting Information.
The main effect of the additional screening is a reduction of exciton binding energies, which are key quantities for the exciton-plasma balance.
The corresponding reduction of quasi-particle band gaps on the other hand plays
no role here, as all bound-state energies and excited-carrier chemical potentials are measured relative to the gap. By convention, we choose the gap between
the spin-up conduction and valence bands at $K$ as reference which belong to the A-exciton resonance.

The calculation of ionization equilibrium requires knowledge of two-particle energies,
which are obtained by solving the Bethe-Salpeter equation~(\ref{eq:bse}).
Fig.~\ref{fig:spectralf}~(b) shows the full exciton spectrum for monolayer WS$_2$ on a SiO$_2$ substrate, for which we assume a dielectric constant $\varepsilon=3.9$. Besides the $K$-excitons
at $Q=0$ the spectra exhibit a rich structure of various inter-valley excitons with large total momenta. Even for direct-band-gap materials, inter-valley excitons between $K$- and $\Sigma$-valleys
at $Q\approx6$ nm$^{-1}$ may be lower than intra-valley $K$-excitons due to a larger exciton binding energy.
As can be seen in Fig.~\ref{fig:bound_states}~(a) the binding energies of the lowest
$Q=0$-excitons (``1s'') are comparable for all considered materials, the main difference being the splitting between excitons involving different conduction bands,
which is larger for tungsten-based materials. For MoS$_2$ bound states belonging to the B exciton are visible at $-175$ meV corresponding to the valence-band splitting of
about $140$ meV. Higher exciton states (``2s'') appear as well. Fig.~\ref{fig:bound_states}~(b) shows that dielectric screening from the environment has a strong impact on the exciton spectrum as it
can reduce exciton binding energies significantly \cite{latini_excitons_2015}. This has a major influence on the ionization equilibrium, as we discuss in the main text. Another tunable parameter in experiments
is the application of strain to the TMDC monolayer, which leads to changes in the band structure \cite{conley_bandgap_2013}. This is reflected by MoS$_2$
changing from an indirect to a direct semiconductor in the exciton picture under tensile strain, see Fig.~\ref{fig:bound_states}~(c).

\subsection{Numerical Details.}

We calculate the ionization equilibrium from the fraction of quasi-free carriers as root of the implicit equation~(\ref{eq:density_final}).
The two highest valence and two lowest conduction bands are considered to cover all excitons that are relevant in a quasi-equilibrium
situation. Likewise, we limit the Brillouin zone to circles with radius $2.7$ nm$^{-1}$ around the $K$,$K'$,$\Sigma$,$\Sigma'$ and $\Gamma$ points using a Monkhorst-Pack mesh
with $30$ mesh points along $\Gamma$-$M$, which yields reasonable convergence of all results. The frequency integrals involved in the Montroll-Ward self-energy (\ref{eq:GW_energy})
are extended from $-600$ to $600$ meV exploiting the relation $V^{\textrm{S},<,ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}(-\omega)=V^{\textrm{S},>,ab}_{\mathbf{k}\bk'\mathbf{k}\bk'}(\omega)$.
For simplicity, we use a dielectric function (\ref{eq:screening}) which is isotropic in momentum by evaluating its dependence on $|\mathbf{q}|$ along the contour $\Gamma$-$K$
and using Coulomb matrix elements $V_{|\mathbf{q}|}$ that are averaged over Wannier orbitals. Both the Lindhard and the excitonic dielectric function (\ref{eq:screening})
are evaluated using ground-state energies and extrapolated to the limit of vanishing phenomenological quasi-particle broadening $\gamma$.
For a sum over bound states, only those states that are below the local (in $\mathbf{k}$-space) renormalized band structure measured at the maximum of the corresponding
exciton wave functions are taken into account.

\textbf{Acknowledgement}
We acknowledge financial support from the Deutsche Forschungsgemeinschaft (JA 14-1 and RTG 2247 "Quantum Mechanical Materials Modelling") and the European Graphene Flagship
as well as resources for computational time at the HLRN (Hannover/Berlin). We thank Michael Lorke, Christopher Gies and Dirk Semkat for fruitful discussions.

\textbf{Supporting Information available}, containing a description of the ab initio procedures to obtain band structures and screened Coulomb matrix elements.

\section{Supporting Information.}

\renewcommand{\thefigure}{S\arabic{figure}}
\renewcommand{\theequation}{S\arabic{equation}}

\subsection*{Ab-initio based parametrization of the TMDCs \label{app:modeling}}

To get an \emph{analytic description} of the Coulomb interaction in semiconducting TMDC monolayers, we apply the approach as presented in \cite{steinhoff_influence_2014,PhysRevB.88.085433,schonhoff_interplay_2016} for MoS$_2$ also to MoSe$_2$, WS$_2$, and WSe$_2$. We start with ab initio calculations for density-density like bare $U_{\alpha\beta} (q)$ and screened $V_{\alpha\beta}(q)$ Coulomb interaction matrix elements in the Wannier basis (with $\alpha, \beta \in [d_{z^2}, d_{xy}, d_{x^2-y^2}]$ ) for the freestanding, undoped TMDC slabs using the FLEUR and SPEX codes \cite{FLEUR,friedrich_efficient_2009,friedrich_efficient_2010} on discrete $18 \times 18 \times 1$ q grids. To interpolate the resulting $3 \times 3$ matrices analytically we make use of the (sorted) eigenbasis of the bare Coulomb interaction $\mathbf{U}$ by diagonalizing it
\begin{align}
\mathbf{U}_\mathrm{diag}(q) =
  \left(
    \begin{array}{ccc}
      U_1(q) & 0 & 0\\
      0 & U_2 & 0 \\
      0 & 0 & U_3
    \end{array}
  \right),
\label{eq:BareCoulombInteractionMatrixEigenbasis}
\end{align}
where the diagonal matrix elements are given by
\begin{equation}
U_i = \braket{ e_i | \mathbf{U} | e_i }
\end{equation}
using the eigenvectors of $\mathbf{U}$ in their long-wavelength limits
\begin{equation}
e_1 = \frac{1}{\sqrt{3}} \begin{pmatrix}  1 \\  1 \\  1 \end{pmatrix},
e_2 = \frac{1}{\sqrt{6}} \begin{pmatrix} +2 \\ -1 \\ -1\end{pmatrix},
e_3 = \frac{1}{\sqrt{2}} \begin{pmatrix}  0 \\ +1 \\ -1 \end{pmatrix}.
\label{eq:vEV}
\end{equation}
While the leading eigenvalue $U_1(q)$ is a function of $q$ the other two eigenvalues can be readily approximated as constants (see Fig. \ref{fig:CompSpexFit}). For the analytic description of the former we use
\begin{equation}
U_1(q) = \frac{3 e^2}{2 \varepsilon_0 A} \frac{1}{q(1 + \gamma q + \delta q^2)},
\label{eq:v1}
\end{equation}
where $A=\frac{\sqrt{3}}{2}a^2$ is the area of the hexagonal unit cell, $a$ is the lattice constant, and $\varepsilon_0$ is the vacuum permittivity.

\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{U_eigenvalues.eps}
\includegraphics[width=0.5\textwidth]{U_eigenvectors.eps}
\includegraphics[width=0.5\textwidth]{Eps_eigenvalues.eps}
\caption{Examplary data for the fit and ab initio calculation of the Coulomb interaction in MoSe$_2$. \textbf{(a)} Bare Coulomb matrix elements in its eigenbasis. Red dots, blue squares and green triangles correspond to the leading, second and third eigenvalue of $U(q)$ as obtained from ab initio calculations. Dashed lines show the corresponding fits using Eq. (\ref{eq:v1}) and Tab. \ref{tab:Fits}. \textbf{(b)} Eigenvectors of the bare Coulomb matrix (from left to right corresponding to the leading, second and third eigenvalue). The corresponding vector elements of the $d_{z^2}$ (red), $d_{xy}$ (green) and $d_{x^2-y^2}$ (blue) orbitals are shown. Dashed lines indicate constant analytic values for $U(q\rightarrow 0)$, see Eq. (\ref{eq:vEV}). \textbf{(c)} Matrix elements of the diagonal dielectric function. Markers indicate ab initio results and dashed lines show the fits using Eq. \ref{eq:BackgroundScreening} and Tab. \ref{tab:Fits}.}
\label{fig:CompSpexFit}
\end{figure}

The matrix elements of the screened interaction $\mathbf{V}(q)$ in the eigenbasis of the bare interaction $\mathbf{U}(q)$ are then obtained via
\begin{equation}
V_i(q) = \varepsilon_i^{-1}(q) \ U_i(q)
\label{eq:CoulombInteractionPartiallyScreened}
\end{equation}
where $\varepsilon_i(q)$ accounts for both the material-specific internal polarizability and the screening by the environment. Its diagonal representation is given by
\begin{equation}
\mathbf{\varepsilon}_\mathrm{diag}(q) =
  \left(
    \begin{array}{ccc}
      \varepsilon_1(q) & 0 & 0\\
      0 & \varepsilon_2 & 0 \\
      0 & 0 & \varepsilon_3
    \end{array}
  \right).
\end{equation}
Once again, the leading eigenvalue $\varepsilon_1(q)$ is a function of $q$ while the other elements are described sufficiently well as constants. Here, the former can be expressed by
\begin{equation}
\varepsilon_1(q) =
  \varepsilon_\infty (q)
    \frac{ 1 - \beta_1 \beta_2 e^{-2q\,h}}
       { 1 + (\beta_1 + \beta_2)  e^{-q\,h} + \beta_1 \beta_2 e^{-2q\,h}}
\label{eq:BackgroundScreening}
\end{equation}
which describes the macroscopic dielectric function of a two-dimensional semiconductor. The parameters $\beta_i$ include the screening effects of substrates (see Ref. \cite{rosner_wannier_2015}) via
\begin{equation}
\beta_i = \frac{\varepsilon_\infty (q) - \varepsilon_{\mathrm{sub},i}}{\varepsilon_\infty (q) + \varepsilon_{\mathrm{sub},i}}
\end{equation}
where the dielectric constants of the substrate ($i=1$) and the superstrate ($i=2$) are introduced. In order to describe the original ab initio data as close as possible we fit $\varepsilon_\infty (q)$ using
\begin{equation}
\varepsilon_\infty (q)= \frac{a + q^2}{\frac{a \sin(q c)}{q b c} + q^2 } + e
\label{eq:EpsInf}
\end{equation}
and $\varepsilon_{\mathrm{sub},1}=\varepsilon_{\mathrm{sub},2}=1$ as the ab intio calculations were performed for freestanding layers.

As soon as all fitting parameters are obtained (see Tab. \ref{tab:Fits}) the screening of a dielectric environment can be included by choosing $\varepsilon_{\mathrm{sub},1}$ or $\varepsilon_{\mathrm{sub},2}$ correspondingly. Thus we have a closed analytic description of the screened Coulomb interaction $\mathbf{V}(q)$ in the eigenbasis of the bare interaction $\mathbf{U}(q)$ at arbitrary momenta $q$ in the first Brillouin zone. In order to transform it to the original orbital basis we make use of the eigensystem given in Eq. (\ref{eq:vEV}). In fact, this model is appropriate for every two-dimensional semiconductor.

Besides the analytical description of the screened Coulomb matrix elements we make use of a tight-binding Hamiltonian to describe the electronic band structure (as obtained from $G_0 W_0$ calculations) of the TMDC slab. To this end, we utilize the same Wannier basis as described before (see Ref. \cite{groenewald_valley_2016}) and derive a minimal three-band model describing the highest valence and two lowest conduction bands using the Wannier90 package \cite{mostofi_updated_2014}. Thereby we solely disentangle our target bands from the rest without performing a maximal localization in order to preserve the original transition metal d-orbital characters. The latter is crucial for the subsequent addition of first and  second order Rashba spin-orbit coupling following Ref. \cite{PhysRevB.88.085433}, which takes into account the large spin-orbit splitting in the conduction- and the valence-band K valleys.

Throughout the whole model-building process we assume that the substrate mainly affects the internal Coulomb interaction and neglect its influence on the band structure.
We have used relaxed lattice constants as given in Tab. \ref{tab:Fits}. The values of the bare and screened Coulomb interaction were extrapolated from vacuum heights of $16\,$\AA\ to $32\,$\AA.

\begin{table}[bt]
  \centering
  \caption{Parameters describing the Coulomb interaction and the static screening in the semiconducting TMDCs $MX_2$.}
  \label{tab:Fits}
  \begin{tabular}{|l|cccc|}
    \hline
    & MoS$_2$ & MoSe$_2$ & WS$_2$ & WSe$_2$ \\
    \hline
    lattice constant $a$(\AA ) & 3.180 & 3.320 & 3.191 & 3.325\\
    \hline
    \hline
    bare Interaction $U$ & & & & \\
    \hline
    $\gamma$ (\AA) & 1.932 & 2.232 & 2.130 & 2.297\\
    \hline
    $\delta$ (\AA$^2$) & 0.395 & -0.356 & 0.720 & 0.174\\
    \hline
    A (\AA$^2$) & 8.758 & 9.546 & 8.818 & 9.574 \\
    \hline
    $U_2$ (eV) & 0.810 & 0.837 &  0.712 & 0.715\\
    \hline
    $U_3$ (eV) & 0.367 & 0.376 & 0.354 & 0.360\\
    \hline
    \hline
    screening $\varepsilon$  & & & & \\
    \hline
    $a$ (1/\AA$^2$) & 2.383 & 2.856 & 3.947 & 2.430\\
    \hline
    $b$  & 17.836 & 11.635 & 29.931 & 20.764\\
    \hline
    $c$ (\AA) & 5.107 & 1.979 & 5.440 & 5.761\\
    \hline
    $h$ (\AA) & 2.740 & 4.298 & 1.578 & 2.489\\
    \hline
    $e$  & 5.739 & 6.303 & 4.497 & 5.305\\
    \hline
    $\varepsilon_2$ & 3.077 & 3.148 & 2.979 & 3.028\\
    \hline
    $\varepsilon_3$ & 2.509 & 2.510 & 2.494 & 2.481\\
    \hline
  \end{tabular}
\end{table}

\bibliographystyle{apsrev}

redpajama_set_name: RedPajamaArXiv


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text:
Authors
=======

Also see https://github.com/magit/magit/graphs/contributors.
Names below are sorted alphabetically.

Author
------

- Marius Vollmer <marius.vollmer@gmail.com>

Maintainer
----------

- Jonas Bernoulli <jonas@bernoul.li>

Retired Maintainers
-------------------

- Nicolas Dudebout <nicolas.dudebout@gatech.edu>
- Peter J. Weisberg <pj@irregularexpressions.net>
- Phil Jackson <phil@shellarchive.co.uk>
- Rémi Vanicat <vanicat@debian.org>
- Yann Hodique <yann.hodique@gmail.com>

Contributors
------------

- aaa707 <aaa707b@gmail.com>
- Aaron Culich <aculich@gmail.com>
- Abdo Roig-Maranges <abdo.roig@gmail.com>
- acple <silentsphere110@gmail.com>
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- Andreas Liljeqvist <andreas.liljeqvist@robacks.se>
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- Brandon W Maister <quodlibetor@gmail.com>
- Brian Warner <warner@lothar.com>
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- Chris Bernard <cebernard@gmail.com>
- Chris Done <chrisdone@gmail.com>
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- Chris Ring <chris@ringthis.com>
- Christian Dietrich <christian.dietrich@informatik.uni-erlangen.de>
- Christian Kluge <ckfrakturfreak@web.de>
- Christopher Monsanto <chris@monsan.to>
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- Craig Andera <candera@wangdera.com>
- Dale Hagglund <dale.hagglund@gmail.com>
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- Feng Li <fengli@blackmagicdesign.com>
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- Hannu Koivisto <azure@iki.fi>
- Hans-Peter Deifel <hpdeifel@gmx.de>
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- Marius Vollmer <marius.vollmer@gmail.com>
- Mark Hepburn <Mark.Hepburn@csiro.au>
- Matus Goljer <dota.keys@gmail.com>
- Miles Bader <miles@gnu.org>
- Mitchel Humpherys <mitch.special@gmail.com>
- Moritz Bunkus <moritz@bunkus.org>
- Nathan Weizenbaum <nex342@gmail.com>
- Nguyễn Tuấn Anh <ubolonton@gmail.com>
- Nic Ferier <nic@ferrier.me.uk>
- Nick Alcock <nick.alcock@oracle.com>
- Nick Alexander <nalexander@mozilla.com>
- Nick Dimiduk <ndimiduk@gmail.com>
- Nicolas Dudebout <nicolas.dudebout@gatech.edu>
- Nicolas Richard <theonewiththeevillook@yahoo.fr>
- Noam Postavsky <npostavs@users.sourceforge.net>
- Ole Arndt <oliver.arndt@cegedim.com>
- Óscar Fuentes <ofv@wanadoo.es>
- Paul Stadig <paul@stadig.name>
- Pavel Holejsovsky <pavel.holejsovsky@upek.com>
- Pekka Pessi <nospam@pessi.fi>
- Peter J. Weisberg <pj@irregularexpressions.net>
- Philippe Vaucher <philippe@stvs.ch>
- Philipp Haselwarter <philipp@haselwarter.org>
- Philip Weaver <philip.weaver@gmail.com>
- Phil Jackson <phil@shellarchive.co.uk>
- Pieter Praet <pieter@praet.org>
- Prathamesh Sonpatki <csonpatki@gmail.com>
- rabio <rabiodev@o2.pl>
- Raimon Grau <raimonster@gmail.com>
- Ramkumar Ramachandra <artagnon@gmail.com>
- Remco van 't Veer <rwvtveer@xs4all.nl>
- Rémi Vanicat <vanicat@debian.org>
- René Stadler <mail@renestadler.de>
- Robert Boone <robo4288@gmail.com>
- Robin Green <greenrd@greenrd.org>
- Roger Crew <crew@cs.stanford.edu>
- Romain Francoise <romain@orebokech.com>
- Ron Parker <rparker@a123systems.com>
- Roy Crihfield <rscrihf@gmail.com>
- Rüdiger Sonderfeld <ruediger@c-plusplus.de>
- Ryan C. Thompson <rct@thompsonclan.org>
- Samuel Bronson <naesten@gmail.com>
- Sanjoy Das <sanjoy@playingwithpointers.com>
- Sean Bryant <sbryant@hackinggibsons.com>
- Sebastian Wiesner <lunaryorn@gmail.com>
- Sébastien Gross <seb@chezwam.org>
- Seong-Kook Shin <cinsky@gmail.com>
- Sergey Pashinin <sergey@pashinin.com>
- Sergey Vinokurov <serg.foo@gmail.com>
- Servilio Afre Puentes <afrepues@mcmaster.ca>
- Štěpán Němec <stepnem@gmail.com>
- Steven Chow <steve@myfreestuffapp.com>
- Steven Thomas <sthomas314@gmail.com>
- Steve Purcell <steve@sanityinc.com>
- Suhail Shergill <suhailshergill@gmail.com>
- Takafumi Arakaki <aka.tkf@gmail.com>
- Teruki Shigitani <teruki.shigitani@gmail.com>
- Thierry Volpiatto <thierry.volpiatto@gmail.com>
- Thomas Frössman <thomasf@jossystem.se>
- Thomas Jost <thomas.jost@gmail.com>
- Thomas Riccardi <riccardi.thomas@gmail.com>
- Tibor Simko <tibor.simko@cern.ch>
- Timo Juhani Lindfors <timo.lindfors@iki.fi>
- Ting-Yu Lin <aethanyc@gmail.com>
- Tom Feist <shabble@metavore.org>
- Wilfred Hughes <me@wilfred.me.uk>
- Win Treese <treese@acm.org>
- Yann Hodique <yann.hodique@gmail.com>


I APOLOGIZE FOR NO MESSAGE ON SUNDAY AS I WAS MOVING. THANKS TO YOU I HAVE MADE IT OVER TO THE NEW PLACE BUT MY BACK, SHOULDERS AND LEGS HAVE SUFFERED. GETTING UP IN THE MORNING IS A HALF HOUR JOB IT SEEMS. MY DEEP THANKS FOR THE HELP.
RIGHT NOW I WAS GOING TO WRITE A BIG ONE ON THE CURRENT SITUATION WHICH IS CRACKING OPEN, BUT THIS MORNING I WAS WARNED TO KEEP SILENT ON MANY THINGS THAT ARE TRANSPIRING. JUST BY THE FACT I WAS TOLD THAT SHOULD TELL YOU LOTS.
I DID RECEIVE CONFIRMATION FROM A VERY HIGH LEVEL THAT YES, PEOPLE HAVE BEEN PAID ON CURRENCY AND ONE ATTORNEY THAT I KNOW PERSONALLY HAS TOLD ME THE SAME, AND THAT HIS SCHEDULE TO GO IN AND GET THE PACKAGES UNDER HIS WING DONE WAS FORTHCOMING AND HE WAS PREPARING TO GO TO THE TTM. THAT TOO IS SIGNIFICANT AND CORROBORATES THE OTHER INFORMATIONS I WAS GIVEN.
ALL OF THIS JUST MEANS WE ARE ABOUT TO GET TO WORK, AND MONEY WILL FLOW.
OUR FUNDS ARE IN THE FINAL STAGE OF THE RELEASE AND GOD WILLING, THEY WILL COME OUT TONIGHT OR TOMORROW TO OUR ACCOUNTS. AFTER THAT, THERE IS NOTHING TO BE DONE THERE BUT MUCH TO DO HERE TO GET TO THE WORK.
I DO HAVE ONE SMALL REQUEST OF YOU THOUGH. I HAVE A SMALL SURGERY COMING UP TOMORROW, AND DO NOT HAVE ANY GAS TO EVEN GET THERE AND I HAVE BEEN WAITING FOR THIS FOR SOME MONTHS NOW. I COULD SURE USE A LITTLE MORE HELP.
ALSO, THE FAMOUS DOCTOR THAT HELPS OTHERS ACROSS BORDERS HAS BEEN RELEASED, BUT HE HAS ABSOLUTELY NO FOOD IN THAT COUNTRY AND LIVING IN A BARE BONES CHURCH IN THE BACK ROOM WAITING FOR THE RECOVERY TEAM TO BE ASSEMBLED AND GET HIM OUT OF THERE TO NORTH AMERICA. IF YOU COULD SPARE ANYTHING FOR HIM THAT WOULD BE MAGNIFICENT.
HE WAS TAKEN AWAY ABOUT 6 MONTHS AGO BECAUSE HE STOOD UP FOR THE POOR. THE SECRET SERVICE TOOK HIM AS A POLITICAL PRISONER AND WE DID NOT KNOW WHERE HE WAS UNTIL A WEEK OR SO AGO. WE GOT HIM OUT THROUGH DIPLOMATIC CHANNELS, BUT HE WI WEAK AND WITHOUT FOOD.
THAT'S IT FOR NOW AS I MUST TAKE TIME TO UNPACK, AND WITH THE MOVE MY BACK GAVE OUT SO I AM EVER SO SLOWLY GETTING TO EACH BOX IN PAIN. IT WILL TAKE A WHILE AND I HAVE TO GET UP AND OPERATIONAL IN THE OFFICE SETUP RIGHT AWAY TO BE ABLE TO PROCESS WHAT IS COMING. I PROMISE TO HAVE MUCH MORE INFORMATION BY THE WEEKEND ON MANY THINGS AS BY THAT TIME THIS GAG ORDER ON ME SHOULD BE LIFTED AND I CAN TELL SOME THINGS.
AGAIN A BIG THANKS FOR YOUR HELP AND SUPPORT OF OUR EFFORTS. I DO PROMISE THAT OUR WORLD IS ABOUT TO CHANGE IN A HUGE WAY.


text:
Home » Celebrities
Alexis Ren Wiki: Age, Net Worth, Boyfriend, Diet, Workout, Instagram & Facts to Know
By: Dontei Wynter - Published: January 13, 2017 at 5:57 pm
Roy Rochlin/ Stringer/ Getty
Where is Alexis Ren and what has she been up to these days? Well, if you're looking for the Instagram bikini model, then look no further than The Chainsmokers' "Paris" music video! That's right! The Chainsmokers' Instagram account gave a sneak peek of their new song and they're excited for fans to tune in and tell them what they think. But there's a familiar face in the new "Paris" music video: Alexis Ren! If you want to know more about Ren and The Chainsmokers, then have a look at our Alexis Ren wiki.
It appears that 2017 is the year of music, or at least expected music. The Chainsmokers just released their newest single, "Paris" and if it's anything like their other songs, then we can expect good reviews from it.
Since the music video was released, fans have been Googling terms such as "The Chainsmokers diet," "The Chainsmokers Paris girl," and "The Chainsmokers boyfriend." And because of Ren's connection to The Chainsmokers and Jay Alvarez (Ren's ex-boyfriend), "The Chainsmokers boyfriend" and "Jay Alvarez" have been trending, as well. But, luckily for you, we have everything you need to know about Alexis Ren right here.
Who is Alexis Ren?
Alexis Renee Gaylord was born on November 23, 1996 in Santa Monica, California, to parents Cynthia Gaylord and Frank Gaylord. She is famous for being an Instagram bikini model and has been in the business of modeling since she was just 13.
She was Discovered at an Early Age
Ren got discovered by scouts at a Los Angeles mall when she was just 13 years old, and she modeled in Japan when she was 14. She didn't become an Internet fan favorite until she was 15—and she's now 20! When she posed on Tumblr in a black bikini for photographer, Lucas Passmore, she instantly became famous. She has traveled the world and has been to place such as Ibiza, Burning Man, and Bali. These exotic locations help keep her 7.0 million Instagram followers wishing they were on a beach with her! To her fans, Ren is the definition of "goals" and every girl wishes they had her life. (We'll be honest, we kind of wish we had it too!) Ren has worked for names such as Calvin Klein, L'Oreal, and Express.
"I started posting on my social media super-young," Alexis said in an interview with The Cut. "I didn't really understand what it was. When I was about 15, I started posting behind the scenes of shoots, little things of me holding up the color corrector, cute things, me in a bikini. It was just all innocent and fun, and I saw people really starting to respond to it."
Alexis Ren's net worth is hard to determine at this time, but she's definitely doing well for herself and has been since before she could even drive! Many of her followers have suggested that the young model doesn't pay for her trips herself, alluding to her being a kept woman.
Easy baby
A photo posted by ALEXIS REN (@alexisren) on Dec 23, 2016 at 12:06pm PST
"I want to show that I make my own money, and I pay for my own things, and that's how I've always been since I was 15," she said. "It just makes me laugh. I laugh. I find it so amusing that people actually think that."
Gigi Hadid is Her Role Model
When it comes to beauty, there's no better role model than famed Victoria's Secret Angel, Gigi Hadid.
"I look up to Gigi Hadid," said Ren. "I love where she's taken herself, I love what brands she's working on. I respect her because I understand … I mean, girls like her open the doors for girls like me. So all I can do is thank her."
She was Involved with Another Instagram Model
Ren was romantically linked to former boyfriend, Jay Alvarez before they broke up last year. The rumors were getting out of hand and between the cryptic Twitter messages and cold unfollowings, fans were starting to connect the dots.
When in doubt, wear red. #AlexisRenxMissguided @missguided
A photo posted by ALEXIS REN (@alexisren) on Nov 22, 2016 at 7:06am PST
"I am too full of life to be half loved," Alexis wrote on Twitter on August 18, confirming the news of the break-up.
The Chainsmokers Love Her!
The Chainsmokers have always been a fan of Ren and it's no surprise that she was sporting a bikini in their "Paris" music video. They had nothing but praise for her when they named her the top girl to watch on Instagram, in Crave magazine. "By far the dopest of all the chicks, she pretty much represents what we all want out of life: a dope relationship, smiles and a cool, hot ass gf," said The Chainsmokers about Ren.
"The Chainsmokers workout" has also been trending, since the band produces some of the best songs to workout to. Ren works out daily (clearly) and gets at least 20 minutes of sun, to maintain her sweet tan. Alexis Ren's age may only be 20, but she's done a lot for herself in a short period of time and we can only hope to see Ren and Hadid sharing a runway very soon!
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redpajama_set_name: RedPajamaCommonCrawl


I've known Emrys for over 3 years due to his efforts at the core to successes of MozFest in 2016, 2017, and 2018. What was only a brief connection in 2016, but the undeniably nice way in which he communicated to me, a volunteer, stuck in my mind. When I later wrangled in 2017 & 2018 his supportive nature shined. Not only in mentoring youth, but openly sharing a tireless comradery and focus of the wrangling experience to his fellow peers. Emrys extolls Mozilla's community spirit.


22 years have come and gone...our lives have been lived, both very different than we expected. There has been heart break, joy, impatience, sorrow, and hope.
She cut my hair for me, broke up with a boy for me (at Disneyland no less....apparently for him it wasn't the happiest place on earth.) What have I done for her? well some computer stuff way back when....I've tried to listen when I could...be a friend.
The past few years for her have been a test. Living day to day, trying to find God in the midst of destruction, frustration and pain. Trying to figure out how to walk through the muck and mire of broken relationships, and learning to shake off the past, the heaviness and re-learn to walk in freedom once again.
And for that, I am grateful. I am thankful, that even though there was an unexpected turn in her life...she doesn't blame God, she still seeks Him. She doesn't want to hold hands with bitterness the rest of her life, but wants to choose to live in forgiveness. And may God walk closely with her, as she strives to move forward.


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Tree-killing beetle confirmed in Johnson County, Kan.
Emergency quarantine enacted for emerald ash borer
Updated: 7:04 PM CDT Jul 15, 2013
A beetle that has killed millions of ash trees in the eastern U.S. and parts of the South has been detected in Johnson County.The Kansas Department of Agriculture said Monday that emerald ash borer was found in a tree near the Johnson County landfill. Trees there were being inspected after the presence of emerald ash borer was found last summer in Wyandotte County.The U.S. Department of Agriculture confirmed the beetle's presence in Johnson County on July 11.Ash trees become infested when adult beetles lay eggs on the bark, leading to larvae that bore into the tree.Kansas has enacted an emergency quarantine for Johnson County, similar to quarantine in place in Wyandotte County, to prevent further spread of emerald ash borer in Kansas.
KANSAS CITY, Kan. —
A beetle that has killed millions of ash trees in the eastern U.S. and parts of the South has been detected in Johnson County.
The Kansas Department of Agriculture said Monday that emerald ash borer was found in a tree near the Johnson County landfill. Trees there were being inspected after the presence of emerald ash borer was found last summer in Wyandotte County.
The U.S. Department of Agriculture confirmed the beetle's presence in Johnson County on July 11.
Ash trees become infested when adult beetles lay eggs on the bark, leading to larvae that bore into the tree.
Kansas has enacted an emergency quarantine for Johnson County, similar to quarantine in place in Wyandotte County, to prevent further spread of emerald ash borer in Kansas.


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