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add quotes to SCDM parameter in pw2wannier90 input files
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qiaojunfeng committed Jan 5, 2020
1 parent b476df3 commit 13fede5
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10 changes: 6 additions & 4 deletions doc/tutorial/tutorial.tex
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Expand Up @@ -24,6 +24,8 @@
%\let\oldundercore=\_
%\def\_{\oldunderscore}

\usepackage{textcomp}

% set fancy headings

\pagestyle{fancy}
Expand Down Expand Up @@ -2906,7 +2908,7 @@ \subsection*{Shift current $\sigma^{abc}$}
\begin{itemize}
\item[1]{Valence bands: In this case we will compute 4 localized WFs corresponding to the 4 valence bands of Silicon. These 4 bands constitute a manifold that is separated in energy from other bands. In this case the columns of the density matrix are already localized in real space and no extra parameter is required.}
\begin{enumerate}
\item Copy the input files {\tt si.scf, si\_4bands.nscf} and {\tt si.pw2wan} from the {\tt input\_files directory} into the {\tt isolated} folder
\item Copy the input files {\tt si.scf} and {\tt si\_4bands.nscf} from the {\tt input\_files} directory into the {\tt isolated} folder
\item Run \pwscf\ to obtain the ground state charge of bulk Silicon. \\
{\tt pw.x < si.scf > scf.out}

Expand All @@ -2933,7 +2935,7 @@ \subsection*{Shift current $\sigma^{abc}$}
\item[2]{Valence bands + conduction bands: In this case we will compute 8 localized WFs corresponding to the 4 valence bands and 4 low-lying conduction bands. Here, we don't have a separate manifold, since the conduction bands are entangled with other high-energy bands and the columns of the density matrix are not exponentially localized by construction. A modified density matrix is required in this case\cite{LinLin-ArXiv2017}, and it is defined as: $$P(\mathbf{r},\mathbf{r}') = \sum_{n,\mathbf{k}} \psi_{n\mathbf{k}}(\mathbf{r})f(\varepsilon_{n,\mathbf{k}})\psi_{n\mathbf{k}}^\ast(\mathbf{r}'),$$
where $\psi_{n\mathbf{k}}$ and $\varepsilon_{n,\mathbf{k}}$ are the energy eigestates and eigenvalues from the first-principle calculation respectively. The function $f(\varepsilon_{n,\mathbf{k}})$ contains two free parameters $\mu$ and $\sigma$ and is defined as a complementary error function: $$f(\varepsilon_{n,\mathbf{k}}) = \frac{1}{2}\mathrm{erfc}\left(\frac{\varepsilon_{n,\mathbf{k}} - \mu}{\sigma}\right).$$ }
\begin{enumerate}
\item Copy the input files {\tt si.scf, si\_12bands.nscf} and {\tt si.pw2wan} from the {\tt input\_files} folder into the {\tt erfc} folder
\item Copy the input files {\tt si.scf} and {\tt si\_12bands.nscf} from the {\tt input\_files} folder into the {\tt erfc} folder
\item Run \pwscf\ to obtain the ground state charge of bulk Silicon. \\
{\tt pw.x < si.scf > scf.out}

Expand All @@ -2958,7 +2960,7 @@ \subsection*{Shift current $\sigma^{abc}$}
\end{enumerate}
\item[3]{Conduction bands only: In this case we will compute 4 localized WFs corresponding to the 4 low-lying conduction bands only. As for the previous point, we need to define a modified density matrix\cite{LinLin-ArXiv2017}. Since we are only interested in a subset of the conduction states, within a bounded energy region, a good choice for $f(\varepsilon_{n,\mathbf{k}})$ is: $$f(\varepsilon_{n,\mathbf{k}}) = \exp\left(-\frac{(\varepsilon_{n,\mathbf{k}} - \mu)^2}{\sigma^2}\right).$$}
\begin{enumerate}
\item Copy the input files {\tt si.scf, si\_12bands.nscf} and {\tt si.pw2wan} from the {\tt input\_files directory} into the {\tt gaussian} folder
\item Copy the input files {\tt si.scf} and {\tt si\_12bands.nscf} from the {\tt input\_files} directory into the {\tt gaussian} folder
\item Run \pwscf\ to obtain the ground state charge of bulk Silicon. \\
{\tt pw.x < si.scf > scf.out}

Expand Down Expand Up @@ -3640,7 +3642,7 @@ \subsection*{Notes}
\item Open {\tt W.pw2wan} and append the following lines
{\tt

scdm\_entanglement = erfc
scdm\_entanglement = \textquotesingle erfc\textquotesingle

scdm\_mu = 20.0169

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2 changes: 1 addition & 1 deletion examples/example27/erfc/si.pw2wan
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Expand Up @@ -7,7 +7,7 @@
write_unk = .true.
! SCDM keywords
scdm_proj = true
scdm_entanglement = erfc
scdm_entanglement = 'erfc'
scdm_mu = 10
scdm_sigma = 4
/
2 changes: 1 addition & 1 deletion examples/example27/gaussian/si.pw2wan
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Expand Up @@ -7,7 +7,7 @@
write_unk = .true.
! SCDM keywords
scdm_proj = true
scdm_entanglement = gaussian
scdm_entanglement = 'gaussian'
scdm_mu = 12.5
scdm_sigma = 2
/
2 changes: 1 addition & 1 deletion examples/example27/isolated/si.pw2wan
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Expand Up @@ -7,5 +7,5 @@
write_unk = .true.
! SCDM keywords
scdm_proj = true
scdm_entanglement = isolated
scdm_entanglement = 'isolated'
/

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