Merge branch 'develop' into io_wallclocktime

CHANGELOG.md

@@ -1,5 +1,10 @@
 # CHANGELOG of Wannier90
 
+### New postw90 features, optimizations and new post-processing codes
+
+- Calculation of spin Hall conductivity according to the formalism given in Junfeng Qiao, Jiaqi Zhou, Zhe Yuan and Weisheng Zhao, PRB 98, 214402 (2018) + example 29,30 + test suites [[#264]](https://github.com/wannier-developers/wannier90/pull/264)
+
+
 ## v3.0.0 (27th February 2019)
 
 ### New Wannier90 features
@@ -71,7 +76,7 @@ Moreover, it generates a new file `seedname_band.labelinfo.dat` with information
 
 - Improvements to the Wigner-Seitz detection routines [[#117]](https://github.com/wannier-developers/wannier90/pull/117) [[#109]](https://github.com/wannier-developers/wannier90/pull/109)
 
-- Fix berry_task check for morb, and add check for kpoint_path block in parameters
+- Fix berry_task check for morb, and add check for kpoint_path block in parameters [[#258]](https://github.com/wannier-developers/wannier90/pull/258)
 
 - Use 64 bit integer in io_wallclocktime [[#266]](https://github.com/wannier-developers/wannier90/pull/266)
 

doc/solution_booklet/Example18.tex

@@ -52,14 +52,14 @@ \subsection*{Berry curvature plots}
 \begin{figure}[b!]
 \centering
 \includegraphics[width=0.5\columnwidth]{figure/example18/Fe_Fermi_surface+Berry_phase.png}
-\caption{(Colour online) Calculated total Berry curvature $−\Omega_z(\bfk)$ in the plane $k_y=0$ (note log scale). Intersections of the Fermi surface
+\caption{(Colour online) Calculated total Berry curvature $-\Omega_z(\bfk)$ in the plane $k_y=0$ (note log scale). Intersections of the Fermi surface
 with this plane are shown.}\label{fig18.3}
 \end{figure}
 
 \subsection*{Anomalous Hall conductivity}
 
 \begin{itemize}
-	\item {\it AHC converges rather slowly with k-point sampling, and a 25 × 25 × 25 does not yield a well-converged value.
+	\item {\it AHC converges rather slowly with k-point sampling, and a $25 \times 25 \times 25$ does not yield a well-converged value.
 	Compare the converged AHC value with those obtained in Refs.~\onlinecite{PhysRevB74} and \onlinecite{PhysRevLett92}.}
 
 	The {\it x,y,z}-components of the AHC for a $25\times25\times25$ BZ mesh are shown in the snippet below. The converged result reported in Refs.~\onlinecite{PhysRevB74} and \onlinecite{PhysRevLett92} for the \textit{z}-component is 756.76 ($(\Omega \mathrm{cm})^{-1}$). Hence, a $25\times25\times25$ BZ mesh clearly gives a very inaccurate value ($\sim 36.4\%$ error). Even with adaptive refinement the error is still very large ($\sim 31.7\%$). It is worth to note that the adaptive refinement slightly breaks the symmetry and gives non-zero values for the \textit{x}-component and \textit{y}-component, although these are opposite in sign.  

doc/solution_booklet/Example29.tex

@@ -0,0 +1,181 @@
+\section{Platinum---Spin Hall conductivity}
+\label{sec29:PtSHC}
+
+\begin{itemize}
+	\item Outline: {\it Calculate spin Hall conductivity (SHC) and 
+			plot Berry curvature-like term  
+			of fcc Pt considering spin-orbit coupling. 
+			To gain a better understanding of this example, 
+			it is suggested to read Ref.~\onlinecite{qiao-prb2018} for a detailed 
+			description of the theory and Ch.~12.5 of the User Guide.}
+\end{itemize}
+
+\begin{itemize}
+	\item[1-6] {\it Compute the MLWFs, spin Hall conductivity and 
+		{\tt kpath}, {\tt kslice} plots.} 
+\end{itemize}
+
+\subsection*{Spin Hall conductivity}
+
+\begin{itemize}
+	\item {\it SHC converges rather slowly with k-point sampling, and a $25 \times 25 \times 25$ kmesh does not yield a well-converged value.
+	To get a converged SHC value, increase the density of kmesh and 
+	then compare the converged result with those obtained in 
+	Refs.~\onlinecite{qiao-prb2018} and \onlinecite{guo-prl2008}.}
+
+	The file {\tt Pt-shc-fermiscan.dat} contains the calculated SHC. 
+	The SHC for a $25\times25\times25$ kmesh are shown in the snippet below. 
+
+\begin{tcolorbox}[title=$25\times25\times25$ kmesh,sharp corners,boxrule=0.5pt]
+{\small
+\begin{verbatim}
+#No.   Fermi energy(eV)   SHC((hbar/e)*S/cm)
+   1     6.000000    0.00000000E+00
+...
+ 120    17.900000    0.17230482E+04
+ 121    18.000000    0.17054542E+04
+...
+ 201    26.000000    0.22665760E+03
+\end{verbatim}
+}
+\end{tcolorbox}
+
+The calculated Fermi energy obtained from {\tt Quantum ESPRESSO} is $17.9919$ eV. 
+It may vary among different calculations due to the differences between versions of {\tt Quantum ESPRESSO} or compilers, 
+and these may lead to deviations from the following results. 
+However, the difference should be acceptable and the calculated SHC should be essentially the same. 
+
+The SHC at the Fermi energy is 1705 $(\hbar/e)\mathrm{S/cm}$. 
+The converged results reported in Refs.~\onlinecite{qiao-prb2018} 
+and \onlinecite{guo-prl2008} are around 2200 $(\hbar/e)\mathrm{S/cm}$. 
+Hence, a $25\times25\times25$ kmesh clearly gives an inaccurate value ($\sim 22.5\%$ error).
+
+Since these are quite demanding calculations, we only report the 
+value of the SHC for a $100\times100\times100$ kmesh (see snippet below). 
+The value for the SHC at Fermi energy is 2207 $(\hbar/e)\mathrm{S/cm}$, which is 
+in much closer agreement with the converged result from 
+Refs.~\onlinecite{qiao-prb2018} and \onlinecite{guo-prl2008}.
+
+\begin{tcolorbox}[title=$100\times100\times100$ kmesh,sharp corners,boxrule=0.5pt]
+{\small
+\begin{verbatim}
+#No.   Fermi energy(eV)   SHC((hbar/e)*S/cm)
+   1     6.000000    0.00000000E+00
+...
+ 120    17.900000    0.21899191E+04
+ 121    18.000000    0.22066678E+04
+...
+ 201    26.000000    0.24919920E+03
+\end{verbatim}
+}
+\end{tcolorbox}
+
+\item To complete the previous discussions, we also 
+compare the Fermi energy scan plots of the two calculations as 
+shown in the \Fig{fig29.3}. 
+\begin{figure}[!htb]
+\centering
+\includegraphics[width=.8\columnwidth]{figure/example29/pt_shc_kmesh.pdf}
+\caption{Fermi energy scan plots for calculations 
+	with $25\times25\times25$ kmesh and $100\times100\times100$ kmesh.}
+\label{fig29.3}
+\end{figure}
+
+\item The {\tt seedname.wpout} will print the percentage of $k$-points which 
+have been calculated at the moment, as well as the corresponding calculation time, as 
+shown in the following snippet. 
+
+\begin{tcolorbox}[title=Pt.wpout,sharp corners,boxrule=0.5pt]
+{\small
+\begin{verbatim}
+ Properties calculated in module  b e r r y
+ ------------------------------------------
+
+   * Spin Hall Conductivity
+
+     Fermi energy scan
+ 
+ Calculation started
+ -------------------------------
+   k-points       wall      diff
+  calculated      time      time
+  ----------      ----      ----
+       0%          0.0       0.0
+      10%         22.7      22.7
+      20%         36.5      13.8
+      30%         50.4      14.0
+      40%         64.4      14.0
+      50%         78.4      14.0
+      60%         92.5      14.1
+      70%        106.5      14.0
+      80%        120.4      13.9
+      90%        134.2      13.8
+     100%        147.9      13.7
+
+
+ Interpolation grid: 25 25 25
+
+ Using adaptive smearing
+       adptive smearing prefactor    1.414
+       adptive smearing max width    1.000 eV
+       
+\end{verbatim}
+}
+\end{tcolorbox}
+This might be helpful as you can roughly 
+estimate the total computational time 
+of your calculation, or it might give credence to the code that it is actually functioning :). 
+Note this report is merely based on the ``root'' computation node. It is accurate if the {\tt postw90} is run in serial, or the load on each node is balanced if running in parallel. However, the estimation is rough if loads are not balanced among nodes. This may happen if the performance of nodes in your cluster are not identical, or adaptive kmesh refinements are triggered so some nodes may compute much more $k$-points than others. 
+Besides, if you are careful enough, you may find the diff time of 10\% is much larger than later ones. This 
+is caused by some done-once-and-for-all computations carried out at the beginning, thus 
+later computations are much faster. 
+\end{itemize}
+
+%\clearpage
+\subsection*{Berry curvature-like term plots}
+\begin{itemize}
+	\item {\it The band-projected Berry curvature-like term $\Omega_{n,\alpha\beta}^{\text{spin} \gamma}({\bm k})$ 
+		is defined as Eq.~(12.22) in the User Guide.}
+	{\it Plot the band structure of Pt and color it 
+		by the magnitude of its band-projected Berry curvature-like term $\Omega_{n,xy}^{\text{spin}z}(\bm k)$, 
+		and plot the k-resolved Berry curvature-like term $\Omega_{xy}^{\text{spin}z}(\bm k)$ along the 
+		same path in the BZ. }
+
+	With Fermi energy set as 17.9919 eV we obtain the energy bands colored by the 
+	$\Omega_{n,\alpha\beta}^{\text{spin} \gamma}({\bm k})$ 
+	and the $k$-resolved Berry curvature-like term 
+	$\Omega_{xy}^{\text{spin}z}(\bm k)$ along high-symmetry lines 
+	as shown in \Fig{fig29.1}, which contains two plots calculated with 
+	different fixed smearing width.
+\end{itemize}
+
+\begin{figure}[htb!]
+	\centering
+	\subfloat[With fixed smearing width of 1 eV]{\includegraphics[width=0.45\columnwidth]{figure/example29/Pt-bands+shc_1.pdf}}\qquad
+	\subfloat[With fixed smearing width of 0.05 eV]{\includegraphics[width=0.45\columnwidth]{figure/example29/Pt-bands+shc_0_05.pdf}}
+	\caption{Top panels: Band structure of Pt along symmetry lines W-L-$\Gamma$-X-W-$\Gamma$, colored by
+		the $\Omega_{n,xy}^{\text{spin}z}({\bm k})$. 
+		Bottom panels: $k$-resolved Berry curvature-like term $\Omega_{xy}^{\text{spin}z}(\bm k)$ along the symmetry lines.}
+	\label{fig29.1}
+\end{figure}
+%\clearpage
+
+\begin{itemize}
+	\item {\it Combine the plot of the Fermi lines on the $(k_x,k_y)$ plane with a heatmap plot of the Berry curvature-like term of spin Hall conductivity.}
+
+	The plots of the Fermi lines with a heatmap of $\Omega_{xy}^{\text{spin}z}(k_x,k_y,0)$ are shown in \Fig{fig29.2}.
+\end{itemize}
+
+\begin{figure}[htb!]
+	\centering
+	\subfloat[With fixed smearing width of 1 eV]{\includegraphics[width=0.45\columnwidth]{figure/example29/Pt-kslice-shc_1.pdf}}\qquad
+	\subfloat[With fixed smearing width of 0.05 eV]{\includegraphics[width=0.45\columnwidth]{figure/example29/Pt-kslice-shc_0_05.pdf}}
+	\caption{Calculated $k$-resolved Berry curvature-like term 
+		$\Omega_{xy}^{\text{spin}z}(\bm k)$ in the plane $k_z=0$ 
+		(note the magnitude of $\Omega_{xy}^{\text{spin}z}(\bm k)$ is in log scale). 
+		Intersections of the Fermi surface
+		with this plane are shown as black lines.}
+	\label{fig29.2}
+\end{figure}
+
+

doc/solution_booklet/Example30.tex

@@ -0,0 +1,69 @@
+\section{Gallium Arsenide---Frequency-dependent spin Hall conductivity}
+\label{sec30:GaAsSHC}
+
+\begin{itemize}
+	\item Outline: {\it Calculate the alternating current (ac) spin Hall conductivity
+	of gallium arsenide considering spin-orbit coupling. 
+	To gain a better understanding of this example, 
+	it is suggested to read Ref.~\onlinecite{qiao-prb2018} for a detailed 
+	description of the theory and Ch.~12.5 of the User Guide.}
+\end{itemize}
+
+\begin{itemize}
+	\item[1-6] {\it Compute the MLWFs and compute the ac spin Hall conductivity.} 
+\end{itemize}
+
+\subsection*{ac spin Hall conductivity}
+
+\begin{itemize}
+	\item {\it The ac SHC of GaAs converges rather slowly with $k$-point sampling, and a $100 \times 100 \times 100$ kmesh does not yield a well-converged value.
+	To get a converged SHC value, increase the density of kmesh and then compare the converged result with those obtained in Refs.~\onlinecite{qiao-prb2018}.}
+
+	The file {\tt GaAs-shc-freqscan.dat} contains the calculated ac SHC. 
+	The snippet below shows a calculated result with 
+	$100\times100\times100$ kmesh, 
+	a fixed smearing width of 0.05~eV and no scissors shift applied.
+
+\begin{tcolorbox}[title=$100\times100\times100$ kmesh,sharp corners,boxrule=0.5pt]
+{\small
+\begin{verbatim}
+#No.   Frequency(eV)   Re(sigma)((hbar/e)*S/cm)   Im(sigma)((hbar/e)*S/cm)
+   1     0.000000    -0.68114601E+00    0.00000000E+00
+...
+ 801     8.000000    -0.39471936E+01   -0.29928198E+02
+\end{verbatim}
+}
+\end{tcolorbox}
+
+The ac SHC is plotted as \Fig{fig30.1}.
+\begin{figure}[htb!]
+\centering
+\includegraphics[width=.8\columnwidth]{figure/example30/gaas_freqscan_100kpt.pdf}
+\caption{Frequency scan plot for GaAs ac SHC, using 
+	a low kmesh of $100\times100\times100$.}
+\label{fig30.1}
+\end{figure}
+
+\item If further increasing the density of kmesh to 
+$250\times250\times250$, and using the adaptive smearing, 
+a nice converged plot could be produced as \Fig{fig30.2}. 
+Note that by using keywords \smallskip {\tt
+	\begin{quote}
+		shc\_bandshift = true
+
+		shc\_bandshift\_firstband = 9
+
+		shc\_bandshift\_energyshift = 1.117
+\end{quote} }
+a scissors shift of 1.117~eV is applied. 
+\Fig{fig30.2} can be viewed as \Fig{fig30.1} translated by 
+$\sim1$~eV along the horizontal axis. 
+\begin{figure}[!htb]
+\centering
+\includegraphics[width=0.8\columnwidth]{figure/example30/gaas_freqscan.pdf}
+\caption{Frequency scan plots for GaAs ac SHC, using 
+	a dense kmesh of $250\times250\times250$. 
+Two kinds of smearing are compared.}
+\label{fig30.2}
+\end{figure}
+\end{itemize}

doc/solution_booklet/about.tex

@@ -1,9 +1,9 @@
 \section*{About this booklet}
 \addcontentsline{toc}{section}{About this booklet}
-This solution manual consists of \numexamples{} sections, each containing the solutions, in the form of plots, tabs, and texts, to the corresponding example in the \Wannier{} \version tutorial! For each example, only the outline and key questions from the tutorial are reported here.   
+This solution manual consists of \numexamples{} sections, each containing the solutions, in the form of plots, tabs, and texts, to the corresponding example in the \Wannier{} \version{} tutorial! For each example, only the outline and key questions from the tutorial are reported here.   
  All of the \Wannier{} input files have been provided. From example 5 onwards, input files for the pwscf interface (\url{http://www.
-quantum-espresso.org}) to \Wannier{} have also been provided. You will need a recent working version of the \QE{} package (\texttt{v6.2} and above), to run these examples. In particular, you will need \texttt{pw.x} and \texttt{pw2wannier90.x}, as explained in the \Wannier{} \version tutorial.
-Please visit \url{http://www.quantum-espresso.org} to download the package and follow the instruction on the website for installation. Further details on how to run the calculations for each example may be found in the corresponding section of the \Wannier{} \version tutorial.
+quantum-espresso.org}) to \Wannier{} have also been provided. You will need a recent working version of the \QE{} package (\texttt{v6.2} and above), to run these examples. In particular, you will need \texttt{pw.x} and \texttt{pw2wannier90.x}, as explained in the \Wannier{} \version{} tutorial.
+Please visit \url{http://www.quantum-espresso.org} to download the package and follow the instruction on the website for installation. Further details on how to run the calculations for each example may be found in the corresponding section of the \Wannier{} \version{} tutorial.
 There are interfaces to a number of other electronic structure codes including: \abinit{} (\url{http://www.
 abinit.org}), \fleur{} (\url{http://www.flapw.de}), \OpenMX{} (\url{http://www.openmx-square.org/}), \GPAW{} (\url{https://wiki.fysik.dtu.dk/gpaw/}), \VASP{} (\url{http://www.vasp.at}), and \Wien{} (\url{http://www.wien2k.at}). 
 

doc/solution_booklet/biblio.bib

@@ -98,4 +98,37 @@ @article{bilbaocrystserver
 volume = "62",
 number = "2",
 pages = "115--128"
+}
+
+@article{qiao-prb2018,
+	title = {Calculation of intrinsic spin Hall conduc
+	tivity by Wannier interpolation},
+	author = {Qiao, Junfeng and Zhou, Jiaqi and Yuan, 
+	Zhe and Zhao, Weisheng},
+	journal = {Phys. Rev. B},
+	volume = {98},
+	issue = {21},
+	pages = {214402},
+	numpages = {10},
+	year = {2018},
+	month = {Dec},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevB.98.214402},
+	url = {https://link.aps.org/doi/10.1103/PhysRevB.9
+	8.214402}
+}
+
+@article{guo-prl2008,
+	title = {Intrinsic Spin Hall Effect in Platinum: First-Principles Calculations},
+	author = {Guo, G. Y. and Murakami, S. and Chen, T.-W. and Nagaosa, N.},
+	journal = {Phys. Rev. Lett.},
+	volume = {100},
+	issue = {9},
+	pages = {096401},
+	numpages = {4},
+	year = {2008},
+	month = {Mar},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevLett.100.096401},
+	url = {https://link.aps.org/doi/10.1103/PhysRevLett.100.096401}
 }

doc/solution_booklet/newcommands.tex

@@ -5,7 +5,7 @@
 \newcommand{\authorname}{Valerio Vitale}
 %\newcommand{\date}{\today} % Date of the first submission
 
-\newcommand{\numexamples}{$22$}
+\newcommand{\numexamples}{$24$}
 
 % ABBREVIATIONS
 \newcommand{\eg}{e.g.}

doc/solution_booklet/solution_booklet.tex

@@ -51,6 +51,8 @@
 \include{Example20}
 \include{Example21}
 \include{Example22}
+\include{Example29}
+\include{Example30}
 
 \cleardoublepage