Skip to content

Commit

Permalink
Included small modifications on kdotp option into the documentation
Browse files Browse the repository at this point in the history 
Included new example33 for kdotp option. It contains files for QE calculation for BC2N,
a pw2wann file for postprocessing, a .win file for W90, and a python script for postprocessing plot of kdotp
bands versus W90 bands. Included brief explanation in README file. Included also pseudopotentials
into pseudo folder for B, C and N.

Noticed that there was no brief explanation for example32 in README file, included
info from tutorial title of that example, please check
  • Loading branch information
@Julen-ia
Julen-ia committed Jul 17, 2020
1 parent 153b584 commit 69be32f
Show file tree
Hide file tree
Showing 10 changed files with 28,632 additions and 10 deletions.
33 changes: 23 additions & 10 deletions doc/user_guide/berry.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -335,18 +335,18 @@ \section{{\tt berry\_task=sc}: shift current}

The shift-current contribution to the second-order response
is characterized by a frequency-dependent third-rank tensor~\cite{sipe-prb00}
\begin{equation}
\begin{equation}\label{eq:shiftcurrent}
\begin{split}
\sigma^{abc}(0;\omega,-\omega)=&-\frac{i\pi e^3}{4\hbar^2 \Omega_c N_k}
\sum_{\bm{k}} \sum_{n,m}f_{nm}
\sum_{\bm{k}} \sum_{n,m}(f_{n\bm{k}}-f_{m\bm{k}})
\times
\left(r^b_{ mn}(\bm{k})r^{c;a}_{nm}(\bm{k}) + r^c_{mn}(\bm{k})r^{b;a}_{ nm}(\bm{k})\right)\\
&\times \left[\delta(\omega_{mn\bm{k}}-\omega)+\delta(\omega_{nm\bm{k}}-\omega)\right],
\end{split}
\end{equation}
where $a,b,c$ are spatial indexes
and $\omega_{mn\bm{k}}=(\epsilon_{n\bm{k}}-\epsilon_{m\bm{k}})/\hbar$.
The above expression involves
The expression in Eq.~\ref{eq:shiftcurrent} involves
the dipole matrix element
\begin{equation}
\label{eq:r}
Expand All @@ -364,8 +364,19 @@ \section{{\tt berry\_task=sc}: shift current}
above expression is technically challenging
due to the presence of an extra $k$-space derivative.
The implementation in {\tt wannier90} follows the scheme proposed in Ref.~\cite{ibanez-azpiroz_ab_2018},
please cite this reference when publishing shift-current results using this method.
following the spirit of the Wannier-interpolation
method for calculating the AHC~\cite{wang-prb06} by reformulating $k\cdot p$
perturbation theory within the subspace of wannierized bands.
This strategy inherits the practical advantages of the sum-over-states
approach, but without introducing the truncation errors usually associated with this procedure~\cite{sipe-prb00}.

As in the case of the optical conductivity, a broadened delta function can be
applied in Eq.~\ref{eq:shiftcurrent} by means of the parameter
$\eta$ (see Eq.~\ref{eq:lorentzian}) using the keyword
{\tt[kubo\_]smr\_fixed\_en\_width}, and adaptive smearing can
be employed using the keyword {\tt [kubo\_]adpt\_smr}.

Please cite Ref.~\cite{ibanez-azpiroz_ab_2018} when publishing shift-current results using this method.

\section{{\tt berry\_task=kdotp}: $k\cdot p$ coefficients}
\label{sec:kdotp}
Expand Down Expand Up @@ -437,13 +448,11 @@ \section{{\tt berry\_task=kdotp}: $k\cdot p$ coefficients}
Collecting terms in \eq{pert-exp} up to second order in $k$
we get
\beq\label{eq:Htilde}
\begin{split}
& \tilde{H}_{mm'}(\bm{k}) =
\overline{H}_{mm'} + \sum_{a} \left(\overline{H}_{a}\right)_{mm'}k_{a}\\
& + \dfrac{1}{2}\sum_{a,b}\left[
\tilde{H}_{mm'}(\bm{k}) =
\overline{H}_{mm'} + \sum_{a} \left(\overline{H}_{a}\right)_{mm'}k_{a}
+ \dfrac{1}{2}\sum_{a,b}\left[
\left(\overline{H}_{ab}\right)_{mm'} + \left({T}_{ab}\right)_{mm'}
\right]k_{a}k_{b}+ \mathcal{O}(k^{3}),
\end{split}
\eeq
where $m,m'\in A$ and we have defined the virtual-transition matrix
\beq\label{eq:Tab}
Expand All @@ -462,7 +471,11 @@ \section{{\tt berry\_task=kdotp}: $k\cdot p$ coefficients}


The implementation in {\tt wannier90} follows the scheme proposed in Ref.~\cite{ibanez-azpiroz-ArXiv2019},
please cite this reference when publishing $k\cdot p$ results using this method.
and outputs $\overline{H}_{mm'}$ in {\tt seedname-kdotp\_0.dat},
$\left(\overline{H}_{a}\right)_{mm'}$ in {\tt seedname-kdotp\_1.dat}, and
$\left[\left(\overline{H}_{ab}\right)_{mm'} + \left({T}_{ab}\right)_{mm'}\right]/2$ in {\tt seedname-kdotp\_2.dat}.

Please cite Ref.~\cite{ibanez-azpiroz-ArXiv2019} when publishing $k\cdot p$ results using this method.

\section{Needed matrix elements}

Expand Down
4 changes: 4 additions & 0 deletions examples/README
View file
Original file line number Diff line number Diff line change
Expand Up @@ -72,3 +72,7 @@ example29: Platinum - Berry curvature-like term and spin Hall conductivity
example30: Gallium Arsenide - ac spin Hall conductivity

example31: Platinum - Selected columns of density matrix algorithm for spinor wavefunctions

example32: Tungsten - SCDM parameters from projectability

example33: BC2N - Expansion coefficients for kdotp bands
141 changes: 141 additions & 0 deletions examples/example33/bc2n.nscf
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,141 @@
&control
verbosity = 'high'
calculation = 'nscf'
wf_collect = .true.
restart_mode = 'from_scratch'
prefix = 'bc2n'
pseudo_dir = '../../pseudo/'
outdir = './'
/
&system
ibrav=0,
celldm(1) = 1.8897261245650618
nat= 4,
ntyp= 3,
ecutwfc=70,
degauss=0.05,
occupations="smearing", smearing="mp",
nbnd = 40
/
&electrons
mixing_beta = 0.1
conv_thr = 1.0d-7
electron_maxstep = 1000
/
&IONS
/
ATOMIC_SPECIES
B 74.000 B.pbe-n-kjpaw_psl.0.1.UPF
C 16.000 C.pbe-n-kjpaw_psl.0.1.UPF
N 18.000 N.pbe-n-kjpaw_psl.0.1.UPF
CELL_PARAMETERS
2.466 0.000000000 0.000000000
0.000000000 20.0 0.000000000
0.000000000 0.000000000 4.323
ATOMIC_POSITIONS alat
B 1.2330000 0.0000000 1.1830592
C 1.2330000 0.0000000 2.6963492
C 0.0000000 0.0000000 3.3885933
N 0.0000000 0.0000000 4.7677273
K_POINTS {crystal}
100
0.0 0.0 0.0 1.0
0.0 0.0 0.1 1.0
0.0 0.0 0.2 1.0
0.0 0.0 0.3 1.0
0.0 0.0 0.4 1.0
0.0 0.0 0.5 1.0
0.0 0.0 0.6 1.0
0.0 0.0 0.7 1.0
0.0 0.0 0.8 1.0
0.0 0.0 0.9 1.0
0.1 0.0 0.0 1.0
0.1 0.0 0.1 1.0
0.1 0.0 0.2 1.0
0.1 0.0 0.3 1.0
0.1 0.0 0.4 1.0
0.1 0.0 0.5 1.0
0.1 0.0 0.6 1.0
0.1 0.0 0.7 1.0
0.1 0.0 0.8 1.0
0.1 0.0 0.9 1.0
0.2 0.0 0.0 1.0
0.2 0.0 0.1 1.0
0.2 0.0 0.2 1.0
0.2 0.0 0.3 1.0
0.2 0.0 0.4 1.0
0.2 0.0 0.5 1.0
0.2 0.0 0.6 1.0
0.2 0.0 0.7 1.0
0.2 0.0 0.8 1.0
0.2 0.0 0.9 1.0
0.3 0.0 0.0 1.0
0.3 0.0 0.1 1.0
0.3 0.0 0.2 1.0
0.3 0.0 0.3 1.0
0.3 0.0 0.4 1.0
0.3 0.0 0.5 1.0
0.3 0.0 0.6 1.0
0.3 0.0 0.7 1.0
0.3 0.0 0.8 1.0
0.3 0.0 0.9 1.0
0.4 0.0 0.0 1.0
0.4 0.0 0.1 1.0
0.4 0.0 0.2 1.0
0.4 0.0 0.3 1.0
0.4 0.0 0.4 1.0
0.4 0.0 0.5 1.0
0.4 0.0 0.6 1.0
0.4 0.0 0.7 1.0
0.4 0.0 0.8 1.0
0.4 0.0 0.9 1.0
0.5 0.0 0.0 1.0
0.5 0.0 0.1 1.0
0.5 0.0 0.2 1.0
0.5 0.0 0.3 1.0
0.5 0.0 0.4 1.0
0.5 0.0 0.5 1.0
0.5 0.0 0.6 1.0
0.5 0.0 0.7 1.0
0.5 0.0 0.8 1.0
0.5 0.0 0.9 1.0
0.6 0.0 0.0 1.0
0.6 0.0 0.1 1.0
0.6 0.0 0.2 1.0
0.6 0.0 0.3 1.0
0.6 0.0 0.4 1.0
0.6 0.0 0.5 1.0
0.6 0.0 0.6 1.0
0.6 0.0 0.7 1.0
0.6 0.0 0.8 1.0
0.6 0.0 0.9 1.0
0.7 0.0 0.0 1.0
0.7 0.0 0.1 1.0
0.7 0.0 0.2 1.0
0.7 0.0 0.3 1.0
0.7 0.0 0.4 1.0
0.7 0.0 0.5 1.0
0.7 0.0 0.6 1.0
0.7 0.0 0.7 1.0
0.7 0.0 0.8 1.0
0.7 0.0 0.9 1.0
0.8 0.0 0.0 1.0
0.8 0.0 0.1 1.0
0.8 0.0 0.2 1.0
0.8 0.0 0.3 1.0
0.8 0.0 0.4 1.0
0.8 0.0 0.5 1.0
0.8 0.0 0.6 1.0
0.8 0.0 0.7 1.0
0.8 0.0 0.8 1.0
0.8 0.0 0.9 1.0
0.9 0.0 0.0 1.0
0.9 0.0 0.1 1.0
0.9 0.0 0.2 1.0
0.9 0.0 0.3 1.0
0.9 0.0 0.4 1.0
0.9 0.0 0.5 1.0
0.9 0.0 0.6 1.0
0.9 0.0 0.7 1.0
0.9 0.0 0.8 1.0
0.9 0.0 0.9 1.0
7 changes: 7 additions & 0 deletions examples/example33/bc2n.pw2wan
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,7 @@
&inputpp
outdir = './'
prefix = 'bc2n'
seedname = 'bc2n'
write_mmn = .true.
write_amn = .true.
/
40 changes: 40 additions & 0 deletions examples/example33/bc2n.scf
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,40 @@
&control
verbosity = 'high'
calculation = 'scf'
wf_collect = .true.
restart_mode = 'from_scratch'
prefix = 'bc2n'
pseudo_dir = '../../pseudo/'
outdir = './'
/
&system
ibrav=0,
celldm(1) = 1.8897261245650618
nat= 4,
ntyp= 3,
ecutwfc=70,
degauss=0.05,
occupations="smearing", smearing="mp",
/
&electrons
mixing_beta = 0.1
conv_thr = 1.0d-7
electron_maxstep = 1000
/
&IONS
/
ATOMIC_SPECIES
B 74.000 B.pbe-n-kjpaw_psl.0.1.UPF
C 16.000 C.pbe-n-kjpaw_psl.0.1.UPF
N 18.000 N.pbe-n-kjpaw_psl.0.1.UPF
CELL_PARAMETERS
2.466 0.000000000 0.000000000
0.000000000 20.0 0.000000000
0.000000000 0.000000000 4.323
ATOMIC_POSITIONS alat
B 1.2330000 0.0000000 1.1830592
C 1.2330000 0.0000000 2.6963492
C 0.0000000 0.0000000 3.3885933
N 0.0000000 0.0000000 4.7677273
K_POINTS automatic
10 1 10 0 0 0
Loading

0 comments on commit 69be32f

Please sign in to comment.