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\begin_body

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newcommand{
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triangleright$}
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\backslash
newcommand{
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MI}[1]{
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texttt{
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textcolor{olive}{#1}}}
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\end_inset


\end_layout

\begin_layout Title
Wannier functions --- band disentangling
\end_layout

\begin_layout Author
Klaus Koepernik
\end_layout

\begin_layout Standard
\begin_inset CommandInset toc
LatexCommand tableofcontents

\end_inset


\end_layout

\begin_layout Section
Introduction
\end_layout

\begin_layout Standard
We assume that the user already got acquainted with the FPLO Wannier function
 (WF) module, so that we do not have to explain the basics.
 Here we focus on the aspect of band disentangling, which plays an important
 role for 
\family typewriter
pyfplo
\family default
.
 The 
\family typewriter
slabify
\family default
 module of 
\family typewriter
pyfplo
\family default
 uses the file 
\family typewriter
+hamdata
\family default
 as input, which in turn is produced by the WF module.
 In most applications the relevant bands are not neatly separated by gaps.
 
\end_layout

\begin_layout Standard
We will walk you through an iteration of intermediate results, which demonstrate
s how to approach the problem in a semi systematic way.
\end_layout

\begin_layout Standard
The solution will be found in the 
\family typewriter
solution
\family default
 directory.
 You will work in the 
\family typewriter
task
\family default
 directory.
 
\end_layout

\begin_layout Section
Bcc Fe: 3d-only Wannier functions
\end_layout

\begin_layout Standard
In the beginning we will produce 3d-only Wannier functions for bcc-Fe.
 We will use a full-relativistic calculation to demonstrate (as a side effect
 of the tutorial) how this is done.
 So, please go into the task directory.
\end_layout

\begin_layout Itemize
Create a directory and copy files:
\end_layout

\begin_deeper
\begin_layout LyX-Code
mkdir bccFe
\end_layout

\begin_layout LyX-Code
cd bccFe
\end_layout

\begin_layout LyX-Code
cp ../=.in .
\end_layout

\begin_layout LyX-Code
cp ../=.dens .
\end_layout

\end_deeper
\begin_layout Itemize
Open 
\family typewriter
fedit
\family default
 and switch on 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{bandplot 
\backslash
RA{} bandstructure plot}
\end_layout

\end_inset

 and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{bandplot 
\backslash
RA{} weights}
\end_layout

\end_inset

.
 Go into the main menu and switch on 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{use data directories}
\end_layout

\end_inset

 and 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Quit/Save}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Run
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\begin_layout LyX-Code
faddwei
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\end_deeper
\begin_layout Itemize
Edit 
\family typewriter
=.addwei
\family default
 to look like this
\end_layout

\begin_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "80col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
\begin_inset CommandInset include
LatexCommand verbatiminput
filename "pics/addweibccFe"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Pay attention to 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{weightinfile}
\end_layout

\end_inset

 and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{spin}
\end_layout

\end_inset

.
\end_layout

\end_deeper
\begin_layout Itemize
Run
\end_layout

\begin_deeper
\begin_layout LyX-Code
faddwei
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout Standard
again and open
\end_layout

\begin_layout LyX-Code
xfbp +bwsum
\end_layout

\end_deeper
\begin_layout Itemize
Open 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Edit 
\backslash
RA{} Sets}
\end_layout

\end_inset

 go to the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Weights}
\end_layout

\end_inset

 tab and check all weights followed by 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Apply}
\end_layout

\end_inset

 to make them all visible:
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/bwei.png
	lyxscale 10
	width 50col%

\end_inset


\begin_inset Graphics
	filename pics/dos.png
	lyxscale 10
	width 45col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-fatbands-of-bcc-Fe"

\end_inset

The fatbands and 3d-dos of bcc Fe.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Close and open
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp +dos/+dos.sort001.nl005
\end_layout

\begin_layout Standard
See Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-fatbands-of-bcc-Fe"

\end_inset

.
 You will notice a little bump around 8--9eV in the DOS and clearly some
 3d-weight in the free-electron like band along 
\begin_inset Formula $\Gamma$
\end_inset

P (2--15eV).
 This is a 3d-4s/4p hybridization tail.
\end_layout

\end_deeper
\begin_layout Standard
The little exercise above should always be done before creating a WF fit.
 Afterall, we need to know where our bands are.
 Please notice the extend of the 3d bands (roughly 
\begin_inset Formula $\left[-5,3\right]$
\end_inset

eV).
 
\end_layout

\begin_layout Standard
We will 
\series bold
not
\series default
 create 
\family typewriter
=.wandef
\family default
 by hand.
 The reasons are simple:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Box Boxed
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "80col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Itemize
We want to write as little as possible.
 
\end_layout

\begin_layout Itemize
We want to avoid missing orbitals.
 
\end_layout

\begin_layout Itemize
For slabify we need always whole sets of orbitals, mostly a complete set
 of a minimum basis.
 Such a basis is defined as spd for d-metals and sp for main group elements.
 
\end_layout

\begin_layout Itemize
Note, that for topological properties it is advised to include all orbitals
 of the topological band complex including bands above the topological bands,
 since especially for topological insulators it it possible to hide the
 topological properties by a wrong choice of WFs (topological obstruction)
 --- use a minimum basis! 
\end_layout

\begin_layout Itemize
Finally, the choice of WFs shall not destroy the symmetry which protects
 the topological properties.
 E.g.
 for TIs one can find a minimal set of WFs which describe the few relevant
 bands but break time reversal symmetry.
 These can be totally valid WFs, but the topology, derived from such a set
 of WFs can be different --- use a minimum basis.
\end_layout

\begin_layout Itemize
An exception of the points above would be a situation where e.g.
 Bi-6p bands form an isolated band complex around the Fermi level.
 If these bands have non-zero p-character at each k-point in the BZ it is
 possible to use a p-only WF set for topological properties.
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Copy a file
\end_layout

\begin_deeper
\begin_layout LyX-Code
cp ../makewandef3d.py .
\end_layout

\end_deeper
\begin_layout Itemize
Edit it to look like this
\end_layout

\begin_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "90col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
\begin_inset CommandInset include
LatexCommand lstinputlisting
filename "pics/makewandef3d_1"
lstparams "language=Python,commentstyle={\\color{red}},stringstyle={\\color{olive}},identifierstyle={\\color{lightblue}},keywordstyle={\\color{orange}},numbers=left,numberstyle={\\tiny},caption={makewandef3d.py},label={makewandef3d}"

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Standard
Note lines 15-18 and 20 (
\family typewriter
3db
\family default
 means all 3d orbitals in real harmonics both spins).
 The sites list 
\family typewriter
[1]
\family default
 contains only one site, but it could contain more sites, if there were
 more Fe sites in the compound.
\end_layout

\begin_layout Standard
Also consult 
\family typewriter
FPLO
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

/DOC/pyfplo/pyfplo.pdf
\family default
.
\end_layout

\begin_layout Itemize
Now, run the script.
 (If a syntax error occurs, due to editing mistakes, correct them until
 you can execute the script without errors.)
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef3d.py
\end_layout

\begin_layout Standard
Have a look at the created 
\family typewriter
=.wandef
\family default
.
\end_layout

\end_deeper
\begin_layout Itemize
Run fplo
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\begin_layout Standard
We should have 
\family typewriter
+wancoeff
\family default
 now.
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee outwf
\end_layout

\end_deeper
\begin_layout Itemize
and when done, interrupt it with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-C}
\end_layout

\end_inset

.
\end_layout

\begin_deeper
\begin_layout Standard
It created 
\family typewriter
+wancoeffbin
\family default
.
 (This file is smaller than 
\family typewriter
+wancoeff
\family default
 and loads faster.
 One could in principle delete 
\family typewriter
+wancoeff
\family default
 now but be aware that the binary file might not be working on another machine.
 In other words 
\family typewriter
+wancoeffbin
\family default
 might not be transferable.).
 
\end_layout

\begin_layout Standard
Furthermore, we have some new subdirectories and the usual files 
\family typewriter
+wanband
\family default
, 
\family typewriter
+wanbandtb,
\family default
 
\family typewriter
+wanbweights,
\family default
 
\family typewriter
WF.net
\family default
 and so forth.
\end_layout

\end_deeper
\begin_layout Itemize
There is a generally very usefull little script.
 Let's copy the file:
\end_layout

\begin_deeper
\begin_layout LyX-Code
cp ../wband.xpy .
\end_layout

\end_deeper
\begin_layout Itemize
and execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp wband.xpy
\end_layout

\begin_layout Standard
to obtain the left panel of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:band,-wanband-and"

\end_inset

.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband1.png
	lyxscale 10
	width 60col%

\end_inset


\begin_inset Graphics
	filename pics/doswin1.png
	lyxscale 10
	width 40col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:band,-wanband-and"

\end_inset

band, wanband and wanbandtb.
 The right panel shows the energy window for orientation.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Note that the highest WF band must connect downwards on the way from 
\begin_inset Formula $\Gamma$
\end_inset

 to H.
 This is so since we cannot describe the free-electron like band, which
 crosses the 3d-bands with a 3d-only basis.
 Also note the wiggliness.
 This is owed to the fact that our energy window is narrow and that the
 free-electron band contains 3d-weight and most importantly that a narrow
 window means that when going through the free-electron band region the
 highest band leaves the window while the lowest enters the window.
 These are rather abrupt changes in the Hilbert space underlying the WF
 projectors.
\end_layout

\begin_layout Standard
We try to cure this by doing something quite unexpected.
 We increase the window to contain the free-electron bands.
\end_layout

\begin_layout Standard
But before we do this let's introduce some work flow aspects.
 We will repeatedly edit 
\family typewriter
makewandef3d.py
\family default
, execute fplo and look at the bands.
 So, let's do this more efficiently.
\end_layout

\end_deeper
\begin_layout Itemize
Open another terminal, change into the bccFe directory and execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee outwf
\end_layout

\begin_layout Standard
Do NOT hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-C}
\end_layout

\end_inset

 as the program says.
 Leave it alone.
\end_layout

\end_deeper
\begin_layout Itemize
In the original window execute (once and for all)
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp wband.xpy &   # the & is important
\end_layout

\end_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Box Boxed
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "90col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
In the original terminal you can now edit/save and execute 
\family typewriter
makewandef3d.py.
\end_layout

\begin_layout Plain Layout
In the fplo-terminal you can hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

 to re-run the WF calculation and in xfbp you can hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

 to reload the files.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Ok, let's continue
\end_layout

\begin_layout Itemize
In 
\family typewriter
makewandef3d.py
\family default
 change the energy window to 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{emax=10}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef3d.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo.
 (If you followed out setup advise, you only need to hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

 in the terminal running fplo.)
\end_layout

\begin_layout Itemize
When this is done hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

 in xfbp to obtain the left panel of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband2"

\end_inset

:
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband2.png
	lyxscale 10
	width 60col%

\end_inset


\begin_inset Graphics
	filename pics/doswin2.png
	lyxscale 10
	width 40col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband2"

\end_inset

band, wanband and wanbandtb: larger energy window.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Well, this looks better except for a few wiggles.
 which again come from a rather abrupt cutoff at 10eV.
 What can remedy this? A smooth cutoff.
\end_layout

\end_deeper
\begin_layout Itemize
change the upper fall-off to 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{deupper=7}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef3d.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo.
\end_layout

\begin_layout Itemize
and when this is done hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

 in xfbp to obtain the left panel of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband3"

\end_inset

:
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband3.png
	lyxscale 10
	width 60col%

\end_inset


\begin_inset Graphics
	filename pics/doswin3.png
	lyxscale 10
	width 40col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband3"

\end_inset

band, wanband and wanbandtb: larger energy window and smooth upper tail.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
This is even better, but still wiggly and most of all the bands get pulled
 to higher energies between PH and PN (not surprising).
\end_layout

\end_deeper
\begin_layout Itemize
change the energy window to 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{emax=0}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef3d.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo.
\end_layout

\begin_layout Itemize
and when this is done hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

 in xfbp to obtain the left panel of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband4"

\end_inset

.
\end_layout

\begin_deeper
\begin_layout Standard
Why does that work.
 The large upper tail covers what we need form higher bands.
 But it also covers the main 3d-part even if we put the upper window boundary
 (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{emax}
\end_layout

\end_inset

) below the main part.
 Moreover, it will pull the bands back down, since the main weight from
 the window function shifts down.
 As a side comment, we cannot choose different energy windows for spin up
 and spin down, since we have a full relativistic calculation.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband4.png
	lyxscale 10
	width 60col%

\end_inset


\begin_inset Graphics
	filename pics/doswin4.png
	lyxscale 10
	width 40col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband4"

\end_inset

band, wanband and wanbandtb.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Yet the wiggles are still there.
 Any idea? It is the lower boundary of the energy window, which is still
 too 
\begin_inset Quotes eld
\end_inset

discontinuous
\begin_inset Quotes erd
\end_inset

.
 Afterall, a free-electron band comes in from below.
\end_layout

\end_deeper
\begin_layout Itemize
change the lower fall-off to 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{delower=7}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef3d.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo.
\end_layout

\begin_layout Itemize
and when this is done hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

 in xfbp to obtain the left panel of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband5"

\end_inset


\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband5.png
	lyxscale 10
	width 60col%

\end_inset


\begin_inset Graphics
	filename pics/doswin5.png
	lyxscale 10
	width 40col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband5"

\end_inset

Magic: band, wanband and wanbandtb.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Standard
Now, one could play with the energy window parameters a bit more to optimize.
 But, this is already a very good choice.
 The WF fit is not perfect (free-electron band problem and some deviations)
 but surprisingly good.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Box Boxed
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "80col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Itemize
The energy window must have large tails.
\end_layout

\begin_layout Itemize
The core-window can be rather narrow, in fact it could be 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{emin=emax}
\end_layout

\end_inset

 in many cases (also in ours).
\end_layout

\begin_layout Itemize
Shifting the window around pulls the resulting WF bands higher or lower.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
We will now draw your attention to the localization aspect.
 
\end_layout

\begin_layout Itemize
Please execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp WFstat.xpy
\end_layout

\begin_layout Standard
Right click on the legend box and chose 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{hide}
\end_layout

\end_inset

 to get Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wextend"

\end_inset

.
 The picture shows the magnitude of the contributions of individual orbitals
 to the WFs as a function of the distance of said orbitals to the WF center
 on a logarithmic plot.
 In other words it depicts the WF extend.
 You will notice that the WF is surprisingly localized.
 In former versions one could the these curves rising again at larger distances
 due to some replica induced by the finite SCF k-mesh, according to the
 Nyquist–Shannon sampling theorem.
 Since Version 19, we use a routine, which eliminates such replica in a
 symmetric way.
 This leads to better agreement between the infinitely accurate transform
 (
\family typewriter
+wanband
\family default
) and the cut-off version, which leads to the actual real space WF model
 (
\family typewriter
+wanbandtb
\family default
).
 This new treatment also means that the number of possible WF matrix elements
 is always finite, although much larger than obtained for our current cut-off.
 
\end_layout

\begin_layout Itemize
Please execute
\end_layout

\begin_layout LyX-Code
grep -4 R-vectors outwf
\end_layout

\begin_layout Standard
to get
\end_layout

\begin_layout LyX-Code
(Number of R-vectors        869 Number of k-vectors      1728
\end_layout

\begin_layout LyX-Code
R-mesh not yet at maximum possible size.
 -> Increase ham_cutoff(rcutoff) 
\end_layout

\begin_layout Standard
This tells us that we use 869 real space vectors around a WF center for
 the model.
 The maximum possible number equals the number of k-vectors.
 Increasing the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rcutoff}
\end_layout

\end_inset

 will of course lead to a slower calculation and a larger 
\family typewriter
+hamdata
\family default
 file.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wextend1.png
	lyxscale 10
	width 70col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wextend"

\end_inset

The extend of the WF orbital contributions.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Section
Minimal basis bcc-Fe Wannier functions.
\end_layout

\begin_layout Standard
For practical applications (
\family typewriter
pyfplo.slabify
\family default
) we want a model, which describes all bands around the Fermi energy well.
 To achieve this we need to add the 4s and 4p orbitals.
 The 4p orbitals are needed e.g.
 for the yellow spot at the N-point in Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-fatbands-of-bcc-Fe"

\end_inset

.
 
\end_layout

\begin_layout Itemize
Copy the script
\end_layout

\begin_deeper
\begin_layout LyX-Code
cp makewandef3d.py makewandef.py
\end_layout

\end_deeper
\begin_layout Itemize
Edit 
\family typewriter
makewandef.py
\family default
 and in line 20 add 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{,'4sb','4pb'}
\end_layout

\end_inset

 to the orbital list.
 Set 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{emin}
\end_layout

\end_inset

 to 
\family typewriter
-9
\family default
 and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{delower}
\end_layout

\end_inset

 to 
\family typewriter
1
\family default
.
 The latter is obviously reasonable since we fit the whole set of occupied
 bands.
\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo and 
\series bold
continue reading this document
\series default
!
\end_layout

\begin_layout Itemize
Oops!
\end_layout

\begin_deeper
\begin_layout Standard
What happend is that the energy window is way too small to encompass a sufficien
t amount of sp weight in the unoccupied bands.
 There are sections in the BZ where the total amount of sp-weight is zero
 or nearly zero.
 This leads to a deletion of Hilbert space vectors such that the resulting
 projected basis is deficient.
\end_layout

\end_deeper
\begin_layout Itemize
Edit 
\family typewriter
makewandef.py
\family default
 and put 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{deupper=10}
\end_layout

\end_inset

.
 Also add 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{printT=False,}
\end_layout

\end_inset

 (including the final coma!) after 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{savespininfo=True,}
\end_layout

\end_inset

.
 This will switch off the output of the lines 
\family typewriter
T=...

\family default
 in the output.
 After all, this information is contained in a much more useful manner in
 
\family typewriter
+hamdata
\family default
.
\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo.
\end_layout

\begin_layout Itemize
No oops, but SVD (singular value decomposition) warnings.
 We still have a problem.
\end_layout

\begin_layout Itemize
In the still running xfbp open the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Edit 
\backslash
RA{} Script/Transformations}
\end_layout

\end_inset

 dialog and change the value in the last line from 10 to 35.
\end_layout

\begin_layout Itemize
Save the script and hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Apply}
\end_layout

\end_inset

 or close the dialog and hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

.
 You will see that the bands needed for the fit reach up to 35 eV.
\end_layout

\begin_layout Itemize
Edit 
\family typewriter
makewandef.py
\family default
 and put 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{deupper=15}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo.
\end_layout

\begin_layout Itemize
and when this is done hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

 in xfbp to obtain the left panel of Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband6"

\end_inset

 (We rescaled the figure, yours shows a larger window.):
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband6.png
	lyxscale 10
	width 60col%

\end_inset


\begin_inset Graphics
	filename pics/doswin6.png
	lyxscale 10
	width 40col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband6"

\end_inset

Minmum basis WFs.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
You will see in Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband6"

\end_inset

 that the tight-binding approximation (green) follows the exact WF-transformatio
n (red) quite closely except for around N and at the band bottom.
 The latter problem has to do with the fact that we approximate nearly free
 electron bands by tight binding.
 This is similar to a Fourier decomposition.
 One needs a number of frequencies to obtain a good approximant.
 In our case we can increase the Hamilton 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rcutoff}
\end_layout

\end_inset

 to 30.
\end_layout

\end_deeper
\begin_layout Itemize
Edit 
\family typewriter
makewandef.py
\family default
 and put 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rcutoff=30}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo and when this is done hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

 in xfbp to obtain Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband7"

\end_inset

.
 Note, that the calculation will take a longer time now.
 This is mostly due to the use of symmetries.
 For larger cells, with less symmetry operations, this overhead reduces.
 In other words the time for this step in the calculation does not scale
 up linearly with the number of sites.
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband7.png
	lyxscale 10
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband7"

\end_inset

Larger cutoff.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
You will see that there is an issue at the band bottom, which has to do
 with the WF extend.
\end_layout

\end_deeper
\begin_layout Itemize
Execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp WFstat.xpy
\end_layout

\begin_layout Standard
and hide the legend box.
 You will see:
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wextend2.png
	lyxscale 10
	width 70col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wextend2"

\end_inset

The extend of the WF orbital contributions.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Standard
This is now less localized than for the 3d-only case in Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wextend"

\end_inset

 because of the inclusion of the more extended 4s- and 4p-orbitals.
\end_layout

\begin_layout Itemize
Please grep the R-vector information:
\end_layout

\begin_deeper
\begin_layout LyX-Code
grep -4 R-vectors out
\end_layout

\begin_layout Standard
and you will see
\end_layout

\begin_layout LyX-Code
(Number of R-vectors       1407 Number of k-vectors      1728
\end_layout

\begin_layout LyX-Code
R-mesh not yet at maximum possible size.
 -> Increase ham_cutoff(rcutoff) 
\end_layout

\begin_layout Standard
We still do not use all possible vectors.
\end_layout

\end_deeper
\begin_layout Standard
Just to see what happens, let's increase the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rcutoff}
\end_layout

\end_inset

 further.
\end_layout

\begin_layout Itemize
Edit 
\family typewriter
makewandef.py
\family default
 and put 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rcutoff=40}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo and when this is done hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R}
\end_layout

\end_inset

 in xfbp to obtain Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband7"

\end_inset


\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband7b.png
	lyxscale 10
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband7b"

\end_inset

More k-points.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Please execute one more grep for the the R-vector information:
\end_layout

\begin_deeper
\begin_layout LyX-Code
grep -4 R-vectors out
\end_layout

\begin_layout Standard
and you will see
\end_layout

\begin_layout LyX-Code
(Number of R-vectors is at maximum Number of k-vectors      1728
\end_layout

\begin_layout Standard
We finally exhausted all possible R-vectors and as can be seen in Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:wband7b"

\end_inset

, the Problems at the band bottom are gone.
 A check of the extend 
\end_layout

\begin_layout LyX-Code

\family typewriter
xfbp WFstat.xpy
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wextend3.png
	lyxscale 10
	width 70col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wextend3"

\end_inset

The extend of the WF orbital contributions.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
reveals that the orbital contributions fall off to 
\begin_inset Formula $10^{-4}$
\end_inset

 at most.
 
\end_layout

\end_deeper
\begin_layout Standard
Please note, that one does not always need to extend the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rcutoff}
\end_layout

\end_inset

 to its maximum.
 In our case this is required by the extended nature of the free electron
 parts and by the disentangling situation.
 There are many cases when a 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rcutoff}
\end_layout

\end_inset

 of 30 seems to be enough.
\end_layout

\begin_layout Standard
If you zoom into the band bottom you will realize that the green bands (from
 the finite model) oscillate around the exact bands.
 This is an error which comes from the finite size of the SCF k-mesh, which
 limits the number of Fourier components.
 To remedy this we will use a larger k-mesh:
\end_layout

\begin_layout Itemize
So, call fedit and set 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{number of iterations}
\end_layout

\end_inset

 to 
\family typewriter
1 
\family default
and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{k-mesh subdivision}
\end_layout

\end_inset

 to 
\family typewriter
16,,
\end_layout

\begin_layout Itemize
Remove the WF data
\end_layout

\begin_deeper
\begin_layout LyX-Code
rm +wancoeff +wancoeffbin
\end_layout

\end_deeper
\begin_layout Itemize
Completely re-run fplo: First interrupt the running fplo: 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-C}
\end_layout

\end_inset

 and re-run it to re-create 
\family typewriter
+wancoeff
\family default
.
\end_layout

\begin_layout Itemize
Then re-run once more to re-calculate the WFs.
\end_layout

\begin_deeper
\begin_layout Standard
You get
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband8.png
	lyxscale 10
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband8"

\end_inset

More k-points.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
We still have some tiny problems at some places, e.g.
 the lowest two bands at 
\family typewriter
H|P
\family default
 are a bit too high.
\end_layout

\end_deeper
\begin_layout Itemize
So, let's reduce the upper boundary a bit: edit 
\family typewriter
makewandef.py
\family default
 and put 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{emax=-1}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
execute the script.
\end_layout

\begin_deeper
\begin_layout LyX-Code
python makewandef.py
\end_layout

\end_deeper
\begin_layout Itemize
Re-run fplo
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/wband9.png
	lyxscale 10
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:wband9"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Standard
When you grep the R-vector information you will notice that with the larger
 k-mesh the possible set of R-vectors also increased.
 One could further increase the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rcutoff}
\end_layout

\end_inset

 and play with the energy window to optimize tiny deviations here and there.
 But around the Fermi level our fit is good enough for our purpose.
\end_layout

\begin_layout Section
Bulk-projected bandstructure
\end_layout

\begin_layout Itemize
Now, copy some prepared files and change into 
\family typewriter
slabify
\family default
.
\end_layout

\begin_deeper
\begin_layout LyX-Code
cp -r ../slabify .
\end_layout

\begin_layout LyX-Code
cd slabify
\end_layout

\end_deeper
\begin_layout Itemize
Execute 
\end_layout

\begin_deeper
\begin_layout LyX-Code
python bpb.py
\end_layout

\end_deeper
\begin_layout Itemize
Study the script.
 Note, that the Fermi surface spectral function is much slower.
 That is due to the fact that the first plot has 
\begin_inset Formula $N_{e}$
\end_inset

 energy points and 
\begin_inset Formula $N_{k}$
\end_inset

 k-points, while the second plot has 1 energy point and 
\begin_inset Formula $N_{k}^{2}$
\end_inset

 k-points.
 Filling the energy axis for each k-point in the first plot requires basically
 one diagonalization, while in the second plot we need one diagonalization
 for each k-point and 
\begin_inset Formula $N_{k}^{2}\gg N_{k}$
\end_inset

.
 To make it shorter we chose a rather course grid for the second plot.
\end_layout

\begin_layout Itemize
When the script is done execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp bpbedc.xpy
\end_layout

\begin_layout Standard
and
\end_layout

\begin_layout LyX-Code
xfbp bpbfs.xpy
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/bpbedc.png
	lyxscale 30
	width 50col%

\end_inset


\begin_inset Graphics
	filename pics/bpbfs.png
	lyxscale 30
	width 50col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
Bulk projected bands and fermi surface.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Section
Fermi surface cuts.
\end_layout

\begin_layout Standard
The Wannier function model (
\family typewriter
+hamdata
\family default
) can also be used to calculate Fermi surface cuts.
 
\end_layout

\begin_layout Itemize
Inside the 
\family typewriter
slabify
\family default
 diretory execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
python fscuts.py
\end_layout

\end_deeper
\begin_layout Itemize
Study the script.
\end_layout

\begin_layout Itemize
When the script is done execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp fscuts.xpy
\end_layout

\begin_layout Standard
You will get Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Fermi-surface-cuts"

\end_inset

.
 Also study the xfbp script (
\family typewriter
fscuts.xpy
\family default
).
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/fscuts.png
	lyxscale 30
	width 70col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Fermi-surface-cuts"

\end_inset

Fermi surface cuts colored by band weights.
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\end_deeper
\end_body
\end_document
