#LyX 2.1 created this file. For more info see http://www.lyx.org/
\lyxformat 474
\begin_document
\begin_header
\textclass article
\begin_preamble
\usepackage{a4wide,cancel}
\renewcommand{\CancelColor}{\color{red}}
\newcommand{\version}{22.00-62}
\end_preamble
\use_default_options false
\maintain_unincluded_children false
\language american
\language_package default
\inputencoding auto
\fontencoding global
\font_roman default
\font_sans default
\font_typewriter default
\font_math auto
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\float_placement H
\paperfontsize 10
\spacing single
\use_hyperref true
\pdf_bookmarks true
\pdf_bookmarksnumbered true
\pdf_bookmarksopen true
\pdf_bookmarksopenlevel 1
\pdf_breaklinks true
\pdf_pdfborder false
\pdf_colorlinks true
\pdf_backref false
\pdf_pdfusetitle true
\pdf_quoted_options "linkcolor=red, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
\papersize a4paper
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 0
\use_package mathtools 1
\use_package mhchem 0
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 0
\boxbgcolor #ffffe1
\index Index
\shortcut idx
\color #008000
\end_index
\leftmargin 2cm
\topmargin 2cm
\rightmargin 2cm
\bottommargin 2cm
\secnumdepth 3
\tocdepth 3
\paragraph_separation skip
\defskip medskip
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\listings_params "basicstyle={\ttfamily}"
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header

\begin_body

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
definecolor{listingbg}{rgb}{1,1,0.886}
\end_layout

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
definecolor{olive}{rgb}{0,0.5,0}
\end_layout

\begin_layout Plain Layout


\backslash
newcommand{
\backslash
RA}{$
\backslash
triangleright$}
\end_layout

\begin_layout Plain Layout


\backslash
newcommand{
\backslash
MI}[1]{
\backslash
texttt{
\backslash
textcolor{olive}{#1}}}
\end_layout

\begin_layout Plain Layout


\backslash
newcommand{
\backslash
FHSPD}[1]{Fig.
 
\backslash
ref{fig:High-symmetry-points}(#1)}
\end_layout

\begin_layout Plain Layout


\backslash
newcommand{
\backslash
FSYMD}[1]{Fig.
 
\backslash
ref{fig:Symmetry-dialog,-with}(#1)}
\end_layout

\end_inset


\end_layout

\begin_layout Title
Unfolding band structure/ bcc-Fe versus DO
\begin_inset Formula $_{3}$
\end_inset

 FeCo/FeAl
\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
In this tutorial you will learn to use the band unfolding tool.
 This task is a bit involved due to the nature of the topic.
 There is a rather detailed documentation of the background of band unfolding
 in 
\family typewriter
FPLO.../DOC/MANUAL/unfolddoc.pdf
\family default
.
 Have fun.
\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 Standard
We will setup a bcc iron calculation and from it create a DO
\begin_inset Formula $_{3}$
\end_inset

 structure, in which we can replace one of four iron by either Co or Al.
 The resulting supercell band structure will be unfolded onto the bcc Brillouin
 zone (BZ) and compared to the original bcc-Fe calculation.
 You will see that although Al presents a rather strong perturbation of
 the iron lattice, similarities are still to be found.
 This is a rather extreme and artificial example and was chosen for its
 speed.
 Yet, unfolding is often rather usefull in real-world applications.
 
\end_layout

\begin_layout Standard
In principle unfolding consists of finding a mapping of all sites (or as
 much as possible) of a supercell (SC) onto corresponding sites in a normal
 (target) cell (NC).
 The mapping is used to create band weights, which in turn are fat for bands
 that survive unfolding and are small for the extinguished bands.
 It is assumed that the SC can be obtained by approximately filling the
 space with 
\begin_inset Formula $f$
\end_inset

 normal cells, followed by some atom substitutions and possibly some atom
 movements.
 However, roughly the two lattices should be commensurate.
 
\end_layout

\begin_layout Standard
The normal cell shall have 
\begin_inset Formula $n$
\end_inset

 sites 
\begin_inset Formula $s_{i},\quad i\in\left[1,n\right]$
\end_inset

 and the SC 
\begin_inset Formula $N=fn$
\end_inset

 sites 
\begin_inset Formula $S_{j},\quad j\in\left[1,N\right]$
\end_inset

.
 Now, the requirement 
\begin_inset Formula $N=fn$
\end_inset

 can be relaxed if some atoms are missing (see 
\family typewriter
unfolddoc.pdf
\family default
), in which case we just imagine the missing atoms among the set of 
\begin_inset Formula $S_{j}$
\end_inset

.
 We assumed that the lattice vectors 
\begin_inset Formula $r$
\end_inset

 of the NC lattice can be approximately mapped on the lattice vectors 
\begin_inset Formula $R$
\end_inset

 of the SC lattice in such a way that the sets of all sites in both lattices
 fulfill 
\begin_inset Formula $\left\{ r+s_{i}\right\} \approx\left\{ R+S_{j}\right\} $
\end_inset

.
 This means that for each SC 
\begin_inset Formula $S_{j}$
\end_inset

 we find a NC site 
\begin_inset Formula $s_{i}$
\end_inset

 and lattice vector 
\begin_inset Formula $r_{j}$
\end_inset

 such that 
\begin_inset Formula $S_{j}=s_{i}+r_{j}$
\end_inset

, which mapps 
\begin_inset Formula $f$
\end_inset

 SC sites 
\begin_inset Formula $S_{sj}$
\end_inset

 onto one single 
\begin_inset Formula $s$
\end_inset

.
 Repeat that for all 
\begin_inset Formula $s$
\end_inset

 and you get a listing like e.g.:
\end_layout

\begin_layout Standard
\begin_inset Box Frameless
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
\begin_inset Wrap figure
lines 0
placement r
overhang 0in
width "50col%"
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/cellmapping.pdf
	width 30col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:a-14-mapping"

\end_inset

a 
\begin_inset Formula $1:4$
\end_inset

 mapping of NC to SC.
 Four white SC sites map onto one white NC site, But only three black SC
 sites map onto the black NC site (partial unfolding).
 The orange arrows are NC lattice vectors.
 The red arrows are the SC lattice vectors.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\noindent
\align center

\family typewriter
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "40col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout LyX-Code

\family typewriter
#NC-site SC-sites
\end_layout

\begin_layout LyX-Code

\family typewriter
s1       S2 S4 S7 S8 
\end_layout

\begin_layout LyX-Code

\family typewriter
s2       S1 S3 S5 
\end_layout

\begin_layout LyX-Code

\family typewriter
s3       S6
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset VSpace defskip*
\end_inset

where 8 SC sites are identified with 3 NC sites according to the translational
 symmetry of the NC lattice (can be approximately translationally connected)
 .
 Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:a-14-mapping"

\end_inset

 shows a realization of such a mapping.
 In this case 
\begin_inset Formula $f=4$
\end_inset

.
 However, we have an atom substitution on the pink sites.
 Hence only three black SC sites can be mapped onto the one black NC site.
 The pink sites is left as a single site and it's unfolding weights will
 be identical to it's SC band weights (so no effect at all).
\end_layout

\end_inset


\end_layout

\begin_layout Standard
That is all what is needed.
 The next step is that one usually wants to plot the band structure along
 a path in the NC BZ.
 However, the SC calculation is setup in the SC geometry.
 The SC can be related to the NC by rather complex transformations.
 So, the second ingredient is to find the special points of the NC BZ in
 the SC BZ.
\end_layout

\begin_layout Standard
Once you understood the principle the main task is to map the two BZs and
 to determine the equivalences of all sites in both unit cells.
 Let's start.
\end_layout

\begin_layout Section
bcc Iron
\end_layout

\begin_layout Itemize
Go to the 
\family typewriter
task
\family default
 directory and create a directory called 
\family typewriter
bcc
\family default
 and change into it
\end_layout

\begin_deeper
\begin_layout LyX-Code
mkdir bcc
\end_layout

\begin_layout LyX-Code
cd bcc
\end_layout

\end_deeper
\begin_layout Itemize
Execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
fedit
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\end_deeper
\begin_layout Itemize
Go to the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{symmetry-menu}
\end_layout

\end_inset

 and set the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{spacegroup}
\end_layout

\end_inset

 to 229, the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{lattice constants}
\end_layout

\end_inset

 to 5.4,, and the first 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Wyckoff position}
\end_layout

\end_inset

 to Fe.
 Call 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{update}
\end_layout

\end_inset

 (hotkey 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{+}
\end_layout

\end_inset

) and go back to the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{main-menu}
\end_layout

\end_inset

 (hotkey 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{x}
\end_layout

\end_inset

).
 Now, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Quit/Save}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Execute
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\end_deeper
\begin_layout Itemize
Go back into 
\family typewriter
fedit
\family default
 and switch on 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bandplot $
\backslash
triangleright$ bandstructure plot}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bandplot $
\backslash
triangleright$ weights}
\end_layout

\end_inset

.
 Back to 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{main-menu}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Quit/Save}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Re-run 
\family typewriter
fplo
\family default
.
\end_layout

\begin_layout Itemize
Execute
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout Standard
and answer 
\family typewriter
y
\family default
.
\end_layout

\end_deeper
\begin_layout Itemize
Edit 
\family typewriter
=.addwei
\family default
 using your favorite editor (
\family typewriter
vi =.addwei
\family default
, 
\family typewriter
emacs -nw
\family default
 =.addwei, ...) to obtain:
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

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

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Execute
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout LyX-Code
xfbp +bwsum
\end_layout

\begin_layout Standard
You got:
\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/bccwei.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:bcc-fatbands"

\end_inset

bcc fatbands
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Standard
For training we will now look at the BZ and remind the user of the Fermi
 surface module of 
\family typewriter
xfplo
\family default
.
 The main purpose of this module is to visualize the Fermi surface.
 But you can also use it to setup the path through high symmetry points.
 There are several ways of invoking this mode.
 For reference we list them in the following (don't do anything yet).
\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 Enumerate

\family typewriter
xfplo -fs
\family default
: opens the Fermi surface window (FSW) with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{show/hide Fermi surface}
\end_layout

\end_inset

 button being switched off
\end_layout

\begin_deeper
\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/fermibutton.png
	width 15col%

\end_inset


\end_layout

\begin_layout Plain Layout
If the screen is blank try this: Hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-C}
\end_layout

\end_inset

 or click the 
\begin_inset Graphics
	filename pics/mini_xfsf16.xpm
	scale 70

\end_inset

 button or select the menu item 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Plot 
\backslash
RA{} Calculate}
\end_layout

\end_inset

 
\begin_inset Formula $\to$
\end_inset

 an empty BZ, the conventional frame and the legend will appear.
\end_layout

\end_deeper
\begin_layout Enumerate

\family typewriter
xfplo =.in
\family default
, followed by 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Activity 
\backslash
RA{} Fermi Surface}
\end_layout

\end_inset

 will also open the FSW.
\end_layout

\begin_layout Enumerate

\family typewriter
xfplo =.xef
\family default
: loads and executes what ever was saved previously into 
\family typewriter
=.xef
\family default
.
 This will switch the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{show/hide Fermi surface}
\end_layout

\end_inset

 button according to the settings in the file.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Now back to the tutorial:
\end_layout

\begin_layout Itemize
Execute 
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo -fs
\end_layout

\end_deeper
\begin_layout Itemize
Hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-C}
\end_layout

\end_inset

.
 Switch on the cartesian frame 
\begin_inset Graphics
	filename pics/framebutton.png
	scale 50

\end_inset

 (hotkey: 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{a a}
\end_layout

\end_inset

).
 Switch of the legend button 
\begin_inset Graphics
	filename pics/legendbutton.png
	scale 50

\end_inset

 and zoom properly (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{mouse wheel}
\end_layout

\end_inset

 or 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{right mouse click+mouse move}
\end_layout

\end_inset

).
\end_layout

\begin_layout Itemize
Now, select 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Plot 
\backslash
RA{} High symemtry points}
\end_layout

\end_inset

 (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-H}
\end_layout

\end_inset

) to open the high symmetry points dialog (HSPD) Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:High-symmetry-points"

\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/HSPD.png
	lyxscale 30
	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:High-symmetry-points"

\end_inset

High symmetry points dialog
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Click the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Import from =.in}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FHSPD{d}
\end_layout

\end_inset

).
 Press 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 
\end_layout

\begin_layout Itemize
Check the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Visible}
\end_layout

\end_inset

 checkbox (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FHSPD{a}
\end_layout

\end_inset

) and the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{User defined}
\end_layout

\end_inset

 checkbox (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FHSPD{b}
\end_layout

\end_inset

).
\end_layout

\begin_layout Itemize
Again press 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

 or click the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{accept}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FHSPD{c}
\end_layout

\end_inset

).
 You should see somthing like Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bcc-BZ"

\end_inset

.
 You will notice that the point coordinates are displayed in the HSPD according
 to FPLO convention 
\begin_inset Formula $\boldsymbol{k}=\frac{2\pi}{a}\left(k_{x},k_{y},k_{z}\right)$
\end_inset

.
 Other reference bases are available via the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Reference basis}
\end_layout

\end_inset

 combobox (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FHSPD{e}
\end_layout

\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/bccBZ.png
	lyxscale 30
	width 50col%

\end_inset


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

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:bcc-BZ"

\end_inset

bcc BZ
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Optionally, you can change the point/font colors, pick new points, export
 the points to 
\family typewriter
=.in
\family default
 or move the labels.
\end_layout

\begin_deeper
\begin_layout Standard
The moving works like this (picking is similar)
\end_layout

\begin_layout Itemize
hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{move labels}
\end_layout

\end_inset

 button once
\end_layout

\begin_layout Itemize
drag the labels in the main view 
\end_layout

\begin_layout Itemize
hit the same button a second time or press 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{esacpe}
\end_layout

\end_inset

 in the main view to stop the move-mode
\end_layout

\begin_layout Standard
The label position/color etc.
 would only be saved in 
\family typewriter
=.xef
\family default
.
\end_layout

\begin_layout Standard
Note, that each label is printed on the screen.
 So, if you want to move them and produce a picture just change the name
 of the superfluous labels in the table to an empty string or delete the
 whole point, if it is not needed for the path (if you want the path, that
 is).
 
\end_layout

\begin_layout Standard
Also, occasionally, read the help screen in the HSPD.
\end_layout

\end_deeper
\begin_layout Itemize
Finally, just for fun close the HSPD and in the FSW save the current state:
 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-S}
\end_layout

\end_inset

 or 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{File 
\backslash
RA{} Save}
\end_layout

\end_inset

, accept the default filename 
\family typewriter
=.xef
\family default
.
 Exit the FSW (
\family typewriter

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-Q}
\end_layout

\end_inset


\family default
, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Activities 
\backslash
RA{} Quit all}
\end_layout

\end_inset

)
\end_layout

\begin_layout Itemize
For reference, please execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo =.xef
\end_layout

\end_deeper
\begin_layout Itemize
and close it again.
\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 Plain Layout
A note on activities.
 As you might have noticed, several activities can be open at the same time.
 This is used by some tools to communicate between them (e.g.
 Fatband editor and structure view).
 Each activity has a 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{File 
\backslash
RA{} Close}
\end_layout

\end_inset

 (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-W}
\end_layout

\end_inset

) which closes this activity.
 The menu entry 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Activities 
\backslash
RA{} Quit all}
\end_layout

\end_inset

 (
\family typewriter

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-Q}
\end_layout

\end_inset


\family default
) closes all connected activities.
\end_layout

\end_inset


\end_layout

\begin_layout Section
DO
\begin_inset Formula $_{3}$
\end_inset

 Fe
\begin_inset Formula $_{3}$
\end_inset

Co
\begin_inset CommandInset label
LatexCommand label
name "sec:DO-FeCo"

\end_inset


\end_layout

\begin_layout Standard
Now, we will derive a supercell from the 
\family typewriter
bcc
\family default
 setup.
\end_layout

\begin_layout Itemize
Go up into the 
\family typewriter
task
\family default
 directory and make a directory called 
\family typewriter
DO3Co
\family default
 and change into it.
 Copy the files 
\family typewriter
=.in
\family default
 and 
\family typewriter
=.addwei
\family default
 from 
\family typewriter
bcc
\family default
 to the current diretory (
\family typewriter
DO3Co
\family default
):
\end_layout

\begin_deeper
\begin_layout LyX-Code
cd ..
\end_layout

\begin_layout LyX-Code
# now we are in task
\end_layout

\begin_layout LyX-Code
mkdir DO3Co
\end_layout

\begin_layout LyX-Code
cd DO3Co
\end_layout

\begin_layout LyX-Code
# we are in DO3Co
\end_layout

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

\begin_layout LyX-Code
cp ../bcc/=.addwei .
\end_layout

\end_deeper
\begin_layout Itemize
Execute 
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo =.in
\end_layout

\end_deeper
\begin_layout Itemize
Open 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Input $
\backslash
triangleright$ Symmetry}
\end_layout

\end_inset

 and in the symmetry dialog click on the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Manipulate}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{h}
\end_layout

\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/symmanip.png
	lyxscale 30
	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:Symmetry-dialog,-with"

\end_inset

Symmetry dialog, with open manipulate extension.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Have a look at the list of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Wyckoff positions}
\end_layout

\end_inset

 (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{i}
\end_layout

\end_inset

) and on the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Spacegroup}
\end_layout

\end_inset

 settings (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{k}
\end_layout

\end_inset

) .
 
\end_layout

\begin_layout Itemize
Now click the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Conventional cell}
\end_layout

\end_inset

 buttom (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{a}
\end_layout

\end_inset

), it changed the list of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Wyckoff positions}
\end_layout

\end_inset

 and the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Spacegroup}
\end_layout

\end_inset

 .
 We, now have a simple cubic setup.
 
\end_layout

\begin_layout Itemize
In the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enlarge-cell}
\end_layout

\end_inset

 table (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{b}
\end_layout

\end_inset

) fill the diagonal with 2 and click the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{apply}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{c}
\end_layout

\end_inset

).
 We now have 16 sites and spacegroup 1.
 
\end_layout

\begin_layout Itemize
Uncheck the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{reduce translations}
\end_layout

\end_inset

 checkbox (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{d}
\end_layout

\end_inset

) and hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Determine Symmetry}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{e}
\end_layout

\end_inset

).
 We now have simple cubic (spacegroup 221) and 5 atoms.
\end_layout

\begin_layout Itemize
Hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{reset}
\end_layout

\end_inset

 button in the structure view (SV) (Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:big-iron-cell"

\end_inset

, arrow) and rotate the image with 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{left mouse click+mouse move}
\end_layout

\end_inset

 such that it looks something like Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:big-iron-cell"

\end_inset

.
\end_layout

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

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/big221.png
	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:big-iron-cell"

\end_inset

big iron cell
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
In the SV click on the atom marked in the Fig 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:big-iron-cell"

\end_inset

.
 This will select the corresponding 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Wyckoff position}
\end_layout

\end_inset

 (5) in the symmetry dialog.
 Change the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Wyckoff position name}
\end_layout

\end_inset

: in the element column of the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Wyckoff positions}
\end_layout

\end_inset

 table click on the selected row (basically at Fe) 
\end_layout

\begin_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Graphics
	filename pics/wycpos.png
	width 39col%

\end_inset


\end_layout

\begin_layout Standard
to give the keyboard focus to the table and type 
\family typewriter
co
\family default
 followed by 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 Hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Accept}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{m}
\end_layout

\end_inset

) or hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

 again.
\end_layout

\begin_layout Standard
Now, you have 8 pinkish Co atoms.
\end_layout

\end_deeper
\begin_layout Itemize
Hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Remove all generators}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{f}
\end_layout

\end_inset

) 
\begin_inset Formula $\to$
\end_inset

 back to 16 Wyckoff positions (8 of them Co).
\end_layout

\begin_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 "70col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
Note, that we have space group 221, but only the identity in 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Subgroup generators}
\end_layout

\end_inset

 .
 This way you can produce a lattice as defined by spacegroup/lattice-parameter/a
ngles without using the group generators to create the sites from the Wyckoff
 positions.
 In other words the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Subgroup generators}
\end_layout

\end_inset

 can be used to reduce site symmetry without changing the lattice setup.
\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Go back to the structure view and click on one Co atom.
 This will select the Wyckoff position in the symmetry dialog 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Wyckoff positions}
\end_layout

\end_inset

 table.
 Change the element back to Fe and hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{accept}
\end_layout

\end_inset

.
 Continue to change another three cobalt into iron to obtain the following
 tetrahedrally coordinated four Co atoms:
\end_layout

\begin_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Graphics
	filename pics/DO3prelim.png
	width 30col%

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
In the symmetry dialog check the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{reduce translations}
\end_layout

\end_inset

 checkbox (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{d}
\end_layout

\end_inset

) and hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Determine Symmetry}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{e}
\end_layout

\end_inset

).
 The result is spacegroup 225 (fcc) with three Wyckoff positions, two Fe
 and one cobalt.
 In the status bar of the SV it says 
\family typewriter
Fe3Co1
\family default
.
 That is our final structure:
\end_layout

\begin_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Graphics
	filename pics/DO3.png
	lyxscale 30
	width 70col%

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
In the symmetry dialog click the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{export}
\end_layout

\end_inset

 button (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{g}
\end_layout

\end_inset

).
 Chose 
\family typewriter
=.in
\family default
 hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

, read the message.
\end_layout

\begin_layout Itemize
Now, in the SV save the state to 
\family typewriter
=.xstr
\family default
 (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-S}
\end_layout

\end_inset

 or 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{File 
\backslash
RA{} Save}
\end_layout

\end_inset

).
 
\end_layout

\begin_layout Itemize
Press 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-Q}
\end_layout

\end_inset

 and ignore warnings.
 We have input.
\end_layout

\begin_layout Itemize
As a confirmation reload the saved 
\family typewriter
=.xstr
\family default
.
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo =.xstr
\end_layout

\end_deeper
\begin_layout Itemize
Close 
\family typewriter
xfplo
\family default
.
\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 "70col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
One note on the symmetry manipulation.
 
\end_layout

\begin_layout Plain Layout
The transformations which can be performed will produce new cells in some
 internally defined default orientation.
 This has to do with the fact that one has to somehow decide where to put
 the 
\begin_inset Formula $\boldsymbol{a}$
\end_inset

, 
\begin_inset Formula $\boldsymbol{b}$
\end_inset

 and 
\begin_inset Formula $\boldsymbol{c}$
\end_inset

-axes.
 If you want to keep the absolute orientation of the resulting crystal the
 same way as the original crystal, please check the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rotate}
\end_layout

\end_inset

 (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{r}
\end_layout

\end_inset

) checkbox 
\series bold
before
\series default
 any manipulations.
 This will record all necessary rotations of the resulting crystal in the
 table below 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{rotate}
\end_layout

\end_inset

.
 If you follow this recipie the resulting crystal's orientation is unaltered
 by axis conventions.
 (This helps a lot with unfolding.) 
\end_layout

\begin_layout Plain Layout
We however, did not use this, since in our case it does not really matter.
 You could repeat the structure creation process above using the rotate
 feature and at most you would get a simple axis permutation.
 Afterall, it is a cubic example.
 (Actually, I got the identity matrix).
\end_layout

\begin_layout Plain Layout
Also there are more options than 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enlarge}
\end_layout

\end_inset

, which you get when you use these arrows (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
FSYMD{n}
\end_layout

\end_inset

).
 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
We will now perform a calculation in the new setup.
\end_layout

\begin_layout Itemize
In 
\family typewriter
fedit
\family default
 switch off 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bandplot $
\backslash
triangleright$ bandstructure plot}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Execute
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\begin_layout Standard
This will take about 1 min.
\end_layout

\end_deeper
\begin_layout Itemize
It will not be converged.
 So re-run 
\family typewriter
fplo
\family default
! Now, it should have worked.
\end_layout

\begin_layout Itemize
Switch on 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bandplot $
\backslash
triangleright$ bandstructure plot}
\end_layout

\end_inset

 in 
\family typewriter
fedit
\family default
 and re-run 
\family typewriter
fplo
\family default
.
 When done have a look at the population analysis or the 
\begin_inset Quotes eld
\end_inset

Atom sites
\begin_inset Quotes erd
\end_inset

 table in the begining of the output file (
\family typewriter
out
\family default
).
 We have four sites, Fe 1---3 an Co 4.
\end_layout

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

\begin_deeper
\begin_layout Standard
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

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

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
and
\end_layout

\end_deeper
\begin_layout Itemize
run
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout LyX-Code
xfbp +bwsum
\end_layout

\begin_layout Standard
You got Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:DO-FeCo,-fatbands"

\end_inset

 and should compare to Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bcc-fatbands"

\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/bweido3co.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:DO-FeCo,-fatbands"

\end_inset

DO
\begin_inset Formula $_{3}$
\end_inset

 Fe
\begin_inset Formula $_{3}$
\end_inset

Co, fatbands
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Section
Interlude 
\begin_inset CommandInset label
LatexCommand label
name "sec:Interlude"

\end_inset


\end_layout

\begin_layout Subsection
Fast argument
\end_layout

\begin_layout Standard
We should take a break from clicking and think about the BZ mapping.
 We started with a bcc normal unit cell.
 This makes an fcc reciprocal cell.
 Remember the steps we took.
 We went from fcc to it's conventional unit cell (simple cubic) by removing
 the centering.
 Then we doubled the conventional cell in all directions and reduced the
 symmetry to obtain an fcc cell with this doubled-lattice-constant conventional
 cell.
 It's reciprocal cell is bcc in a reciprocal conventional cell which now
 must be 2-times smaller in all directions.
 Hence, in the supercell setup, we need to define an fcc Brillouin zone
 (as the original reciprocal cell) in a conventional reciprocal cell of
 twice the reciprocal lattice constant of the SC setup.
 Have a look at Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:All-cells-in"

\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/allcells.jpg
	lyxscale 40
	width 40col%

\end_inset


\begin_inset Graphics
	filename pics/fccbccrealspace.jpg
	lyxscale 40
	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:All-cells-in"

\end_inset

All cells in one picture.
 Left: the yellow cube is the NC conventional reciprocal cell.
 The magenta Wigner-Seitz cell is the NC BZ (reciprocal fcc).
 The blue-ish cube is the SC conventional reciprocal cell and the black
 Wigner-Seitz cell is the SC BZ (reciprocal bcc).
 Right: the same colors are used to depict the NC and SC primitive and conventio
nal cells.
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Slow argument
\end_layout

\begin_layout Standard
If this was to much here we do the math.
 The conventional cubic cell is 
\begin_inset Formula 
\[
A_{c}=\left(\begin{array}{ccc}
a\\
 & a\\
 &  & a
\end{array}\right)
\]

\end_inset

where each row is a lattice vector.
 The primitive cell is 
\begin_inset Formula 
\[
A_{p}=B_{bc}A_{c}
\]

\end_inset

where 
\begin_inset Formula 
\[
B_{bc}=\left(\begin{array}{ccc}
-\frac{1}{2} & \frac{1}{2} & \frac{1}{2}\\
\frac{1}{2} & -\frac{1}{2} & \frac{1}{2}\\
\frac{1}{2} & \frac{1}{2} & -\frac{1}{2}
\end{array}\right)
\]

\end_inset

is the body-centering matrix.
 The primitive reciprocal lattice is obtained by the inverse-transpose of
 the direct lattice:
\begin_inset Formula 
\begin{eqnarray*}
G_{p} & = & A_{p}^{-T}\\
 & = & B_{bc}^{-T}A_{c}^{-T}\\
 & = & B_{bc}^{-T}A_{c}^{-1}
\end{eqnarray*}

\end_inset

Note, that 
\begin_inset Formula $A_{c}^{T}=A_{c}$
\end_inset

 and that we do not use the 
\begin_inset Formula $2\pi$
\end_inset

 factor usually used in the definition of the reciprocal lattice vectors.
 It just hurts the eye.
 Furthermore, both inversion and transposition would reverse the order of
 matrices in a product: 
\begin_inset Formula $\left(AB\right)^{T}=B^{T}A^{T}$
\end_inset

.
 But we have a combined inverse-transpose, which restores the original matrix
 order.
 Lastly, you might have learned that the reciprocal of the bcc is an fcc
 lattice, but not quite.
 In fact
\begin_inset Formula 
\begin{equation}
B_{bc}^{-T}=B_{bc}^{-1}=2B_{fc}\label{eq:Bbcinv}
\end{equation}

\end_inset


\begin_inset Formula 
\begin{equation}
B_{fc}^{-T}=B_{fc}^{-1}=2B_{bc}\label{eq:Bfcinv}
\end{equation}

\end_inset

where 
\begin_inset Formula 
\[
B_{fc}=\left(\begin{array}{ccc}
0 & \frac{1}{2} & \frac{1}{2}\\
\frac{1}{2} & 0 & \frac{1}{2}\\
\frac{1}{2} & \frac{1}{2} & 0
\end{array}\right)
\]

\end_inset

is the face-centring matrix.
 This factor of two is important.
 So, finally our normal cell reciprocal space is spanned by 
\begin_inset Formula 
\[
G_{p}=B_{fc}\left(2A_{c}^{-1}\right)
\]

\end_inset

which is why we call two-times the reciprocal of the direct conventional
 lattice the reciprocal conventional lattice: 
\begin_inset Formula 
\begin{equation}
G_{c}=2A_{c}^{-1}\label{eq:NCrecconv}
\end{equation}

\end_inset

Only then the centering relation 
\begin_inset Formula $G_{p}=B_{fc}G_{c}$
\end_inset

 holds.
 (Note that this factor of two also appears in the reciprocal of base-centered
 lattices, but only in the two centering directions.
 The axis opposite to the centered plane does not have such a factor.)
\end_layout

\begin_layout Standard
To build the BZ we need to find the planes which are perpendicular to lattice
 vectors and closest to the 
\begin_inset Formula $\Gamma$
\end_inset

-point, which lie half-way to the next lattice vector.
 A plane is defined by a plane equation with a normal 
\begin_inset Formula $\boldsymbol{n}$
\end_inset

 and a distance 
\begin_inset Formula $d$
\end_inset

:
\begin_inset Formula 
\[
\boldsymbol{n}\boldsymbol{k}=d,\quad\left|\boldsymbol{n}\right|^{2}=1
\]

\end_inset

A half-way plane perpendicular to a 
\begin_inset Formula $\boldsymbol{G}$
\end_inset

 is then
\begin_inset Formula 
\[
\frac{\boldsymbol{G}}{\left|\boldsymbol{G}\right|}\boldsymbol{k}=\frac{1}{2}\left|\boldsymbol{G}\right|
\]

\end_inset


\end_layout

\begin_layout Standard
One of the shortest reciprocal vectors in our case is 
\begin_inset Formula $\boldsymbol{G}=\left(\frac{1}{2}\frac{1}{2}0\right)^{T}G_{c}$
\end_inset

 (a centering vector in the fcc reciprocal lattice).
 When defining faces for a polyhedron in xfplo we can chose a basis.
 Typically we chose the conventional basis 
\begin_inset Formula $G_{c}$
\end_inset

.
 Then by definition this particular face is defined by the input 
\begin_inset Formula $n=\left(\frac{1}{2}\frac{1}{2}0\right),\;d=\frac{1}{2}$
\end_inset

 or if you want to use another scale 
\begin_inset Formula $\boldsymbol{G}^{\prime}=\lambda\left(\frac{1}{2}\frac{1}{2}0\right)^{T}G_{c}=\lambda\boldsymbol{G}$
\end_inset

 the following is equivalent
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{eqnarray*}
\boldsymbol{G}\boldsymbol{k} & = & \frac{1}{2}\left|\boldsymbol{G}\right|^{2}\\
\lambda\boldsymbol{G}\boldsymbol{k} & = & \frac{1}{2\lambda}\left|\lambda\boldsymbol{G}\right|^{2}\\
\boldsymbol{G}^{\prime}\boldsymbol{k} & = & \frac{1}{2\lambda}\left|\boldsymbol{G}^{\prime}\right|^{2}
\end{eqnarray*}

\end_inset

which results in input 
\begin_inset Formula $n=\lambda\left(\frac{1}{2}\frac{1}{2}0\right),\;d=\frac{1}{2\lambda}$
\end_inset

.
 We come back to this later.
\end_layout

\begin_layout Standard
Let's turn to the supercell.
 First, we transform the primitive normal cell to conventional
\begin_inset Formula 
\[
B_{bc}^{-1}A_{p}=A_{c}
\]

\end_inset

then we double the size
\begin_inset Formula 
\[
2B_{bc}^{-1}A_{p}=2A_{c}
\]

\end_inset

and add the face-centering to obtain the new primitive lattice basis:
\begin_inset Formula 
\[
A_{p}^{\prime}=B_{fc}2B_{bc}^{-1}A_{p}=B_{fc}2A_{c}
\]

\end_inset

It's primitive reciprocal lattice is
\begin_inset Formula 
\begin{eqnarray*}
G_{p}^{\prime} & = & A_{p}^{\prime-T}=B_{fc}^{-T}\frac{1}{2}A_{c}^{-T}\\
 & = & 2B_{bc}\frac{1}{2}A_{c}^{-1}\\
 & = & B_{bc}A_{c}^{-1}
\end{eqnarray*}

\end_inset

and hence it's reciprocal conventional must be 
\begin_inset Formula $G_{c}^{\prime}=A_{c}^{-1}$
\end_inset

.
 If you compare to Eq.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:NCrecconv"

\end_inset

 you see that indeed the SC reciprocal conventional cell is half as big
 in all directions (missing factor 2).
 This gives 
\begin_inset Formula $2G_{c}^{\prime}=2A_{c}^{-T}=G_{c}$
\end_inset

 or 
\begin_inset Formula $G_{c}=2G_{c}^{\prime}$
\end_inset

.
 The original reciprocal fcc lattice can now be expressed in SC reciprocal
 conventional basis:
\begin_inset Formula 
\[
g_{fcc}^{NC}=B_{fc}G_{c}=2B_{fc}G_{c}^{\prime}
\]

\end_inset

Our faces in SC conventional basis are hence spanned by all permutations
 of 
\begin_inset Formula $n=\left(\pm1\pm10\right),\;d=\frac{1}{2}$
\end_inset

 (or alternatively 
\begin_inset Formula $n=\left(\pm\frac{1}{2}\pm\frac{1}{2}0\right),\;d=1$
\end_inset

).
 
\end_layout

\begin_layout Subsection
Could have been so much easier
\end_layout

\begin_layout Standard
Last, we have a look at the list of high symmetry points found in the fedit
 bandplot menu in the original bcc calculation.
 The k-points are always given in units of 
\begin_inset Formula $\frac{2\pi}{a}$
\end_inset

.
 In the SC calculation we need to define them in units of 
\begin_inset Formula $\frac{2\pi}{a_{SC}}$
\end_inset

, with 
\begin_inset Formula $a_{SC}=2a$
\end_inset

.
 No other transformations need to be taken into account, since the centering
 does not enter the definition of the k-points in the menu.
 Hence, an original 
\begin_inset Formula $k$
\end_inset

-point tranforms as
\begin_inset Formula 
\begin{eqnarray*}
k_{NC} & = & \frac{2\pi}{a}\left(k_{x}k_{y}k_{z}\right)\\
 & = & \frac{2\pi}{a_{SC}}\frac{a_{SC}}{a}\left(k_{x}k_{y}k_{z}\right)\\
 & = & \frac{2\pi}{a_{SC}}\left(2k_{x}2k_{y}2k_{z}\right)
\end{eqnarray*}

\end_inset

All we had to do is to take the original points and multiply them by a factor
 of two.
 We will however not do this in order to teach more features of the programs.
 The path of transformations eluded to above might be usefull in more involved
 cases.
 There might be additional rotations involved in the most general case,
 which we did not take into account in our little detour.
 
\end_layout

\begin_layout Section
Back on track: the BZ mapping
\end_layout

\begin_layout Standard
We will show you two ways of creating the normal cell BZ inside the supercell
 setup.
 The first uses smart tools.
 The second is taking a stroll through the GUI and is more general.
 Use the first method if time is of the essence and come back for the second
 method when time allows it.
 It is teaching more GUI elements.
\end_layout

\begin_layout Subsection
The smart way
\end_layout

\begin_layout Standard
We will use the fact that in our case the normal cell BZ in the supercell
 setup is identical to the normal cell BZ in the normal setup, since we
 did not have any rotations in the transformation between the two setups.
 If the supercell is derived by the symmetry manipulation tool of xfplo,
 rotations can be avoided by using the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{rotate}
\end_layout

\end_inset

 (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
FSYMD{r}
\end_layout

\end_inset

) feature in the symmetry dialog during structure manipulation.
\end_layout

\begin_layout Itemize
So, go to the 
\family typewriter
bcc
\family default
 directory and launch 
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo -fs
\end_layout

\end_deeper
\begin_layout Itemize
open the Boundary dialog 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Input 
\backslash
RA{} boundary}
\end_layout

\end_inset

 (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-B}
\end_layout

\end_inset

).
\end_layout

\begin_layout Itemize
In the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Boundary Type}
\end_layout

\end_inset

 selectbox choose 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{User defined}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
In the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{reference basis}
\end_layout

\end_inset

 combobox (at the top of the dialog) select 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{cartesian basis vectors}
\end_layout

\end_inset

 
\end_layout

\begin_layout Itemize
Click on the arrow of the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Load}
\end_layout

\end_inset

 button to open a menu.
 Choose 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Wigner Seitz Faces}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Click the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Save current}
\end_layout

\end_inset

 button.
\end_layout

\begin_layout Itemize
Close the dialog and the Fermi surface window (FSW).
\end_layout

\begin_layout Standard
This saves the normal cell (bcc) Wigner Seitz cell in the file 
\family typewriter
~/.xfplo/userfaces.ini
\family default
.
 We are going to load it now.
\end_layout

\begin_layout Itemize
Change back into the 
\family typewriter
DO3Co
\family default
 directory.
\end_layout

\begin_layout Itemize
Execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo -fs
\end_layout

\end_deeper
\begin_layout Itemize
Hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-C}
\end_layout

\end_inset

 if you have a blank screen.
\end_layout

\begin_layout Itemize
In the Fermi surface window (FSW) open the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Plot 
\backslash
RA{} Annotations}
\end_layout

\end_inset

 dialog and click on last item (
\begin_inset Quotes eld
\end_inset

Primitive
\begin_inset Quotes erd
\end_inset

) in left panel.
\end_layout

\begin_layout Itemize
click the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{plus}
\end_layout

\end_inset

 button above the left panel or hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-I}
\end_layout

\end_inset

 or the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{ins}
\end_layout

\end_inset

-key.
\end_layout

\begin_layout Itemize
Hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 You should see a magenta box in the FSW.
\end_layout

\begin_layout Itemize
In the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Boundary type}
\end_layout

\end_inset

 selectbox choose 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{user defined}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Click on the arrow of the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Load}
\end_layout

\end_inset

 button to open a menu.
 Choose 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{User saved faces}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

, close the dialog, switch off the legend 
\begin_inset Graphics
	filename pics/legendbutton.png
	scale 50

\end_inset

 and switch on the cartesian frame (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{a a}
\end_layout

\end_inset

).
 Finally, in the FSW save the state via 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-S}
\end_layout

\end_inset

 or 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{File 
\backslash
RA{} Save}
\end_layout

\end_inset

.
\end_layout

\begin_deeper
\begin_layout Standard
You should see a magenta normal cell BZ together with the super cell Brillouin
 zone, Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-BZ-of"

\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/bigcell.png
	lyxscale 30
	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:The-BZ-of"

\end_inset

The BZ of the normal cell together with the BZ of the supercell.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Open the high symmetry points dialog (HSPD) via 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Plot 
\backslash
RA{} High symemtry points}
\end_layout

\end_inset

 (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-H}
\end_layout

\end_inset

)
\end_layout

\begin_layout Itemize
Check the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Visible}
\end_layout

\end_inset

 checkbox and the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{User defined}
\end_layout

\end_inset

 checkbox.
\end_layout

\begin_layout Itemize
Hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{import from =.in}
\end_layout

\end_inset

 button, change into the 
\family typewriter
bcc
\family default
 directory and click on =.in.
\end_layout

\begin_layout Itemize
Hit 
\family typewriter

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
\end_layout

\begin_deeper
\begin_layout Standard
Now, we have loaded the bcc high symmetry points of the bcc calculation
 into the super cell setup.
 This works, as we already explained, because in absolute coordinates the
 bcc sym-points are the same in both case.
 It was not necessary to load the magenta BZ.
 The point import works without this.
 But it helps orienting yourself.
\end_layout

\end_deeper
\begin_layout Itemize
In the HSPD 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{export to =.in}
\end_layout

\end_inset

: make sure you export into 
\family typewriter
DO3Co/=.in
\family default
!! 
\end_layout

\begin_layout Itemize
Close the dialog and in the FSW save the state.
\end_layout

\begin_layout Subsection
The hard, more general way
\end_layout

\begin_layout Itemize
Execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo =.in
\end_layout

\end_deeper
\begin_layout Itemize
Select the menu item 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Activities $
\backslash
triangleright$ Fermi surface}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
In the Fermi surface window (FSW) open the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Plot 
\backslash
RA{} Annotations}
\end_layout

\end_inset

 dialog and click on last item (
\begin_inset Quotes eld
\end_inset

Primitive
\begin_inset Quotes erd
\end_inset

) in left panel.
\end_layout

\begin_layout Itemize
click the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{plus}
\end_layout

\end_inset

 button above the left panel or hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-I}
\end_layout

\end_inset

 or the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{ins}
\end_layout

\end_inset

-key.
\end_layout

\begin_layout Itemize
Hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 You should the a magenta box in the FSW.
\end_layout

\begin_layout Itemize
In the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Boundary type}
\end_layout

\end_inset

 selectbox choose 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{user defined}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Now convince yourself that we have a the conventional basis as the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{reference basis}
\end_layout

\end_inset

 (should be default).
\end_layout

\begin_layout Itemize
Remove all items from the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Faces}
\end_layout

\end_inset

 table: either click into the table and use the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{delete}
\end_layout

\end_inset

-key or use the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{delete button}
\end_layout

\end_inset

 
\begin_inset Graphics
	filename pics/delbutton.png
	scale 70

\end_inset

.
\end_layout

\begin_layout Itemize
Insert the following table.
 To insert a new line use the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{plus}
\end_layout

\end_inset

 button right of the table or click into the table (to get the keyboard
 focus there) and hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{ins}
\end_layout

\end_inset

 or 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-I}
\end_layout

\end_inset

-key.
 If a cell is highlighted in the table, insertion will copy this line.
 Use the cursor keys to move around and just start typing.
 Use enter to finish editing a cell.
 You can use the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{tab}
\end_layout

\end_inset

-key to jump to the next cell without hitting enter.
 You can enter fractionals like 
\begin_inset Quotes eld
\end_inset

1/2
\begin_inset Quotes erd
\end_inset

.
\end_layout

\begin_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="13" columns="4">
<features rotate="0" tabularvalignment="middle">
<column alignment="right" valignment="top">
<column alignment="right" valignment="top">
<column alignment="right" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
x
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
y
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
z
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
d0
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="right" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
When done with the table hit the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{accept}
\end_layout

\end_inset

-button or hit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 You should see Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-BZ-of"

\end_inset

.
 This is the normal cell BZ which we derived in Sec.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Interlude"

\end_inset

.
\end_layout

\begin_layout Itemize
Close the Annotations dialog.
\end_layout

\begin_layout Itemize
In the FSW save the state via 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-S}
\end_layout

\end_inset

 or 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{File 
\backslash
RA{} Save}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Open the high symmetry points dialog (HSPD) via 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Plot 
\backslash
RA{} High symemtry points}
\end_layout

\end_inset

 (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-H}
\end_layout

\end_inset

)
\end_layout

\begin_layout Itemize
Check the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Visible}
\end_layout

\end_inset

 checkbox and the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{User defined}
\end_layout

\end_inset

 checkbox.
\end_layout

\begin_layout Itemize
Click on the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Pick points}
\end_layout

\end_inset

 button, go to the FSW and type 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{p l}
\end_layout

\end_inset

 (as in 
\family typewriter
P-key
\family default
 followed by the 
\family typewriter
L-key
\family default
) to switch off the high-symmetry lines and pick points equivalent to the
 
\begin_inset Formula $\Gamma$
\end_inset

, H, N and P points in the magenta box according to the geometry of Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bcc-BZ"

\end_inset

.
 Use zoom (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{mouse wheel}
\end_layout

\end_inset

 or 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{right-click+move}
\end_layout

\end_inset

) and rotation (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{left-click+move}
\end_layout

\end_inset

) to get a clear shot at the points.
 
\end_layout

\begin_deeper
\begin_layout Standard
When done clicking the four points, hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{escape}
\end_layout

\end_inset

 in the FSW window or click the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{stop picking}
\end_layout

\end_inset

 button in the HSPD.
 Now, the table in the HSPD should contain four points 
\begin_inset Formula $\Gamma$
\end_inset

, 
\begin_inset Formula $\Gamma$
\end_inset

, 
\begin_inset Formula $\mathrm{X}_{2}$
\end_inset

, 
\begin_inset Formula $\Gamma$
\end_inset

.
 The names are according to the supercell symmetry.
 We now rename the last three points into H,N and P and hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 Compare to 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bcc-BZ"

\end_inset

 and correct names if needed.
\end_layout

\end_deeper
\begin_layout Itemize
Click into the HSPD table.
 Go to the first line (should be the real 
\begin_inset Formula $\Gamma$
\end_inset

 point) and hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-I}
\end_layout

\end_inset

 followed by the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{p}
\end_layout

\end_inset

-key and then 2 times 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-down}
\end_layout

\end_inset

.
 You should have 
\begin_inset Formula $\Gamma$
\end_inset

HN
\begin_inset Formula $\Gamma$
\end_inset

P.
 
\end_layout

\begin_layout Itemize
Go to the H.
 Hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-I}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{p}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-down}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-down}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-down}
\end_layout

\end_inset

 to get 
\begin_inset Formula $\Gamma$
\end_inset

HN
\begin_inset Formula $\Gamma$
\end_inset

PH.
 
\end_layout

\begin_layout Itemize
Now, go to the bottom of the table and hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-I}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{b}
\end_layout

\end_inset

 to get 
\begin_inset Formula $\Gamma$
\end_inset

HN
\begin_inset Formula $\Gamma$
\end_inset

PH
\begin_inset Formula $\left\langle \mbox{Break}\right\rangle $
\end_inset

.
 
\end_layout

\begin_layout Itemize
Go to the lowest P and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-I}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{p}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-down}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-down}
\end_layout

\end_inset

 to get 
\begin_inset Formula $\Gamma$
\end_inset

HN
\begin_inset Formula $\Gamma$
\end_inset

PH
\begin_inset Formula $\left\langle \mbox{Break}\right\rangle $
\end_inset

P.
\end_layout

\begin_layout Itemize
Go to the N and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-I}
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{p}
\end_layout

\end_inset

 5 
\begin_inset Formula $\times$
\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-down}
\end_layout

\end_inset

 to get the final 
\begin_inset Formula $\Gamma$
\end_inset

HN
\begin_inset Formula $\Gamma$
\end_inset

PH
\begin_inset Formula $\left\langle \mbox{Break}\right\rangle $
\end_inset

PN.
\end_layout

\begin_layout Itemize
Hit enter (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{accept}
\end_layout

\end_inset

 button).
 
\end_layout

\begin_deeper
\begin_layout Standard
Your FSW should have a magenta BZ which looks like 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bcc-BZ"

\end_inset

.
\end_layout

\end_deeper
\begin_layout Itemize
In 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Reference basis}
\end_layout

\end_inset

 choose 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{fplo (units 2pi/a)}
\end_layout

\end_inset

.
 According to our theory in Sec.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Interlude"

\end_inset

 we have the table as in Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bcc-BZ"

\end_inset

 but each coordinate doubled.
 
\end_layout

\begin_layout Itemize
Click on the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Export to =.in}
\end_layout

\end_inset

 button and hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 (We do not need to chose the FPLO basis for export.
 It will be exported just fine, whatever basis is chosen.)
\end_layout

\begin_layout Itemize
Leave the dialog and in the FSW save the state via 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-S}
\end_layout

\end_inset

 or 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{File 
\backslash
RA{} Save}
\end_layout

\end_inset

.
\end_layout

\begin_layout Section
The supercell bandstructure on the normal cell path.
\end_layout

\begin_layout Standard
To show the difference to Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:DO-FeCo,-fatbands"

\end_inset

 we will re-calculate the band structure on the newly defined path.
\end_layout

\begin_layout Itemize
Have a look at the fedit 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bandstructure submenu}
\end_layout

\end_inset

 of fedit to convince yourself that the new high symmetry points are indeed
 there and run 
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\end_deeper
\begin_layout Itemize
followed by
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout LyX-Code
xfbp +bwsum
\end_layout

\begin_layout Standard
Compare the result (Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-SC-fatbands"

\end_inset

) to Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:DO-FeCo,-fatbands"

\end_inset

 and Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bcc-fatbands"

\end_inset

.
 The latter comparison demonstrates the band backfolding due to the larger
 unit cell.
\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/SCbccpath.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:The-SC-fatbands"

\end_inset

The SC fatbands along the NC path.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Section
The unfolding mapping
\end_layout

\begin_layout Standard
We will now map the SC sites onto the NC sites.
 For this we could collect the site mapping table by hand, or we could use
 a tool.
 The tool requests the matrix which transforms the NC direct lattice unit
 cell into the SC direct lattice unit cell.
 So, let's do the math (also see Sec.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Interlude"

\end_inset

).
 We have to map the primitive cells, since these determine the number of
 sites!
\end_layout

\begin_layout Standard
In the NC we have the primitive basis
\begin_inset Formula 
\[
A_{p}=B_{bc}A_{c}
\]

\end_inset

We un-center
\begin_inset Formula 
\[
B_{bc}^{-1}A_{p}=A_{c}
\]

\end_inset

multiply by 2 in all directions
\begin_inset Formula 
\[
2B_{bc}^{-1}A_{p}=2A_{c}
\]

\end_inset

and re-center as fcc to get the SC primitive unit cell
\begin_inset Formula 
\[
A_{p}^{\prime}=B_{fc}2B_{bc}^{-1}A_{p}=B_{fc}2A_{c}
\]

\end_inset

Use the relations for the inverse of the centering matrix Eq.
 (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Bbcinv"

\end_inset

)
\begin_inset Formula 
\begin{eqnarray}
A_{p}^{\prime} & = & 4B_{fc}^{2}A_{p}\nonumber \\
 & = & \left(\begin{array}{ccc}
2 & 1 & 1\\
1 & 2 & 1\\
1 & 1 & 2
\end{array}\right)A_{p}\label{eq:Umatrix}
\end{eqnarray}

\end_inset


\end_layout

\begin_layout Standard
This expresses the SC primitive lattice in terms of the NC lattice.
 Now, for input:
\end_layout

\begin_layout Itemize
Execute 
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo =.in
\end_layout

\end_deeper
\begin_layout Itemize
Open the unfold editor via 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Tools 
\backslash
RA{} Unfold}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Chose 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{large cell in small cell units}
\end_layout

\end_inset

 in the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{units}
\end_layout

\end_inset

 combobox.
\end_layout

\begin_layout Itemize
Enter the matrix Eq.
 (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Umatrix"

\end_inset

) into the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{basis}
\end_layout

\end_inset

 table and hit the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{apply}
\end_layout

\end_inset

 button.
 
\end_layout

\begin_deeper
\begin_layout Standard
You will note that the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{unfold site list}
\end_layout

\end_inset

 now looks much like the example in the introduction, only that we only
 have one type in the NC.
\end_layout

\end_deeper
\begin_layout Itemize
Hit the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{save}
\end_layout

\end_inset

 button and save it to 
\family typewriter
=.unfold
\family default
.
\end_layout

\begin_layout Itemize
Leave the dialog and close 
\family typewriter
xfplo
\family default
.
\end_layout

\begin_layout Itemize
Execute
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\begin_layout Standard
Now we have a new file 
\family typewriter
+bweights_unfold
\family default
.
 We need a new 
\family typewriter
=.addwei
\family default
 to add all the weights.
 The weights in 
\family typewriter
+bweights_unfold will
\family default
 have atom number as given in 
\family typewriter
=.unfold
\family default
 in the NCsite column (first column).
\end_layout

\begin_layout Standard
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

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

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Try to understand why the new 
\family typewriter
=.addwei_unfold
\family default
 must looks like
\end_layout

\begin_layout Standard
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

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

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize

\color red
Especially, note the first two lines and the 
\family typewriter
sites
\family default
!
\end_layout

\begin_layout Itemize
Ok, we assume you have created 
\family typewriter
=.addwei_unfold
\family default
.
 Then execute
\end_layout

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

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 -s =.addwei_unfold
\end_layout

\begin_layout LyX-Code
xfbp +bwsum_unfold
\end_layout

\begin_layout Standard
Voila, you probably got Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-unfolded-SC"

\end_inset

, which looks a lot like Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bcc-fatbands"

\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/unfolded.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:The-unfolded-SC"

\end_inset

The unfolded SC Fe fatbands
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
You should be able to switch on the Co-weight in xfbp to get this
\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/unfoldedall.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:All-unfolded-SC"

\end_inset

All unfolded SC fatbands
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Section
To wrap it up: DO
\begin_inset Formula $_{3}$
\end_inset

 Fe
\begin_inset Formula $_{3}$
\end_inset

Al
\end_layout

\begin_layout Standard
If you want to see what happens if we take Al instead of Co, please repeat
 everything with Al inplace of Co.
 
\end_layout

\begin_layout Itemize
Go back into the 
\family typewriter
task
\family default
 directory.
\end_layout

\begin_layout Itemize
Create a directory called DO3Al and copy files
\end_layout

\begin_layout LyX-Code
mkdir DO3Al
\end_layout

\begin_layout LyX-Code
cd DO3Al
\end_layout

\begin_layout LyX-Code
cp ../DO3Co/=.in .
\end_layout

\begin_layout LyX-Code
cp ../DO3Co/=.addwei .
\end_layout

\begin_layout LyX-Code
cp ../DO3Co/=.addwei_unfold .
\end_layout

\begin_layout Itemize
Use 
\family typewriter
fedit
\family default
 to change Co into Al in the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{symmetry menu}
\end_layout

\end_inset

.
 Don't forget the symmetry 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{update}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Switch off 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


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

\end_inset

.
\end_layout

\begin_layout Itemize
Run fplo to convergence
\end_layout

\begin_layout Itemize
Switch on 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


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

\end_inset

.
\end_layout

\begin_layout Itemize
Re-run fplo.
\end_layout

\begin_layout Itemize
edit 
\family typewriter
=.addwei to look like this (
\color red
element names and orbitals!
\color inherit
)
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

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

\end_inset


\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 open

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout LyX-Code
xfbp +bwsum
\end_layout

\begin_layout Standard
to produce Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:DO-FeAl-fatbands-NCpath"

\end_inset

.
\end_layout

\end_deeper
\begin_layout Itemize
Copy 
\family typewriter
=.unfold
\end_layout

\begin_deeper
\begin_layout LyX-Code
cp ../DO3Co/=.unfold .
\end_layout

\end_deeper
\begin_layout Itemize
and edit it.
 (Replace Co by Al)
\end_layout

\begin_layout Itemize
run fplo.
\end_layout

\begin_layout Itemize
edit 
\family typewriter
=.addwei_unfold to look like this (ORBITALS!)
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

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

\end_inset


\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 open

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 -s =.addwei_unfold
\end_layout

\begin_layout LyX-Code
xfbp +bwsum_unfold
\end_layout

\begin_layout Standard
to get Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:DO-FeAl-unfolded"

\end_inset

 (and/or Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:DO-FeAl-unfolded-all"

\end_inset

 )
\end_layout

\end_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/bweiFe3Al.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:DO-FeAl-fatbands-NCpath"

\end_inset

DO
\begin_inset Formula $_{3}$
\end_inset

 Fe
\begin_inset Formula $_{3}$
\end_inset

Al fatbands along the NC path
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename ../solution/DO3Al/bweiFeAlunfolded.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:DO-FeAl-unfolded"

\end_inset

DO
\begin_inset Formula $_{3}$
\end_inset

 Fe
\begin_inset Formula $_{3}$
\end_inset

Al unfolded
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename ../solution/DO3Al/bweiAllFeAlunfolded.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:DO-FeAl-unfolded-all"

\end_inset

DO
\begin_inset Formula $_{3}$
\end_inset

 Fe
\begin_inset Formula $_{3}$
\end_inset

Al unfolded, all weights
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_body
\end_document
