As an example, let us calculate a invariant of a 3D topological insulator BiSe [83].
SCF calculation
You can perform the SCF calculation using 'Bi2Se3Z2.dat' stored in the directory 'work'
with the following keyword:
HS.fileout on #onoff, default=offAfter finishing the SCF calculation normally, the out file 'Bi2Se3Z2.scfout' is generated.
Calculation of Z invariant
Before computing the invariant by using the code 'Z2FH.c', please
compile the code in directory 'source' as
% make Z2FHAfter the compilation, you may obtain the excutable file 'Z2FH' in the directory 'work'. Then, let us move on the calculation of the Z invariant as
% ./Z2FH Bi2Se3Z2.scfout or % ./Z2FH Bi2Se3Z2.scfout < Z2FH.in > Z2FH.out or % mpirun np 4 ./Z2FH Bi2Se3Z2.scfout < Z2FH.in > Z2FH.out
5 1 1In the first case above, you will be interactively asked from the program as follows:
****************************************************************** ****************************************************************** Z2FH: code for calculating the Z2 invariant of bulk systems by FukuiHatsugai method. Copyright (C), 2019, Hikaru Sawahata, Naoya Yamaguchi, Fumiyuki Ishii and Taisuke Ozaki This is free software, and you are welcome to redistribute it under the constitution of the GNUGPL. Please cite the following article: H. Sawahata, N. Yamaguchi, H. Kotaka and F. Ishii, Jpn. J. Appl. Phys. 57, 030309 (2018). ****************************************************************** ****************************************************************** Mesh1 Number(Half Direction):5 Calculate All plane?(0:No,1:Yes)1 Restart?[1:x0,2:xpi,3:y0....]1 Read the scfout file (Bi2Se3Z2.scfout) *** The file format of the SCFOUT file: 3 And it supports the following functions:  jx  polB  kSpin  Z2FH  calB ***
Parameters for Z2FH
Let us explain the parameters in the input file 'Z2FH.in'.
Output files
After the calculation by 'Z2FH', the following files are generated.
This file stores the computational result of invariant. In case of computing all the plane (you set the second row parameter as '1'.), the invariants on the six planes are on the first line, and four of invariant are on the second line as shown below:
Z2 invariant:(x0,xpi,y0,ypi,z0,zpi)=(1.000000,0.000000,1.000000,0.000000,1.000000,0.000000) Z2 invariant:(nu0,nu1,nu2,nu3):(1,0,0,0)
Data files of integervalued field . The '*' behind 'LCNum' is the index running from 1 to 6. The number (1,2,3,4,5,6) corresponds to , respectively. When you calculate only four planes, four files 'LCNum(2,4,5,6).dat' are generated, corresponding to .
Script files for gnuplot. The '*' behind 'LCNum' is the index running from 1 to 6. The number (1,2,3,4,5,6) corresponds to , respectively. When you calculate only four planes, four files 'LCNum(2,4,5,6).dat' are generated, corresponding to . You can visualize of integervalued field by
% gnuplot LCNum1.pl
This is a copy of input file, which was used for the SCF calculation, reconstructed from the scfout file.
As an example, we show the integervalued field on in Fig. 77, which can be obtained by the procedure explained above as 'gnuplot LCNum1.pl'. Since is the gauge dependent value, you may find a different result in your calculation, while the Z invariant should be reproduced.
