WannierTools¶
WannierTools: an open-source software package for novel topological materials
Source on Github : https://github.com/quanshengwu/wannier_tools
Aiming to investigate topoligical properties of
- Electron systems (Tested)
- Phonon systems (Testing)
Updates¶
WannierTools V2.4.0
Sep 1 2018 1. We have a big update in this version, since Changming Yue put his symmetrization code into WannierTools.
So now we can symmetrize the Wannier functions based tight binding model. This funcionality is included in the wannhr_symm/ folder.
- Fixed a bug about reading Rcut.
- Distinguish two dual surface in the slab band calculation.
- Update an example about calculating the mirror Chern number of ZrTe.
:blue:`Develop branch 2018 June 27 We added the test version of phonon system. Welcome to git clone the develop branch and test it. git clone https://github.com/quanshengwu/wannier_tools.git`
WannierTools V2.3.0
- Fixed a bug.
- Add Translate_to_WS_calc in the CONTROL namelist. This works for BulkFS_plane_calc.
WannierTools V2.2.9 1. Fixed several bugs.
- Added two new functionalities:
- Calculate the energy levels at given k points in the KPOINTS_3D card. This is called the point mode.
- Calculate anomalous Hall conductivity (AHC).
WannierTools V2.2.6
- Discard the Miller indicies
- Discard the third vector in the SURFACE card. The surface plane is specified only by two lattice vectors sitting on it.
Preliminaries¶
Installation of WannierTools (Linux or Mac)¶
Prerequisites¶
You need to install the following (mandatory) packages:
- Fortran compiler (Gfortran or ifort)
- MPICH version higher than 2.1.5
- Lapack and Blas library
Compilation¶
First Check out the repository by
git clone https://github.com/quanshengwu/wannier_tools.git
Or download the .zip file directly from https://github.com/quanshengwu/wannier_tools, then uncompress it
Then Go into wannier_tools/src directory, Choose and Edit Makefile, Change the blas library ” libs= ” to your lapack+blas library
At present, we prepared 3 typical Makefiles, which are squential+gfotran, sequential+ifort and mpi+ifort.
For the mpi compiler, you should switch on the compile flag “-DMPI”, see Makefile.intel-mpi
After the compliation, the binary ‘wann_tools’ is copied to wannier_tools/bin/, you can put this path to the system PATH with
export PATH=/where/you/downloaded/wannier_tools/bin:$PATH
to the .bashrc file in your home directory.
Usage¶
Now you can enjoy your exploration for topological materials with WannierTools.
There are two files you have to prepare,
- wt.in. All the control and user specified parameters are inclued in this file.
- wannier90_hr.dat. Tight binding model constructed by Wannier90 or written in the format as wannier90_hr.dat.
After the preparation of these two files, you can just run wann_tools in the same folder
wt.x &
or in multi-cores
mpirun -np 4 wt.x &
The output information during the running are written in WT.out.
Introduction of input files¶
Attention: From WannierTools 2.2, the name of input file changes from ‘input.dat’ to ‘wt.in’. The excutable binary changes from ‘wann_tools’ to ‘wt.x’
There are two input files you should prepare wt.in and wannier90_hr.dat
- Main input file wt.in
- Special tags for phonon system (under testing)
- Tight-binding model wannier90_hr.dat
Main input file wt.in¶
- Basic Parameters
- TB_FILE
- SYSTEM
- CONTROL
- PARAMETERS
- LATTICE
- ATOM_POSITIONS
- PROJECTORS
- SURFACE
- KPATH_BULK
- KPOINTS_3D
- KPATH_SLAB
- KPLANE_SLAB
- KPLANE_BULK
- KCUBE_BULK
- EFFECTIVE_MASS
- SELECTED_ATOMS
- WANNIER_CENTRES
Before executing wann_tools, you should cp the wt.in file in the directory wannier_tools/example by your own necessary.
For version later than 2.0, we updated the format of wt.in. The input file is structured in a number of NAMELIST and INPUT_CARDS.
Here we introduce the wt.in for Bi2Se3 as an example
&TB_FILE
Hrfile = 'wannier90_hr.dat'
Package = 'VASP' ! obtained from VASP, it could be 'VASP', 'QE', 'Wien2k', 'OpenMx'
/
LATTICE
Angstrom
-2.069 -3.583614 0.000000 ! crystal lattice information
2.069 -3.583614 0.000000
0.000 2.389075 9.546667
ATOM_POSITIONS
5 ! number of atoms for projectors
Direct ! Direct or Cartisen coordinate
Bi 0.3990 0.3990 0.6970
Bi 0.6010 0.6010 0.3030
Se 0 0 0.5
Se 0.2060 0.2060 0.1180
Se 0.7940 0.7940 0.8820
PROJECTORS
3 3 3 3 3 ! number of projectors
Bi px py pz ! projectors
Bi px py pz
Se px py pz
Se px py pz
Se px py pz
SURFACE ! See doc for details
1 0 0
0 1 0
&CONTROL
BulkBand_calc = T
BulkFS_calc = T
BulkGap_cube_calc = T
BulkGap_plane_calc = T
SlabBand_calc = T
WireBand_calc = T
SlabSS_calc = T
SlabArc_calc = T
SlabQPI_calc = T
SlabSpintexture_calc = T
Wanniercenter_calc = T
BerryCurvature_calc = T
EffectiveMass_calc = T
/
&SYSTEM
NSLAB = 10 ! for thin film system
NSLAB1= 4 ! nanowire system
NSLAB2= 4 ! nanowire system
NumOccupied = 18 ! NumOccupied
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
Bx= 0, By= 0, Bz= 0 ! Bx By Bz
surf_onsite= 0.0 ! surf_onsite
/
&PARAMETERS
Eta_Arc = 0.001 ! infinite small value, like brodening
E_arc = 0.0 ! energy for calculate Fermi Arc
OmegaNum = 100 ! omega number
OmegaMin = -0.6 ! energy interval
OmegaMax = 0.5 ! energy interval
Nk1 = 21 ! number k points odd number would be better
Nk2 = 21 ! number k points odd number would be better
Nk3 = 21 ! number k points odd number would be better
NP = 1 ! number of principle layers
Gap_threshold = 1.0 ! threshold for GapCube output
/
KPATH_BULK ! k point path
4 ! number of k line only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000
KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5
KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane
0.2 0.0 ! The first vector to define 2D k plane
0.0 0.2 ! The second vector to define 2D k plane for arc plots
KPLANE_BULK
-0.00 -0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane
KCUBE_BULK
-0.50 -0.50 -0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
EFFECTIVE_MASS ! optional
2 ! The i'th band to be calculated
0.01 ! k step in unit of (1/Angstrom)
0.0 0.0 0.0 ! k point where the effective mass calculated.
WANNIER_CENTRES ! copy from wannier90.wout
Cartesian
-0.000040 -1.194745 6.638646
0.000038 -1.196699 6.640059
-0.000032 -1.192363 6.640243
-0.000086 -3.583414 2.908040
0.000047 -3.581457 2.906587
-0.000033 -3.585864 2.906443
-0.000001 1.194527 4.773338
0.000003 1.194538 4.773336
-0.000037 1.194536 4.773327
0.000006 -1.194384 1.130261
-0.000018 -1.216986 1.140267
0.000007 -1.172216 1.140684
0.000011 -3.583770 8.416406
-0.000002 -3.561169 8.406398
-0.000007 -3.605960 8.405979
0.000086 -1.194737 6.638626
-0.000047 -1.196693 6.640080
0.000033 -1.192286 6.640223
0.000040 -3.583406 2.908021
-0.000038 -3.581452 2.906608
0.000032 -3.585788 2.906424
0.000001 1.194548 4.773330
-0.000003 1.194537 4.773332
0.000037 1.194539 4.773340
-0.000011 -1.194381 1.130260
0.000002 -1.216981 1.140268
0.000007 -1.172191 1.140687
-0.000006 -3.583766 8.416405
0.000018 -3.561165 8.406400
-0.000007 -3.605935 8.405982
Basic Parameters¶
TB_FILE, LATTICE, ATOM_POSITIONS, PROJECTORS and SURFACE are the necessary basic parameters. They are used by almost all functionalities listed in CONTROL namelist.
NAMELISTS¶
NAMELISTS are a standard input construct in Fortran90. The use of NAMELISTS is relatively flexible. All the variables in the NAMELISTS have default values. You should set them only when it is needed. Variables can be inserted in any order. Such as
&NAMELIST
needed_variable2=XX, needed_variable1=YY,
character_variable1='a suitable string'
/
There are 4 NAMELISTS included in wt.in. They are TB_FILE, SYSTEM, CONTROL, PARAMETERS.
Note
If you want to comment one line, please use ‘!’ instead of ‘#’, because our codes were written in Fortran.
TB_FILE¶
Set the filename of the tight-binding Hamiltonian. At present, we use the format of wannier90_hr.dat specified in Wannier90.
&TB_FILE
Hrfile = 'wannier90_hr.dat'
Package = 'VASP' ! obtained from VASP, it could be 'VASP', 'QE', 'Wien2k', 'OpenMx'
/
The default value for Hrfile is ‘wannier90_hr.dat’. You could specify the first-principle package that used for obtaining wannier90_hr.dat. Default value for Package is ‘VASP’. We support VASP, QE, Wien2k, OpenMx, Abinit at present. Please report new software package to me if you needed.
Note
Package is very important if you use QE to generate your tight binding model. Because the orbital order in QE is different from VASP, Wien2k et al.. And it will affect the results of spin texture. If you got strange spin texture, please carefully check this tag.
SYSTEM¶
In this namelists, we specify the system you need to compute.
&SYSTEM
Nslab = 10
Nslab1= 6
Nslab2= 6
NumOccupied = 18 ! NumOccupied
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
Bx= 0, By= 0, Bz= 0 ! Bx By Bz
surf_onsite= 0.0 ! surf_onsite
/
- NSlab : integer, Number of slabs for slab band, The default value is 10.
- NSlab1, Nslab2 : integers, The thickness of nano ribbon. If you don’t want to calculate the band structure of it, then don’t set it. The default values are Nslab1= 1, Nslab2= 1.
- NumOccupied : integer, Number of occupied Wannier bands. No default value.
Important: please set NumOccpuied correctly. It represents the “occpuied” wannier bands, not the total number of electrons. In the calculation of Wilson loop, the Wilson loop is the trace of NumOccupied bands. If you want to study the topology between the 8th and the 9th band, then set NumOccupied=8.
When you search Weyl points, nodal line or study the gap in some k slices, NumOccupied is also a very important. WannierTools will look for touching point or calculate the energy gap between the NumOccupied’th band and the (NumOccupied+1)’th band.
When you calculate the Fermi surface with BulkFS_calc= T, In order to save the storage, WannierTools only writes out 8(16) energy bands around NumOccupied’th band for SOC=0 (SOC=1) system into FS3D.bxsf.
If you don’t put any physical meaning into this tag, then it is very easy to understand.
- SOC : integer, Flag for spin-orbital coupling. If SOC=0, it means there is no SOC included in your given tight binding model. if SOC=1 or >0, it means SOC is already included in the tight binding model.
- E_FERMI : real-valued, Fermi level for the given tight binding model.
- Bx, By, Bz : real-valued, magnetic field value. Ignore it in this version.
- surf_onsite : real-valued, Additional onsite energy on the surface, you can set this to see how surface state changes. But don’t set it if you don’t know what it is.
CONTROL¶
In this name list, you can set the keywords to setup the tasks. All these tasks can be set to be true at the same time.
&CONTROL
BulkBand_calc = T ! bulk band structure calculation flag
BulkFS_calc = F
BulkGap_cube_calc = F
BulkGap_plane_calc = F
SlabBand_calc = T
WireBand_calc = F
SlabSS_calc = T
SlabArc_calc = F
SlabSpintexture_calc = T
wanniercenter_calc = F
BerryCurvature_calc = F
/
Note
New features : :red: FindNodes_calc; WeylChirality_calc; Z2_3D_calc; Chern_3D_calc
We listed those features in the table below.
| Flag options | Function | Output | Tested |
|---|---|---|---|
| BulkBand_calc | Band structure for bulk | bulkek.dat, bulkek.gnu | yes |
| BulkFS_calc | Fermi surface for bulk system | FS3D.dat, FS3D.bxsf | yes |
| BulkGap_cube_calc | Energy gap for a given k cube for bulk system | GapCube.dat, GapCube.gnu | yes |
| BulkGap_plane_calc | Energy gap for a given k plane for bulk system | GapPlane.dat, GapPlane.gnu | yes |
| FindNodes_calc | Find touching points between the Numoccpuied’th band and (Numoccpuied+1)’th band | Nodes.dat, Nodes.gnu | yes |
| SlabBand_calc | Band structure for 2D slab system | slabek.dat,slabek.gnu | yes |
| WireBand_calc | Band structure for 1D ribbon system | ribbonek.dat,ribbonek.gnu | yes |
| Dos_calc | Density of state for 3D bulk system | dos.dat | yes |
| JDos_calc | Joint Density of state for 3D bulk system | jdos.dat | yes |
| SlabSS_calc | Surface spectrum A(k,E) along a kline and energy interval for slab system | dos.dat_l, dos.dat_r, dos.dat_bulk,surfdos_l.gnu, surfdos_r.gnu, surfdos_l_only.gnu, surfdos_r_only.gnu, surfdos_bulk.gnu | yes |
| SlabArc_calc | Surface spectrum A(k,E0) for fixed energy E0 in 2D k-plane for slab system | arc.dat_l, arc.dat_r, arc_l.gnu, arc_r.gnu, arc_l_only.gnu, arc_l_only.gnu, | yes |
| SlabQPI_calc | Surface QPI for fixed energy E0 in 2D k-plane for slab system | arc.dat_l, arc.dat_r, arc_l.gnu, arc_r.gnu, arc_l_only.gnu, arc_l_only.gnu, arc.jdat_l, arc.jdat_r, arc.jsdat_l, arc.jsdat_r, arc_l_jdos.gnu, arc_l_jsdos.gnu, arc_r_jdos.gnu, arc_r_jsdos.gnu, | yes |
| SlabSpintexture_calc | Spin texture in 2D k-plane for slab system | spindos_l.dat spindos_r.dat spintext_l.gnu spintext_r.gnu spintext_l.dat spintext_r.dat | yes |
| wanniercenter_calc | Wilson loop of a given 3D k-plane for bulk system | wcc.dat, wcc.gnu | yes |
| Z2_3D_calc | Wilson loop in all 6 3D k-planes for bulk system Z2 number calculation | wanniercenter3D_Z2.gnu, wanniercenter3D_Z2_{1-6}.dat | yes |
| Chern_3D_calc | Wilson loop in all 6 3D k-planes for bulk system Chern number calculation | wanniercenter3D_Z2.gnu, wanniercenter3D_Z2_{1-6}.dat | yes |
| WeylChirality_calc | Weyl Chirality calculation for given k points | find chiralities in WT.out, wanniercenter3D_Weyl.dat, wanniercenter3D_Weyl_*.gnu | yes |
| BerryPhase_calc | Berry phase with a 3D k path for bulk system | find Berry phase in WT.out | Yes |
| BerryCurvature_calc | Berry Curvature in 3D k-plane for bulk system | BerryCurvature.dat, BerryCurvature.gnu Berrycurvature-normalized.dat Berrycurvature-normalized.gnu | yes |
| AHC_calc | Calculate anomalous Hall conductivity for bulk system | sigma_ahe.txt in unit of (Ohm*cm)^-1 | yes |
| FindNodes_calc | Find touch point between the N’th band to the (N+1)’th band in 3D BZ N=NumOccupied | Nodes.dat Nodes.gnu | yes |
PARAMETERS¶
In this namelists, we listed some parameters necessary in the task you specified in namelists CONTROL.
&PARAMETERS
E_arc = 0.0 ! energy for calculate Fermi Arc
Eta_Arc = 0.001 ! infinite small value, like broadening
OmegaNum = 200 ! omega number
OmegaMin = -0.6 ! energy interval
OmegaMax = 0.5 ! energy interval
Nk1 = 50 ! number k points
Nk2 = 50 ! number k points
Nk3 = 50 ! number k points
NP = 2 ! number of principle layers
Gap_threshold = 1.0 ! threshold for GapCube output
/
E_arc : real-valued, energy for calculate Fermi arc, used if SlabArc_calc = T. The default value is 0.0.
Eta_Arc : real-valued, infinite same value for broadening used in Green’s function calculation. used if SlabArc_calc = T. Default value is 0.001.
[OmegaMin, OmegaMax] : real-valued, energy interval for surface state calculation. used if SlabSS_calc= T. No default value.
OmegaNum : integer valued, Number of slices in the energy interval [OmegaMin, OmegaMax]. used if SlabSS_calc= T. The default value is 100.
Nk1, Nk2, Nk3 : integer valued, Number of k points for different purpose. I will explain that later. Default value is Nk1=20, Nk2=20, Nk3=20.
NP : integer valued, Number of principle layers, see details related to iterative green’s function. Used if SlabSS_calc= T, SlabArc_calc=T, SlabSpintexture_calc=T. Default value is 2. You need to do a convergence test by setting Np= 1, Np=2, Np=3, and check the surface state spectrum. Basically, the value of Np depends on the spread of Wannier functions you constructed. One thing should be mentioned is that the computational time grows cubically of Np.
Gap_threshold : real valued. This value is used when you do energy gap calculation like BulkGap_cube_calc=T, BulkGap_plane_calc=T. The k points will be printed out in a file when the energy gap is smaller than Gap_threshold.
Input Card¶
The second important format in wt.in is the input_card format, which is relatively fixed format. First, we need a keyword like LATTICE, which is name of this card. After this keyword, the number of lines is fixed until it is done. There are several INPUT_CARDS in the wt.in. There is no order between the INPUT_CARDS. And any comments or blank lines could be added between the INPUT_CARDS. Lets introduce them one by one.
LATTICE¶
In this card, we set three lattice vectors coordinates. For the unit, you can use both Angstrom and Bohr. However, in the program, we use Angstrom. Bohr unit will be transformed to Angstrom automatically. No default values for the LATTICE CARD.
LATTICE
Angstrom
-2.069 -3.583614 0.000000 ! crystal lattice information
2.069 -3.583614 0.000000
0.000 2.389075 9.546667
ATOM_POSITIONS¶
In this card, we set the atom’s position.
ATOM_POSITIONS
5 ! number of atoms for projectors
Direct ! Direct or Cartisen coordinate
Bi 0.3990 0.3990 0.6970
Bi 0.6010 0.6010 0.3030
Se 0 0 0.5
Se 0.2060 0.2060 0.1180
Se 0.7940 0.7940 0.8820
Note
1. Here the atom means that the atoms with projectors. not the whole atoms in the unit cell. 2. You can use “Direct” or “Cartesian” coordinates. “Direct” means the fractional coordinate based on the primitive lattice vector listed in LATTICE CARDS.
PROJECTORS¶
In this card, we set the Wannier projectors for the tight binding.
PROJECTORS
3 3 3 3 3 ! number of projectors
Bi pz px py ! projectors
Bi pz px py
Se pz px py
Se pz px py
Se pz px py
Here we don’t take into account the spin degeneracy, only consider the orbital part. The name of orbitals should be “s”, “px”, “py”, “pz”, “dxy”, “dxz”, “dyz”, “dx2-y2”, “dz2”. I will add f orbitals latter. The order of the orbitals is very important if you want to analyze the symmetry properties. The default order in Wannier90 is “s”, “pz”, “px”, “py”, “dz2”, “dxz”, “dyz”, “dx2-y2”, “dxy”. You can find the orbital order from wannier90.wout.
Note
If you don’t care about the calculation related to symmetry like mirror chern number. The order or the name is not important. So for the f electrons, please write 7 random orbitals like px or dz2 or what else you want.
SURFACE¶
Attention: from version v2.2.6 on, you can specify a surface with SURFACE card with only two lattice vectors.
MILLER_INDICES CARD¶
Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices. You can find more information from Wikipedia https://en.wikipedia.org/wiki/Miller_index. In WannierTools, you only need to specfiy three integers like
MILLER_INDICES
0 0 1
Note
Since this is very confusing, we discard it from version V2.2.6. You should notice that the Miller indices mentioned here are based on three vectors specified in LATTICE card.
SURFACE CARD¶
This card is very important for slabs calculation. You need to read the following text carefully
SURFACE ! See doc for details
1 0 0 a11, a12, a13
0 1 0 a21 a22 a23
In this card, we specify the surface you want to investigate. Basically, you should be aware of which surface you want to investigate, and of which direction you want to study the ribbon. So we need to define the new lattice vector system like this,
Choose two lattice vectors on the surface we want to study, and choose another vector which is not on this plane.
The slab calculations are base on the surface constructed by vector \(R_1', R_2'\).
Note
a11, a12, a13 …, a23 should be integers, in unit of three lattice vectors
KPATH_BULK¶
This is the k path for bulk band structure calculation.
KPATH_BULK ! k point path
4 ! number of k line only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000
These k points are in unit of the reciprocal lattice constant built by the lattice vector LATTICE CARD. The number of k points is Nk1, which is set in NAMELISTS PARAMETERS. There are no default values for this CARD. So you must set some value in the input file when choosing BulkBand_calc=T.
KPOINTS_3D¶
You can calculate the properties on some kpoints you specified in point mode. e.g. the energy bands
KPOINTS_3D
4 ! number of k points
Direct ! Direct or Cartesian
0.00000 0.00000 0.0000
0.00000 0.00000 0.5000
0.50000 0.50000 0.0000
0.00000 0.00000 0.0000
The number of lines below “Direct” should be the same as the number above “Direct”. You could add comments at the end of each line. But you can’t add additional comment lines between the formatted lines.
KPATH_SLAB¶
This is the k path for slab system.
KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5
including the band structure calculation and the surface state calculation. It is necessary to set it when SlabBand_calc=T or SlabSS_calc=T. Number of k points along the line is Nk1.
KPLANE_SLAB¶
Define a 2D k space plane for arc plots.
KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane
0.2 0.0 ! The first vector to define 2D k plane
0.0 0.2 ! The second vector to define 2D k plane for arc plots
The first line is the start point of the plane. The second and third line are the two vectors defining the plane. The number of k points for the 1st and 2nd vector is Nk1 and Nk2 respectively. Set this CARD when SlabArc_calc=T, SlabSpintexture_calc= T. The default values are
KPLANE_SLAB
-0.5 -0.5 ! Original point for 2D k plane
1.0 0.0 ! The first vector to define 2D k plane
0.0 1.0 ! The second vector to define 2D k plane for arc plots
KPLANE_BULK¶
The same set as KPLANE_SLAB CARD, but for 3D case.
KPLANE_BULK
-0.50 -0.50 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
We can use these two vectors to calculate the band gap of a plane in 3D BZ, then we can check whether there are Weyl points or nodal line in that plane. Notice that these vectors is in unit of reciprocal vectors. Set this CARD when BulkGap_plane_calc=T, BerryCurvature_calc=T, wanniercenter_calc=T. Default values are
KPLANE_BULK
0.00 0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane
KCUBE_BULK¶
The same set as KPLANE_BULK CARD
KCUBE_BULK
-0.50 -0.50 -0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
We add another k vector to construct a k cube. Set this for BulkGap_cube_calc=T. The values list above are default values.
EFFECTIVE_MASS¶
This card is set for effective mass calculation
EFFECTIVE_MASS ! optional
2 ! The i'th band to be calculated
0.01 ! k step in unit of (1/Angstrom)
0.0 0.0 0.0 ! k point where the effective mass calculated.
SELECTED_ATOMS¶
This card is useful if you want to get some energy spectrum that only projected on some specific atoms. For example, we can calculate the surface projected spin texture in the bulk system with vacuum.
The example is listed in the example/Bi2Se3-6Qlayers
SELECTED_ATOMS
2 ! number groups of selected atoms
6 12 18 24 30 ! top surface's atoms
1 7 13 19 25 ! bottom surface's atoms
WANNIER_CENTRES¶
This card will be usefull for Wilson loop calculations.
WANNIER_CENTRES ! copy from wannier90.wout
Cartesian
-0.000040 -1.194745 6.638646
0.000038 -1.196699 6.640059
-0.000032 -1.192363 6.640243
-0.000086 -3.583414 2.908040
0.000047 -3.581457 2.906587
-0.000033 -3.585864 2.906443
-0.000001 1.194527 4.773338
0.000003 1.194538 4.773336
-0.000037 1.194536 4.773327
0.000006 -1.194384 1.130261
-0.000018 -1.216986 1.140267
0.000007 -1.172216 1.140684
0.000011 -3.583770 8.416406
-0.000002 -3.561169 8.406398
-0.000007 -3.605960 8.405979
0.000086 -1.194737 6.638626
-0.000047 -1.196693 6.640080
0.000033 -1.192286 6.640223
0.000040 -3.583406 2.908021
-0.000038 -3.581452 2.906608
0.000032 -3.585788 2.906424
0.000001 1.194548 4.773330
-0.000003 1.194537 4.773332
0.000037 1.194539 4.773340
-0.000011 -1.194381 1.130260
0.000002 -1.216981 1.140268
0.000007 -1.172191 1.140687
-0.000006 -3.583766 8.416405
0.000018 -3.561165 8.406400
-0.000007 -3.605935 8.405982
Those centres can be obtained from wannier90.wout by searching “Final state”. The default values for this card are atomic positions.
Special tags for phonon system (under testing)¶
Now we have one testing version of phonon system, you can write to wuquansheng@gmail.com for testing. There are two steps for using WannierTools for phonon system.
1. Use phonon_hr.py to get the tight-binding Hamiltonian from the FORCE_CONSTANTS or FORCE_SETS which generated with phonopy. This part was written by Changming Yue (yuechangming8 at gmail.com). You can write email to him to get the source. By default the hrfile name of the Hamiltonian is phonopyTB_hr.dat. You can change the name of it as whatever you want.
2. After the generation of hrfile. You need another wt.in file as the same as the electron system. One difference is that you need to specify Particle = ‘phonon’ in the TB_FILE namelist like
&TB_FILE
Hrfile = 'phonopyTB_hr.dat'
Particle = 'phonon'
/
LO-TO splitting¶
The LO-TO splitting can be treated as a pertubation see phonopy.
We need the following necessary CARDs in the wt.in. Take FeSi as an example
ATOM_MASS
2 ! number of types of atom, for FeSi, we have 2
4 4 ! number of atoms for each atom-type Fe4Si4
55.845 28.0855 ! atomic mass for each type of atom
LOTO_DT ! Dielectric constant tensor
199.480 0 0
0 199.480 0
0 0 199.480
LOTO_BC ! Born charge tensor for each type of atom
-4.3431500 0.6899200 -0.4140700
-0.4140800 -4.3431600 0.6899300
0.6898900 -0.4140600 -4.3431500
4.3909800 0.2300200 -0.1092900
-0.1093100 4.3909900 0.2300100
0.2300400 -0.1092800 4.3909800
LOTO_DT is a 3*3 matrix. LOTO_BC are Number-of-atom-types 3*3 matrices.
Tight-binding model wannier90_hr.dat¶
This file contains the TB parameters. Usually, it can be generated by Wannier90.
Of cource, you can generate it from the Slater-Koster method or discretize k.p model onto a cubic lattice. The format should like this
written on 8May2016 at 13:57:00
30
547
2 2 1 1 1 1 1 1 1 1 2 2 2 2 2
1 1 1 2 1 1 1 2 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 4
2 2 2 2 2 2 2 4 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
2 2 2 2 2 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 2 2 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 1 1 1 2 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 1 1 1 2 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 2 1 1 1 1 1 1 1 2 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 2 2 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 2 1 1 1 1 1 1 1 2 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 2 2 2 2 2 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 4
2 2 2 2 2 2 2 4 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
1 1 1 2 1 1 1 2 2 2 2 2 1 1 1
1 1 1 1 1 2 2
-6 2 -3 1 1 -0.000002 0.000003
-6 2 -3 2 1 0.000002 0.000017
-6 2 -3 3 1 -0.000053 0.000002
-6 2 -3 4 1 -0.000031 0.000002
-6 2 -3 5 1 0.000001 -0.000000
-6 2 -3 6 1 -0.000003 0.000002
-6 2 -3 7 1 0.000037 -0.000001
-6 2 -3 8 1 -0.000001 -0.000003
-6 2 -3 9 1 -0.000005 -0.000003
-6 2 -3 10 1 -0.000062 -0.000001
-6 2 -3 11 1 -0.000001 0.000001
-6 2 -3 12 1 -0.000031 0.000002
-6 2 -3 13 1 0.000011 -0.000000
-6 2 -3 14 1 -0.000001 0.000001
-6 2 -3 15 1 0.000003 0.000003
-6 2 -3 16 1 0.000000 -0.000010
-6 2 -3 17 1 -0.000010 -0.000001
-6 2 -3 18 1 -0.000000 -0.000008
-6 2 -3 19 1 0.000000 0.000000
-6 2 -3 20 1 0.000012 -0.000002
......
- The 1st line is a comment line with any content.
- The 2nd line is the number of Wannier orbitals, in consideration of spin degeneracy. We call it NUM_WANNS
- The 3rd line is the number of R lattice vectors, we call it NRPTS
- This section is about the degeneracy of R points. If you generate wannier90_hr.dat by you self, please set it to 1. There are NRPTS number of 1.
- This section gives the TB parameters. The first three integers are the coordinates or R vectors in unit of three lattice vectors. The 4th and 5th column are the band index (Row first). The 6th and 7th are complex entities of the Hamiltonian.
Capabilities of WannierTools¶
- Bulk band calculation (points mode, line mode and plane mode)
- BulkFS calculation
- BulkFS plane calculation
- Bulk spin texture calculations New
- Density state(DOS) calculations
- Find Nodes calculation
- Energy gap calculations (plane and cube mode)
- Slab band calculation
- Nanowire/nanoribbon band calculation
- Surface state ARPES calculation
- Surface state QPI calculation
- Fermi arc calculation
- Spin texture calculation
- Berry phase calculation
- Berry curvature calculation for 3D bulk case
- Berry curvature calculation for slab system New
- Anomalous Hall conductivity (AHC)
- Wannier charge center/Wilson loop calculation
- Z2 number for 3D bulk materials
- Chern number for 3D bulk materials
- Mirror Chern number calculation New
- Weyl Chirality calculation
- Landau level calculations
Bulk band calculation (points mode, line mode and plane mode)¶
Points mode¶
You can calculate the energy bands with the given k points in the KPOINTS_3D KPOINTS_3D card.
Input¶
Typical flags for this mode in the wt.in.
&CONTROL
BulkBand_points_calc = T
/
KPOINTS_3D
4 ! number of k points
Direct ! Direct or Cartesian
0.00000 0.00000 0.0000
0.00000 0.00000 0.5000
0.50000 0.50000 0.0000
0.00000 0.00000 0.0000
Output¶
The outputs for this mode is bulkek-pointsmode.dat
Line mode¶
Calculate bulk energy band for a series k lines. This is the basic calculation after the construction of Wannier functions. You have to compare your Wannier interpolated bands with the DFT bands. Those two bands should match well around the Fermi level.
Input¶
Typical flags for bulk band calculation in the wt.in.
&CONTROL
BulkBand_calc = T
/
&PARAMETERS
Nk1 = 101 ! Number of k points for each k line
/
KPATH_BULK ! k point path
4 ! number of k lines only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000
See CONTROL, PARAMETERS, KPATH_BULK
Output¶
The outputs for bulk band calculation are bulkek.dat and bulkek.gnu. You can get the band plot by running
gnuplot bulkek.gnu
or
xmgrace bulkek.dat
to get bandstucture plot.
The data structure for bulkek.dat
0.000000000 -2.673821992 119 80 80 119 80 80 205 138 138 70 40 40 70 40 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.016453872 -2.681536808 118 78 78 118 78 78 203 134 134 82 41 41 82 41 41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
- The 1st column represents k points for the given kpath (KPATH_BULK)
- The 2nd column is the energy level
- From the 3rd to the n’th column are the projected weight of the wave function at each k point and each band onto each wannier orbitals. Those weights are normalized to 255 for the color plot convinence.
The subrotine for this feature is ek_bulk.f90 .
Plane mode¶
Calculate band structure in a k slice(plane) specified by KPLANE_BULK card. The mode is very useful to visualize the Dirac/Weyl cone. You have to set the following tags in wt.in
&CONTROL
BulkBand_plane_calc = T
/
&PARAMETERS
Nk1 = 51 ! Number of k points along the first vector in KPLANE_BULK
Nk2 = 51 ! Number of k points along the second vector in KPLANE_BULK
/
KPLANE_BULK ! fractional coordinates
0.00 0.00 0.30 ! Middle point for a k slice(plane) in 3D BZ. Usually, the position of Dirac points.
0.50 0.00 0.00 ! The first vector to define k plane(slice) in 3D BZ
0.00 0.50 0.00 ! The second vector to define k plane(slice) in 3D BZ
The output file is bulkek_plane.dat, bulkek_plane-matlab.dat and bulkek_plane.gnu. You can get bulkek_plane.png with
gnuplot bulkek_plane.gnu
The bulkek_plane-matlab.dat is in MATLAB data format. You can plot the Dirac cone with matlab.
The format of bulkek_plane.dat is as follows:
# kx ky kz k1 k2 k3 E(Numoccupied-1) E(Numoccupied) E(Numoccupied+1) E(Numoccupied+2)
-0.299354337 -0.518496963 0.180167841 -0.518496936 -0.299354384 0.180167841 -1.311721381 -1.311705191 0.588683811 0.588872215
-0.299354337 -0.504670376 0.180167841 -0.511583643 -0.287380208 0.180167841 -1.294078082 -1.293904952 0.586780093 0.587249790
...
Column 1-3rd are k points in cartesian coordinates. Column 4-6th are k points in a rotated cartesian coordinates where the x and y direction are line in the k plane and the z direction is perpendicular to the k plane you specified. Column 7-10th are energies at each k point. Here we only print out 4 energy bands around the fermilevel. It depends on NumOccupied. Usually, I choose column 4th and 5th as k coordinates and choose 8 and 9 as energy bands to show the Dirac cone shown below.
BulkFS calculation¶
Bulk Fermi surface calculation.
Input¶
You should specify the number of k points for each three reciprocal vectors Nk1, Nk2, Nk3 in NAMELISTS PARAMETERS
&CONTROL
BulkFS_calc = T
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
Nk2 = 101 ! No. of slices for the 2nd reciprocal vector
Nk3 = 101 ! No. of slices for the 3rd reciprocal vector
/
KCUBE_BULK
0.00 0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
See CONTROL, PARAMETERS
BulkFS plane calculation¶
Bulk Fermi surface in a fixed k plane specified by KPLANE_BULK
Input¶
You should specify the number of k points for each three reciprocal vectors Nk1, Nk2 in NAMELISTS PARAMETERS
&CONTROL
BulkFS_Plane_calc = T
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
Nk2 = 101 ! No. of slices for the 2nd reciprocal vector
/
KPLANE_BULK ! in fractional coordinates
0.00 0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
See CONTROL, PARAMETERS
Bulk spin texture calculations¶
Calculate spin texture for bulk system that with vacuum or without inversion symmetry. For the bulk system with vacuum, you can calculate the surface projected spin texture. This is useful for comparing with the ARPES experiments. if you cut a slab system from a periodic tight binding model, then there is no charge relaxation on the surface which would change the surface state a lot. In this case, you have to do the first-principle calculations for a finite thickness slab system that with vacuum. Then you can construct Wannier functions for this system and use WannierTools to get the iso-energy plot of the Fermi surface (BulkFS_plane_calc =T) and get the surface projected spin texture (Bulkspintext_calc=T).
There is one example in the examples/Bi2Se3-6Qlayers.
Density state(DOS) calculations¶
Calculation density of state for the bulk system. The typical setup in wt.in:
&CONTROL
DOS_calc = T
/
&PARAMETERS
OmegaNum = 601 ! number of slices of energy
OmegaMin = -1.0 ! erergy range for DOS
OmegaMax = 1.0
Nk1 = 51 ! No. of slices for the 1st reciprocal vector
Nk2 = 51 ! No. of slices for the 2nd reciprocal vector
Nk3 = 51 ! No. of slices for the 3nd reciprocal vector
/
KCUBE_BULK
0.00 0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
Outputs are dos.dat and dos.gnu. dos.eps will be obtained with
gnuplot dos.gnu
Energy gap calculations (plane and cube mode)¶
We support two modes for energy gap calculations.The formula is \(gap(k)= E_{NumOccupied+1}(k)- E_{NumOccpuied}(k)\)
Gap_plane mode¶
Calculate the energy gap for the k points in the KPLANE_BULK. This is useful to show Weyl points and nodal line structure.
Input¶
Typical input parameters for BulkGap_plane calculation
&CONTROL
BulkGap_Plane_calc = T
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
Nk2 = 101 ! No. of slices for the 2nd reciprocal vector
/
KPLANE_BULK
0.00 0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane(slice)
0.00 0.50 0.00 ! The second vector to define 3d k space plane(slice)
See CONTROL, PARAMETERS, KPATH_BULK
Output¶
The outputs for Gap_plane mode are GapPlane.dat, GapPlane.gnu. The GapPlane.png will get by
gnuplot GapPlane.gnu
The head of GapPlane.dat
kx ky kz gap Ev4 Ev3 Ev2 Ev1 Ec1 Ec2 Ec3 Ec4 k1 k2 k3
0.00000000 0.00000000 0.00000000 0.45569845 -0.69109275 -0.69109055 -0.29654328 -0.29654073 0.15915772 0.15915871 1.24348171 1.24348457 0.00000000 0.00000000 0.00000000
0.03796028 -0.02191637 0.00548462 0.43770730 -0.77636510 -0.77598312 -0.26035113 -0.26027881 0.17742849 0.17771545 1.29499437 1.29505298 0.00000000 0.02500000 0.00000000
- Column 1-3 are the Cartesian coordinates of the k points in the KPLANE_BULK, in unit of \(\frac{1}{Angstrom}\)
- Column 4 is the energy gap
- Column 5-12 are the energy value for valence and conduction bands close to the Fermi level. There are 4 conduction bands and 4 valence bands.
- Column 13-15 are the Direct coordinates of the k points in the KPLANE_BULK
Gap_Cube mode¶
This helps us to find Weyl points and nodal line structure in the 3D BZ.
Input¶
Typical input parameters for BulkGap_cube calculation
&CONTROL
BulkGap_Cube_calc = T
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
Nk2 = 101 ! No. of slices for the 2nd reciprocal vector
Nk3 = 101 ! No. of slices for the 3rd reciprocal vector
/
KCUBE_BULK
-0.50 -0.50 -0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The 1st vector to define 3d k cube
0.00 1.00 0.00 ! The 2nd vector to define 3d k cube
0.00 0.00 1.00 ! The 3rd vector to define 3d k cube
See CONTROL, PARAMETERS, KCUBE_BULK
Output¶
The outputs for Gap_plane mode are GapCube.dat, GapCube.gnu. The GapCube.png will get by
gnuplot GapCube.gnu
The head of GapCube.dat are
kx (1/A) ky (1/A) kz (1/A) Energy gap Ev Ec k1 (2pi/a) k2 (2pi/b) k3 (2pi/c)
0.00000000 0.87665487 -0.54846229 0.79075142 -0.34827281 0.44247861 -0.50000000 -0.50000000 -0.50000000
0.00000000 0.87665487 -0.51555455 0.86792416 -0.38635069 0.48157346 -0.50000000 -0.50000000 -0.45000000
- Column 1-3 are the Cartesian coordinates of the k points where energy gap is small than Gap_threshold, in unit of \(\frac{1}{Angstrom}\)
- Column 4 is the energy gap. Those values are smaller than Gap_threshold, see PARAMETERS
- Column 5-6 are the energy value for valence and conduction bands close to the Fermi level. There are 4 conduction bands and 4 valence bands.
- Column 7-9 are the Direct coordinates of the k points.
Find Nodes calculation¶
Beside by using GapCube and GapPlane to find Weyl/Dirac nodes or node lines, we can directly using FindNodes function. \(gap(k)= E_{NumOccupied+1}(k)- E_{NumOccpuied}(k)\)
Input¶
Typical input parameters for FindNodes_cube calculation
&CONTROL
FindNodes_calc = T
/
&PARAMETERS
Nk1 = 8 ! No. of slices for the 1st reciprocal vector
Nk2 = 8 ! No. of slices for the 2nd reciprocal vector
Nk3 = 8 ! No. of slices for the 3rd reciprocal vector
Gap_threshold = 0.0001 ! a value to determine which point should be identified as a node
/
KCUBE_BULK
-0.50 -0.50 -0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The 1st vector to define 3d k cube
0.00 1.00 0.00 ! The 2nd vector to define 3d k cube
0.00 0.00 1.00 ! The 3rd vector to define 3d k cube
Note
Please don’t set Nk1, Nk2, Nk3 too large. Otherwise, it will become very time consuming. Usually, 15*15*15 is enough to get converged number of Weyl/Dirac points.
Output¶
Outputs are Nodes.dat and Nodes.gnu. Nodes.png will be obtained by
gnuplot Nodes.gnu
Here are heads of output for WTe2 Nodes.dat
# local minimal position and the related energy gap
# kx ky kz gap E k1 k2 k3
0.219436 -0.045611 -0.000001 0.000000 0.056688 0.121432 -0.045363 -0.000003
-0.219515 -0.045063 -0.000001 0.000000 0.056461 -0.121476 -0.044818 -0.000002
0.220195 -0.038682 -0.000002 0.000000 0.051264 0.121852 -0.038472 -0.000003
-0.220183 -0.038936 -0.000001 0.000000 0.051618 -0.121845 -0.038724 -0.000003
0.219514 0.045063 0.000001 0.000000 0.056459 0.121475 0.044818 0.000003
-0.219434 0.045620 0.000002 0.000000 0.056692 -0.121431 0.045371 0.000004
-0.220194 0.038678 0.000000 0.000000 0.051259 -0.121851 0.038468 0.000001
0.220181 0.038941 0.000000 0.000000 0.051620 0.121844 0.038729 0.000001
You will find that there are 8 Weyl points in the BZ as expected.
Weyl Chirality calculation¶
After you identify the positions of Weyl points, you could use this function to calculate the chirality, which tells you whether a Weyl point is a sink or a source of the Berry Curvature.
Input¶
Typical input parameters for WeylChirality_calc calculation
&CONTROL
WeylChirality_calc = T
/
&PARAMETERS
Nk1 = 41 ! No. of slices for the 1st reciprocal vector, berry phase integration direction
Nk2 = 21 ! No. of slices for the 2nd reciprocal vector
/
WEYL_CHIRALITY
8 ! Num_Weyls
Cartesian ! Direct or Cartesian coordinate
0.004 ! Radius of the ball surround a Weyl point
0.219436 -0.045611 -0.000000 ! Positions of Weyl points, No. of lines should larger than Num_weyls
-0.219515 -0.045063 -0.000000
0.220195 -0.038682 -0.000000
-0.220183 -0.038936 -0.000000
0.219514 0.045063 0.000000
-0.219434 0.045620 0.000000
-0.220194 0.038678 0.000000
0.220181 0.038941 0.000000
Output¶
Outputs are wanniercenter3D_Weyl.dat and wanniercenter3D_Weyl_i.gnu. wanniercenter3D_Weyl.png will be obtained by
gnuplot wanniercenter3D_Weyl_i.gnu
for ((i=1; i<9; i++)); do gnuplot wanniercenter3D_Weyl_$i.gnu;done
Note
i is an integer from 1 to Num_weyls
Here are heads of output for WTe2 wanniercenter3D_Weyl.dat
# Chirality -1 1 1 -1 1 -1 1 -1
# k phase phase phase phase phase phase phase phase
0.00000000 0.99970932 0.00005854 0.00004671 0.99975139 0.00005851 0.99970861 0.00004736 0.99975087
0.05000000 0.89229069 0.08696587 0.08941971 0.90855415 0.08723118 0.89170870 0.09022452 0.90795187
0.10000000 0.79659821 0.16589558 0.17112299 0.82248889 0.16697194 0.79511289 0.17279423 0.82108022
The first line shows the chiralities of each Weyl point. The first column is k point. From the 2nd to the last column show the Wannier charge center phase. In total, there are Num_weyls columns.
Slab band calculation¶
Before using iterative green’s function to get the surface state spectrum for semi-infinite system. We also can just construct a finite thickness slab system and calculate the band structure for it.
Note
For slab calculations, please read carefully the input card SURFACE
Input¶
&CONTROL
SlabBand_calc = T
/
&SYSTEM
NSLAB = 10
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
/
KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5
See CONTROL, SYSTEM PARAMETERS, KPATH_SLAB
Output¶
Outputs are slabek.dat and slabek.gnu
The heads of slabek.dat are
0.0000000 -4.9575466 240
0.0508687 -5.0110528 226
0.1017373 -5.0566963 221
0.1526060 -5.0671994 220
...
- The 1st column are k points in the KPATH_SLAB
- The 2nd column are energy values.
- The 3rd column represent the surface weight, which is normalized to 255.
The colorfull plot slabek.png of the slab energy bands can be obtained by
gnuplot slabek.gnu
Nanowire/nanoribbon band calculation¶
Band calculation for wire system. Only one direction is periodic, the other two directions are confined.
Input¶
You don’t have to set the k path, because it only has one direction.
&CONTROL
WireBand_calc = T
/
&SYSTEM
NSLAB1 = 4
NSLAB2 = 4
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
/
See CONTROL, SYSTEM PARAMETERS
Output¶
Outputs are ribbonek.dat and ribbonek.gnu. The data format of ribbonek.dat is the same as slabek.dat. Get plot ribbonek.png with
gnuplot ribbonek.gnu
Surface state ARPES calculation¶
One important feature for topological materials is the surface state. The bulk-edge correspondence tells us, if the topological property of the bulk system is nontrivial, then there will be nontrivial states on the surface. Nowadays, there are several method to detect the surface states. One direct way is the angle resolved photoemission spectroscopy (ARPES). Such spectrum can be obtained by the iterative Green’s function.
Note
For slab calculations, please read carefully the input card SURFACE
Input¶
&CONTROL
SlabSS_calc = T
/
&PARAMETERS
OmegaNum = 101
OmegaMin = -1.0
OmegaMax = 1.0
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
NP = 2 ! principle layer
/
KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5
See CONTROL, PARAMETERS, KPATH_SLAB
NP : integer valued, Number of principle layers, see details related to iterative green’s function. Used if SlabSS_calc= T, SlabArc_calc=T, SlabSpintexture_calc=T. Default value is 2. You need to do a convergence test by setting Np= 1, Np=2, Np=3, and check the surface state spectrum. Basically, the value of Np depends on the spread of Wannier functions you constructed. One thing should be mentioned is that the computational time grows cubically of Np.
Output¶
The output files are surfdos_l.dat, surfdos_r.dat, surfdos_l.gnu, surfdos_r.gnu. You could get the the spectral function plots with
gnuplot surfdos_l.gnu
gnuplot surfdos_r.gnu
_l and _r means the top and bottom surface.
Surface state QPI calculation¶
Settings for this feature are almost the same as Fermi arc calculation. Only difference is that you should set
# please set SlabQPI_kplane_calc = T from V2.4.2
&CONTROL
SlabQPI_kplane_calc = T
/
Output¶
- There are a lot of outputs for QPI calculation. including
arc.dat_l, arc.dat_r, arc_l.gnu, arc_r.gnu, arc.jdat_l, arc.jdat_r, arc.jsdat_l, arc.jsdat_r, arc_l_jdos.gnu, arc_l_jsdos.gnu, arc_r_jdos.gnu, arc_r_jsdos.gnu.
The gnu script with ‘only’ means we only plot the spectrum with the surface contribution, exclude the bulk contribution. (we remove file arc_l_only.gnu after v2.4.1 for the reason of misleading) jdat_l is the QPI data without consideration of spin scattering. jsdat_l is the QPI data in consideration of spin scattering.
Fermi arc calculation¶
Surface state spectrum at fixed energy level E_arc set in NAMELISTS PARAMETERS . Set SlabArc_calc=T, and set Nk1, Nk2, in NAMELISTS PARAMETERS, set k plane in KPLANE_SLAB CARD. Get the plots with “gnuplot arc_l.gnu”, “gnuplot arc_r.gnu”. _l and _r means the top and bottom surface.
Spin texture calculation¶
Spin texture calculation at a fixed energy level E_arc set in NAMELISTS PARAMETERS . Set Slabspintexture_calc=T, and set Nk1, Nk2, in NAMELISTS PARAMETERS, set k plane in KPLANE_SLAB CARD. Get the plots with “gnuplot spintext_l.gnu”, “gnuplot spintext_r.gnu”.
Note
Here we asumme that the tight-binding basis are pure spin up or pure spin down, which means that the spin up and spin down are not mixed in the basis. This could be realized if you don’t do the maximal-localized step by setting num_iter=0 in wannier90.win and select the projectors, disentanglement windown properly. If your Wannier functions are the maximal localized ones, then this feature doesn’t work. I suggest you using Wannier90 to get spin-texture which needs information from the first-principle calculations.
Berry phase calculation¶
Calculate Berry phase of a closed k path in 3D BZ. This is useful in a nodal line system. It is demonstrated that the Berry phase around a closed mirror symmetric k loop is either 0 or pi for a mirror protect nodal line system.
In WannierTools, you can specify a k path by a serials k points. Here we take the WC example, which has two nodal lines around K point.
Input¶
&CONTROL
BerryPhase_calc = T
/
&SYSTEM
NumOccupied = 10 ! Number of occupied Wannier orbitals
/
&PARAMETERS
Nk1 = 21 ! No. of slices for the 1st reciprocal vector
/
KPATH_BERRY
11
Direct
0.3 0.333 -0.2
0.3 0.333 -0.1
0.3 0.333 -0.0
0.3 0.333 0.1
0.3 0.333 0.2
0.33 0.333 0.2
0.33 0.333 0.1
0.33 0.333 0.0
0.33 0.333 -0.1
0.33 0.333 -0.2
0.3 0.333 -0.2
Output¶
The value of Berry phase can be found in the WT.out.
Note
1. In principlely, the Berry phase for around a nodal line should be interger. However, the MLWF-TB model usally is not symmetric. So the value of Berry phase is close to zero or one.
- The first and the last kpoints in the KPATH_BERRY should be the same to form a loop.
Berry curvature calculation for 3D bulk case¶
Calculate Berry curvature at a fixed k plane in 3D BZ. Set BerryCurvature_calc=T, and set Nk1, Nk2, in NAMELISTS PARAMETERS, set k plane in KPLANE_BULK CARD. Get the plot with “gnuplot Berrycurvature.gnu”.
please set NumOccpuied correctly. It represents the “occpuied” wannier bands, not the total number of electrons. In this application, the Berrycurvature is the summation over NumOccupied bands.
A typical input (take ZrTe as an example):
&CONTROL
BerryCurvature_calc=T
/
&SYSTEM
NumOccupied = 8 ! Number of occupied Wannier orbitals
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
Nk2 = 101 ! No. of slices for the 2st reciprocal vector
/
KPLANE_BULK
0.00 0.00 0.00 ! Central point for 3D k slice k3=0
1.00 0.00 0.00 ! The first vector. Integrate along this direction to get WCC
0.00 1.00 0.00 ! WCC along this direction, for Z2, usually half of the reciprocal lattice vector
Berry curvature calculation for slab system¶
Note
Not well tested.. Use it carefully.
A typical input:
&CONTROL
BerryCurvature_slab_calc=T
/
&SYSTEM
NumOccupied = 8 ! Number of occupied Wannier orbitals of the unit cell
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
Nk2 = 101 ! No. of slices for the 2st reciprocal vector
/
KPLANE_SLAB
0.00 0.00 ! Central point for 3D k slice k3=0
1.00 0.00 ! The first vector. Integrate along this direction to get WCC
0.00 1.00 ! WCC along this direction, for Z2, usually half of the reciprocal lattice vector
Anomalous Hall conductivity (AHC)¶
Calculate AHC in the energy range [OmegaMin, OmegaMax]. AHC is in unit of (Ohm*cm)^-1.
Relevant inputs are
&CONTROL
AHC_calc=T
/
&PARAMETERS
OmegaNum = 601 ! number of slices of energy
OmegaMin = -1.0 ! erergy range for AHC
OmegaMax = 1.0
Nk1 = 51 ! No. of slices for the 1st reciprocal vector
Nk2 = 51 ! No. of slices for the 2nd reciprocal vector
Nk3 = 51 ! No. of slices for the 3nd reciprocal vector
/
KCUBE_BULK
0.00 0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
Output is sigma_ahe.txt.
Wannier charge center/Wilson loop calculation¶
Wannier charge center, which is sometimes called Wilson loop can be calculated by set WannierCenter_calc=T and set KPLANE_BULK CARD, set number of k points for two vectors is Nk1, Nk2 in NAMELISTS PARAMETERS. Notice: You should notice that the first vector in KPLANE_BULK CARD is the integration direction, this vector should be equal to one primitive reciprocal lattice vector. If you want to calculate the Z2 number, Please set the second vector to be half of the reciprocal lattice vector. You can get the Wannier charge center along the second k line. See more details In the paper written by Alexey. Soluyanov (2011). If you want to calculate the Chern number, Please set the second vector to be one primitive reciprocal lattice vector.
Note
Important: please set NumOccpuied correctly. It represents the “occpuied” wannier bands, not the total number of electrons. In this application, the Wilson loop is the trace of NumOccupied bands. If you want to study the topology between the 8th and the 9th band, then set NumOccupied=8.
Output¶
Outputs are wcc.dat and wcc.gnu, the format of wcc.dat is:
# k largestgap sum(wcc(:,ik)) wcc(i, ik)(i=1, NumOccupied)
0.00000000 0.60940556 0.99998388 0.00000850 0.07701431 0.07702018 0.19328973 0.19329593 0.28118760 0.28119336 0.49998615 0.50000060 0.71881052 0.71881646 0.80675987 0.80676424 0.92297767 0.92298328 0.99993530 0.99994085 0.99999935
0.00312500 0.61256609 0.99998716 0.00030351 0.00082300 0.07688154 0.07709302 0.19117885 0.19525313 0.27952027 0.28297172 0.49188658 0.50810192 0.71703027 0.72048573 0.80480135 0.80887751 0.92290159 0.92311931 0.99908212 0.99967575
0.00625000 0.61569946 0.99999557 0.00061525 0.00168708 0.07668131 0.07711296 0.18887026 0.19709893 0.27796336 0.28485788 0.48373617 0.51625672 0.71514220 0.72204447 0.80295562 0.81118878 0.92287871 0.92332259 0.99821913 0.99936414
......
The second column is the position of the largest gap of WCC. It is used for drawing a line to calculate the Z2 number (see A. Soluyanov 2011), From the fourth column to the last column, they are wcc for the occupied bands specified with “NumOccupied”. The third line is the summation of the WCC over all the “occupied” bands. It’s usefull for telling the Chern number.
Example¶
Take Bi2Se3 for example, we calculate the Wilson loop (WCC) at k3=0 plane, where k1, k2, k3 is in unit of reciprocal lattice vector. The you should set the particular inputs like this
&CONTROL
WannierCenter_calc=T
/
&SYSTEM
NumOccupied = 10 ! Number of occupied Wannier orbitals
/
&PARAMETERS
Nk1 = 41 ! No. of slices for the 1st reciprocal vector
Nk2 = 41 ! No. of slices for the 2st reciprocal vector
/
KPLANE_BULK
0.00 0.00 0.00 ! Original point for 3D k slice k3=0
1.00 0.00 0.00 ! The first vector. Integrate along this direction to get WCC
0.00 0.50 0.00 ! WCC along this direction, for Z2, usually half of the reciprocal lattice vector
For 2D materials stacked along z direction, you could think it as a 3D material with weak coupling along z direction. You can use this function to get the Z2 value at k3=0 plane to characterize the topology.
Use “gnuplot wcc.gnu” to get “wcc.eps” plot.
Here is an example.
Mirror Chern number calculation¶
At present, We can only calculate mirror Chern number for the simplest case (1. There is only one atom per atom’s type in the unit cell e.g. ZrTe. 2. kz=0 is the mirror plane we concern). For the more complex case, you can modify the source code by setting the mirror operator properly. Define your own mirror operator based on the atomic like Wannier functions in the symmetry.f90 and change the subroutine wanniercenter_mirror in wanniercenter.f90.
After properly setting of the mirror operator, you can run WannierTools with the basic parameters and the following additional parameters (Here we take ZrTe at kz=0 plane as an example)
&CONTROL
MirrorChern_calc=T
/
&SYSTEM
NumOccupied = 8 ! Number of occupied Wannier orbitals
/
&PARAMETERS
Nk1 = 101 ! No. of slices for the 1st reciprocal vector
Nk2 = 101 ! No. of slices for the 2st reciprocal vector
/
KPLANE_BULK
0.00 0.00 0.00 ! Original point for 3D k slice k3=0
1.00 0.00 0.00 ! The first vector. Integrate along this direction to get WCC, should be a close path
0.00 1.00 0.00 ! WCC along this direction, for Chern, usually one reciprocal lattice vector
Output¶
The mirror Chern number can be found in the WT.out. The WCC/Wilson loop is included in the files wcc-mirrorminus.dat and wcc-mirrorplus.dat. The gnuplot script is wcc-mirrorchernnumber.gnu. The format of wcc-mirrorplus.dat is:
# k sum(wcc(:,ik)) wcc(:, ik)
0.00000000 0.93401098 0.26748313 0.33122324 0.37761566 0.95768895
0.01000000 0.93458410 0.26776394 0.33149191 0.37747362 0.95785463
0.02000000 0.93515725 0.26806334 0.33205065 0.37717770 0.95786557
0.03000000 0.93572256 0.26838206 0.33288980 0.37673021 0.95772050
...
The first column is k=i/Nk2 (i=0, Nk2), we take the second vector defined in KPLANE_BULK as unit of 1. The second line is the summation of the WCC over all the “occupied/2” bands. It’s usefull for telling the Chern number. From the third column to the last column, they are wcc for the occupied/2 bands specified with “NumOccupied”.
Z2 number for 3D bulk materials¶
We can get Z2 topological index (v0, v1v2v3) from the z2 calculations of six time reversal invariant planes, i.e. (a) k1=0.0; (b) k1=0.5; (c) k2=0.0; (d) k2=0.5; (e) k3=0.0; (f) k3=0.5; Usually, you can call “Wannier charge center calculation for a plane” six times. Here we packed them up to get another function. You can set the input file like the following.
Input¶
The necessary tags that you should set in the wt.in
&CONTROL
Z2_3D_calc = T
/
&PARAMETERS
NumOccpuied = 18 ! No. of occupied wannier bands
Nk1 = 41 ! No. of slices of the k points for WCCs
Nk2 = 41 ! No. of slices of the k points for WCCs
/
Output¶
Outputs are wanniercenter3D_Z2_1.dat, wanniercenter3D_Z2_2.dat, wanniercenter3D_Z2_3.dat, wanniercenter3D_Z2_4.dat, wanniercenter3D_Z2_5.dat, wanniercenter3D_Z2_6.dat and wanniercenter3D_Z2.gnu. The z2 value can be found in the WT.out by searching “z2 number for 6 planes”. The WCC (Wilson loop) plots wanniercenter3D_Z2.eps can be got with:
gnuplot wanniercenter3D_Z2.gnu
Note
Important: please set NumOccpuied correctly. It represents the “occpuied” wannier bands, not the total number of electrons. In this application, the Wilson loop is the trace of NumOccupied bands. If you want to study the topology between the 8th and the 9th band, then set NumOccupied=8.
About the Z2 index for 3D system.
v0= (z2(ki=0)+z2(ki=0.5))mod 2
vi= z2(ki=0.5)
For the 2D system, if you set the Z axis as the stack axis, please only take the Z2 number at k3=0 plane.
Chern number for 3D bulk materials¶
- Basically, you can calculate the Chern number for a closed manifold, for example, a 2D torus. For this purpose, I would suggest you using
- WannierCenter_calc=T in the calculation.
We can get Chern number of six k planes, i.e. k1=0.0; k1=0.5; k2=0.0; k2=0.5; k3=0.0; k3=0.5; where k1, k2, k3 is in fractional units. Usually, you can call “Wannier charge center calculation for a plane” six times. Here we packed them up to get another function. You can set the input file like the following.
Basically, the method used here is very similar to the one used in the Z2 number calculations. We also use the Wilson loop method. However, for Z2 calculation, you only take half of the size of a time reversal invariant slice. For Chern number calculation, you need a closed momentum surface. For example, for the k1=0.0 plane, half of the time reversal invariant slice would be defined like this:
k2 is in [0, 0.5]
k3 is in [0, 1]
The full closed momentum surface would defined like this
k2 is in [0, 1]
k3 is in [0, 1]
Input¶
The necessary tags that you should set in the wt.in
&CONTROL
Chern_3D_calc = T
/
&PARAMETERS
NumOccpuied = 18 ! No. of occupied wannier bands
Nk1 = 41 ! No. of slices of the k points for WCCs
Nk2 = 41 ! No. of slices of the k points for WCCs
/
Output¶
Outputs are wanniercenter3D_Chern.dat and wanniercenter3D_Chern.gnu. The Chern number can be found in the WT.out by searching “Chern number for 6 planes”. The WCC (Wilson loop) plots wanniercenter3D_Chern.eps can be got with:
gnuplot wanniercenter3D_Chern.gnu
Note
Important: please set NumOccpuied correctly. It represents the “occpuied” wannier bands, not the total number of electrons. In this application, the Wilson loop is the trace of NumOccupied bands. If you want to study the topology between the 8th and the 9th band, then set NumOccupied=8.
For the 2D system, if you set the Z axis as the stack axis, please only take the Chern number at k3=0 plane.
Landau level calculations¶
This functionality is under testing, not released yet. Developed by QSWu and YFGuan
By applying the uniform magnetic field along one lattice vector, the Landau level spectrum can be calculated by the Peierls substitution.
Here we put one example of Graphene. The input file wt.in is like this
&TB_FILE
Hrfile = 'wannier90_hr.dat'
/
!> bulk band structure calculation flag
&CONTROL
BulkBand_calc = T
Hof_Butt_calc = T
LandauLevel_k_calc = T
LandauLevel_wavefunction_calc = F
/
&SYSTEM
NSLAB = 200 ! the size of magnetic supercell
NumOccupied = 1 ! NumOccupied
SOC = 0 ! soc
E_FERMI = -1.2533 ! e-fermi
/
&PARAMETERS
E_arc = 0.00 ! energy for calculate Fermi Arc
OmegaNum = 201 ! number of eigenvalues to calculate the Landau levels
Nk1 = 100 ! number k points for each line in the kpath_bulk
/
LATTICE
Angstrom
2.1377110 -1.2342080 0.0000000
0.0000000 2.4684160 0.0000000
0.0000000 0.0000000 10.000000
!> used when you want to study the projections on the orbital for each band
SELECTEDORBITALS
1 ! NumberofSelectedOrbitals without spin degeneracy
1 ! SelectedOrbitals indices without spin degeneracy
ATOM_POSITIONS
2 ! number of atoms for projectors
Direct ! Direct or Cartisen coordinate
C 0.333333 0.666667 0.500000 C
C 0.666667 0.333333 0.500000 C
PROJECTORS
1 1 ! number of projectors
C pz
C pz
SURFACE
0 0 1 ! magnetic field direction in units of lattice vectors
1 0 0
KPATH_BULK ! k point path
1 ! number of k line only for bulk band
M 0.50000 0.00000 0.00000 G 0.00000 0.00000 0.00000
WANNIER_CENTRES
Cartesian
0.712570 1.234209 5.000000
1.425141 -0.000001 5.000000
We can calculate the Hofstader butterfly plot by setting Hof_Butt_calc = T. Nslab is the size of the supercell. The corresponding magnetic field strength can be found in the output WT.out.
Since the calculation for magnetic supercell is very heavy, we have two versions of eigenvalue solvers. One is direct diagonalization, the other one is the ARPACK solver, which is based on the sparse matrix. So you have to install the ARPACK package, and specify the library in the Makefile. You don’t have to choose the solvers. It is automatically chosen according to the matrix dimensionality. If the dimensionality of the Hamiltonian matrix of the magnetic supercell is larger than 1600, WannierTools will call the sparse matrix solver.
Once the sparse matrix solver is chosen. You have to set E_arc and OmegaNum, which means you are going to calculate 2*OmegaNum+1 Landau energy levels around E_arc respect to the Fermi level.
The magnetic field is along the first vector specified in the SURFACE card.
Symmetrization of wannier90_hr.dat New¶
Here is a brief introduction of the symmetrization functionalities. Basically, wannhr_symm is an independent package based on Python2.7 written by Changming Yue (yuechangming8@gmail.com). Although this package is very useful, its requirement is also very restrict.
- The Wannier functions must be atomic like, which means there should be very weak hybridization between orbitals. It’s not possible to deal with the sp2, sp3 like wannier orbitals.
- At present, it can only take care of the s, p, d, t2g, eg orbitals. p orbitals means all three orbitals ordered with pz, px, py. d orbitals are ordered as “dz2”, “dxz”, “dyz”, “dx2-y2”, “dxy”. Such situation is automatically satisfied with in VASP+Wannier90
- The file name of tight binding Hamiltonian should be ‘wannier90_hr.dat’
Tutorial: learning WannierTools through examples¶
Bi2Se3 (3D strong TI)¶
Bi2Se3 is a strong topological insulator. The Z2 topological index is (1, 000). Theoretical and experimental validation can be found in Nature Physics 5, 438-442 (2009) and Nature Physics 5, 398-402 (2009) respectively. Here we show you how to use WannierTools to study strong topological materials. The input file and some related files are included in each distribution.
Here is the primitive unit cell of Bi2Se3
First principle calculation¶
Firstly, you need to study the electronic structure of Bi2Se3 with first-principle software package, like VASP, Wien2k, Abinit, Quantum-espresso et al. In this tutorial, we select VASP. Here is the calculated band structure.
Band structure¶
Then Wannier90 is applied to construct MLWF tight binding (TB) model (see more details from http://www.wannier.org). Here we only tell you that the p orbitals of Bi and Se are selected as the initial projectors for Wannier90. The band structure calculated from the MLWF-TB model is as follows
This band structure can be calculated directly from Wannier90. Also can be calculated from WannierTools. The settings in WT.in are
&CONTROL
BulkBand_calc = T
/
&SYSTEM
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
/
&PARAMETERS
Nk1 = 41 ! number k points odd number would be better
/
KPATH_BULK ! k point path
4 ! number of k line only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000
Z2 topological number¶
From the band structure above, it is clear that it is a insulator. This is also can be checked by calculating the density of state (DOS). In order to identify the topological properties, we have to calculate the Z2 topological number, which is valid for time-reversal invariant system with a continuous full gap in the Brilloin Zone. The Z2 topological number for 3D bulk system can be obtained from the calculation of the Wilson loop (Wannier charge center) for the six time-reversal invariant momentum plane. k1=0.0, k1=0.5; k2=0.0; k2=0.5; k3=0.0, k3=0.5. It can be done using WannierTools with setting in WT.in
&CONTROL
Z2_3D_calc = T
/
&SYSTEM
SOC = 1 ! soc
NumOccupied = 18 ! Number of occupied Wannier bands
/
&PARAMETERS
Nk1 = 41 ! number k points odd number would be better
Nk2 = 41 ! number k points odd number would be better
/
The resutls are
(a) k1=0.0, z2=1; (b) k1=0.5, z2=0; (c) k2=0.0, z2=1; (d) k2=0.5, z2=0; (e) k3=0.0, z2=1; (f) k3=0.5, z2=0;
So the bulk Z2 topological number is (1, 000), which means a strongly topological insulator.
Surface state¶
The surface states are the correspondence to the non-trivial bulk topology. They are detectable from ARPES experiments. The calculated surface states of Bi2Se3 on (0001) surface are
The settings in WT.in are
&CONTROL
SlabSS_calc = T
SlabArc_calc = T
/
&SYSTEM
SOC = 1 ! soc
NumOccupied = 18 ! Number of occupied Wannier bands
E_FERMI = 4.4195 ! e-fermi
/
&PARAMETERS
Eta_Arc = 0.001 ! infinite small value, like brodening
E_arc = 0.0 ! energy for calculate Fermi Arc
OmegaMin = -0.6 ! energy interval
OmegaMax = 0.5 ! energy interval
OmegaNum = 401 ! omega number
Nk1 = 101 ! number k points odd number would be better
Nk2 = 101 ! number k points odd number would be better
/
SURFACE ! See doc for details
1 0 0
0 1 0
0 0 1
KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5
KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane
0.2 0.0 ! The first vector to define 2D k plane
0.0 0.2 ! The second vector to define 2D k plane for arc plots
Spin texture¶
Spin orbital coupling (SOC) is a very important to topological insulator. The spin texture of the surface states will form due to SOC. WannierTools can calculate spin texture like this
by setting
&CONTROL
SlabSpintexture_calc = F
/
&SYSTEM
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
/
&PARAMETERS
Eta_Arc = 0.001 ! infinite small value, like brodening
E_arc = 0.0 ! energy for calculate Fermi Arc
Nk1 = 101 ! number k points odd number would be better
Nk2 = 101 ! number k points odd number would be better
/
SURFACE ! See doc for details
1 0 0
0 1 0
0 0 1
KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane
0.2 0.0 ! The first vector to define 2D k plane
0.0 0.2 ! The second vector to define 2D k plane for arc plots
Full settings in WT.in of Bi2Se3¶
&TB_FILE
Hrfile = 'wannier90_hr.dat'
/
&CONTROL
BulkBand_calc = T
BulkFS_calc = F
BulkGap_cube_calc = F
BulkGap_plane_calc = F
SlabBand_calc = T
WireBand_calc = F
SlabSS_calc = T
SlabArc_calc = T
SlabQPI_calc = F
Z2_3D_calc = T
Chern_3D_calc = F
SlabSpintexture_calc = F
Wanniercenter_calc = F
BerryPhase_calc = F
BerryCurvature_calc = F
EffectiveMass_calc = F
/
&SYSTEM
NSLAB = 10 ! for thin film system
NSLAB1= 4 ! nanowire system
NSLAB2= 4 ! nanowire system
NumOccupied = 18 ! NumOccupied
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
Bx= 0, By= 0, Bz= 0 ! Bx By Bz
surf_onsite= 0.0 ! surf_onsite
/
&PARAMETERS
Eta_Arc = 0.001 ! infinite small value, like brodening
E_arc = 0.0 ! energy for calculate Fermi Arc
OmegaNum = 401 ! omega number
OmegaMin = -0.6 ! energy interval
OmegaMax = 0.5 ! energy interval
Nk1 = 41 ! number k points odd number would be better
Nk2 = 41 ! number k points odd number would be better
Nk3 = 21 ! number k points odd number would be better
NP = 1 ! number of principle layers
Gap_threshold = 1.0 ! threshold for GapCube output
/
LATTICE
Angstrom
-2.069 -3.583614 0.000000 ! crystal lattice information
2.069 -3.583614 0.000000
0.000 2.389075 9.546667
ATOM_POSITIONS
5 ! number of atoms for projectors
Direct ! Direct or Cartisen coordinate
Bi 0.3990 0.3990 0.6970
Bi 0.6010 0.6010 0.3030
Se 0 0 0.5
Se 0.2060 0.2060 0.1180
Se 0.7940 0.7940 0.8820
PROJECTORS
3 3 3 3 3 ! number of projectors
Bi px py pz ! projectors
Bi px py pz
Se px py pz
Se px py pz
Se px py pz
SURFACE ! See doc for details
1 0 0
0 1 0
0 0 1
KPATH_BULK ! k point path
4 ! number of k line only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000
KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5
KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane
0.2 0.0 ! The first vector to define 2D k plane
0.0 0.2 ! The second vector to define 2D k plane for arc plots
KPLANE_BULK
0.00 0.00 0.50 ! Original point for 3D k plane k3=0.5, bar{a}, along k1
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane
!> The following 5 matrices are for backup using, will not affect the main input for WannierTools
0.00 0.00 0.00 ! Original point for 3D k plane k3=0.0, bar{a}, along k1
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane
0.00 0.50 0.00 ! Original point for 3D k plane k2=0.5, bar{c}, along ka
0.00 0.00 1.00 ! The first vector to define 3d k space plane
0.50 0.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 0.00 ! Original point for 3D k plane k2=0, bar{c}, along ka
0.00 0.00 1.00 ! The first vector to define 3d k space plane
0.50 0.00 0.00 ! The second vector to define 3d k space plane
0.50 0.00 0.00 ! Original point for 3D k plane k1=0.5, bar{c}, along kb
0.00 0.00 1.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane
0.00 0.00 0.00 ! Original point for 3D k plane k1=0, bar{c}, along kb
0.00 0.00 1.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane
KCUBE_BULK
-0.50 -0.50 -0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
EFFECTIVE_MASS ! optional
2 ! The i'th band to be calculated
0.01 ! k step in unit of (1/Angstrom)
0.0 0.0 0.0 ! k point where the effective mass calculated.
WANNIER_CENTRES ! copy from wannier90.wout
Cartesian
-0.000040 -1.194745 6.638646
0.000038 -1.196699 6.640059
-0.000032 -1.192363 6.640243
-0.000086 -3.583414 2.908040
0.000047 -3.581457 2.906587
-0.000033 -3.585864 2.906443
-0.000001 1.194527 4.773338
0.000003 1.194538 4.773336
-0.000037 1.194536 4.773327
0.000006 -1.194384 1.130261
-0.000018 -1.216986 1.140267
0.000007 -1.172216 1.140684
0.000011 -3.583770 8.416406
-0.000002 -3.561169 8.406398
-0.000007 -3.605960 8.405979
0.000086 -1.194737 6.638626
-0.000047 -1.196693 6.640080
0.000033 -1.192286 6.640223
0.000040 -3.583406 2.908021
-0.000038 -3.581452 2.906608
0.000032 -3.585788 2.906424
0.000001 1.194548 4.773330
-0.000003 1.194537 4.773332
0.000037 1.194539 4.773340
-0.000011 -1.194381 1.130260
0.000002 -1.216981 1.140268
0.000007 -1.172191 1.140687
-0.000006 -3.583766 8.416405
0.000018 -3.561165 8.406400
-0.000007 -3.605935 8.405982
MoS2 (2D QSHE)¶
WannierTools also works fine with 2D materials. The way we handle it is just like what we simulated in the first principle calculations. A 2D material is just a layer structured 3D material with zero coupling along z direction. The settings of WannierTools for 2D materials are the same of 3D materials. However, you should only care about the properties happen in the kz=0 plane, since the properties are the same for different kz.
Monolayer square transition metal dichalcogenides (MoS2, MoSe2, MoTe2, WS2, WSe2, and WTe2) was predicted to be robust topological insulators (TIs) with Z2=1. As a good 2D TI, 1T’-MoS2 is taken as an example to test WannitrTolls.
Here is the primitive unit cell of 1T’-MoS2
Band structure¶
Firstly, you need to study the electronic structure of MoS2 with first-principle software package, like VASP, Wien2k, Abinit, Quantum-espresso et al. In this tutorial, we select VASP. Here is the calculated band structure. Then Wannier90 is applied to construct MLWF tight binding (TB) model (see more details from http://www.wannier.org). Here we only tell you that the s, d orbitals of Mo and s, p orbitals of S are selected as the initial projectors for Wannier90. The band structure calculated from the MLWF-TB model is as follows
This band structure can be calculated directly from Wannier90. Also can be calculated from WannierTools. The settings in WT.in are
&CONTROL
BulkBand_calc = T
/
&SYSTEM
SOC = 1 ! soc
E_FERMI = -3.9151 ! e-fermi
/
&PARAMETERS
Nk1 = 101 ! number k points odd number would be better
/
KPATH_BULK ! k point path
4 ! number of k line only for bulk band
X 0.50000 0.00000 0.00000 G 0.00000 0.00000 0.00000
G 0.00000 0.00000 0.00000 Y 0.00000 0.50000 0.00000
Y 0.00000 0.50000 0.00000 M 0.50000 0.50000 0.00000
M 0.50000 0.50000 0.00000 G 0.00000 0.00000 0.00000
Z2 topological number¶
From the band structure above, it is clear that it is a insulator. This is also can be checked by calculating the density of state (DOS). In order to identify the topological properties, we have to calculate the Z2 topological number, which is valid for time-reversal invariant system with a continuous full gap in the Brilloin Zone. The Z2 topological number for 3D bulk system can be obtained from the calculation of the Wilson loop (Wannier charge center) for the six time-reversal invariant momentum plane. (a) k1=0.0, (b) k1=0.5; (c) k2=0.0; (d) k2=0.5; (e) k3=0.0, (f) k3=0.5. It can be done using WannierTools with setting in WT.in
&CONTROL
Z2_3D_calc = T
/
&SYSTEM
SOC = 1 ! soc
NumOccupied = 36 ! Number of occupied Wannier bands
/
&PARAMETERS
Nk1 = 101 ! number k points odd number would be better
Nk2 = 41 ! number k points odd number would be better
/
The resutls are
(a) k1=0.0, z2=0; (b) k1=0.5, z2=0; (c) k2=0.0, z2=0; (d) k2=0.5, z2=0; (e) k3=0.0, z2=1; (f) k3=0.5, z2=1;
So the bulk Z2 topological number is (0, 001), which means a weak topological insulator in 3-dimension picture, while a strong TI in 2D picture. For a 2D material, you only need the topological index in figure (e).
Edge state¶
The edge states of a 2D material is the side surface of a 3D model. The calculated edge states of MoS2 on (100) surface is
The settings in WT.in are
&CONTROL
SlabSS_calc = T
/
&SYSTEM
SOC = 1 ! soc
NumOccupied = 36 ! Number of occupied Wannier bands
E_FERMI = -3.9151 ! e-fermi
/
&PARAMETERS
Eta_Arc = 0.001 ! infinite small value, like brodening
E_arc =-0.05 ! energy for calculate Fermi Arc
OmegaMin = -0.8 ! energy interval
OmegaMax = 0.4 ! energy interval
OmegaNum = 401 ! omega number
Nk1 = 101 ! number k points odd number would be better
Nk2 = 101 ! number k points odd number would be better
Np = 2 ! number k points odd number would be better
/
MILLER_INDICES
1 0 0
!SURFACE ! See doc for details
0 1 0
0 0 1
1 0 0
KPATH_SLAB
2 ! numker of k line for 2D case
X 0.5 0.0 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 X 0.5 0.0
KPLANE_SLAB
-0.5 -0.5 ! Original point for 2D k plane
1.0 0.0 ! The first vector to define 2D k plane
0.0 1.0 ! The second vector to define 2D k plane for arc plots
Full settings in WT.in of 1Tp-MoS2¶
&TB_FILE
Hrfile = 'wannier90_hr.dat'
Package = 'VASP'
/
!> bulk band structure calculation flag
&CONTROL
BulkBand_calc = T
BulkFS_calc = F
Z2_3D_calc = T
DOS_calc = F
BulkFS_plane_calc = F
BulkGap_cube_calc = F
BulkGap_plane_calc = F
SlabBand_calc = F
WireBand_calc = F
SlabSS_calc = T
SlabArc_calc = T
SlabSpintexture_calc = F
wanniercenter_calc = F
BerryPhase_calc = F
BerryCurvature_calc = F
/
&SYSTEM
NSLAB = 20
NumOccupied = 36 ! NumOccupied
SOC = 1 ! soc
E_FERMI = -3.9151 ! e-fermi
surf_onsite= 0.0 ! surf_onsite
/
&PARAMETERS
Eta_Arc = 0.001 ! infinite small value, like brodening
E_arc = -0.05 ! energy for calculate Fermi Arc
OmegaNum = 401 ! omega number
OmegaMin = -0.8 ! energy interval
OmegaMax = 0.4 ! energy interval
Nk1 = 101 ! number k points
Nk2 = 101 ! number k points
Nk3 = 3 ! number k points
NP = 2 ! number of principle layers
Gap_threshold = 0.10 ! threshold for GapCube output
/
LATTICE
Angstrom
3.1770280139589571 0.0000000000000000 0.0000000000000000
0.0000000000000000 5.7281689431742455 -0.0157118470068534
0.0000000000000000 0.3756910330601151 30.2151819975086902
ATOM_POSITIONS
6 ! number of atoms for projectors
Direct ! Direct or Cartisen coordinate
Mo 0.5000000049999969 0.4188543132266640 0.5873016275251595
Mo -0.0000000000000000 0.0233088607917941 0.5925355564141651
S 0.5000000049999969 0.1358785901303858 0.6473858970202739
S 0.0000000000000000 0.6405161490437790 0.6337728762151337
S -0.0000000000000000 0.3062864083475208 0.5324524179435783
S 0.5000000049999969 0.8016452854598629 0.5460646648816858
PROJECTORS
6 6 4 4 4 4 ! number of projectors
Mo s dxy dyz dxz dx2-y2 dz2 ! projectors
Mo s dxy dyz dxz dx2-y2 dz2 ! projectors
S s px py pz
S s px py pz
S s px py pz
S s px py pz
MILLER_INDEX ! this is equal to the SURFACE card
1 0 0
!SURFACE ! MoS2 conventional (010) surface
0 1 0
0 0 1
1 0 0
KPATH_BULK ! k point path
4 ! number of k line only for bulk band
X 0.50000 0.00000 0.00000 G 0.00000 0.00000 0.00000
G 0.00000 0.00000 0.00000 Y 0.00000 0.50000 0.00000
Y 0.00000 0.50000 0.00000 M 0.50000 0.50000 0.00000
M 0.50000 0.50000 0.00000 G 0.00000 0.00000 0.00000
KPATH_SLAB
2 ! numker of k line for 2D case
X 0.5 0.0 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 X 0.5 0.0
KPLANE_SLAB
-0.5 -0.5 ! Original point for 2D k plane
1.0 0.0 ! The first vector to define 2D k plane
0.0 1.0 ! The second vector to define 2D k plane for arc plots
KPLANE_BULK
-0.50 -0.50 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
KCUBE_BULK
-0.50 -0.50 -0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
WANNIER_CENTRES
Cartesian
1.582112 2.389848 17.807782
1.588504 2.609305 17.734627
1.588512 2.615066 17.729182
1.588518 2.627199 17.745843
1.588498 2.598550 17.729411
1.588498 2.629729 17.732881
-0.004616 0.781697 17.681791
-0.000012 0.362382 17.901360
0.000001 0.357923 17.918636
-0.000009 0.350028 17.898957
-0.000005 0.365927 17.908526
-0.000007 0.366124 17.901329
1.588504 1.034466 19.413821
1.588523 1.032565 19.619308
1.588472 1.012794 19.497202
1.588484 1.034341 19.536688
-0.000085 3.898045 19.004023
-0.000043 3.932819 19.131844
-0.000018 3.905334 19.041137
0.000028 3.922253 19.122079
-0.000005 1.945318 16.239885
-0.000014 1.949702 16.018513
-0.000042 1.987244 16.143671
-0.000004 1.954899 16.130450
1.588449 4.785448 16.618078
1.588486 4.728185 16.486681
1.588469 4.865486 16.580409
1.588453 4.810723 16.489254
1.595220 2.389977 17.807534
1.588525 2.609305 17.734627
1.588517 2.615065 17.729183
1.588510 2.627201 17.745844
1.588530 2.598543 17.729408
1.588531 2.629735 17.732878
0.004808 0.781415 17.681511
0.000013 0.362387 17.901363
-0.000001 0.357918 17.918638
0.000009 0.350028 17.898959
0.000005 0.365927 17.908525
0.000007 0.366134 17.901324
1.588524 1.034460 19.413819
1.588506 1.032552 19.619299
1.588559 1.012789 19.497215
1.588545 1.034346 19.536661
0.000087 3.898051 19.004022
0.000044 3.932824 19.131846
0.000018 3.905353 19.041145
-0.000027 3.922253 19.122048
0.000005 1.945317 16.239895
0.000014 1.949708 16.018506
0.000043 1.987240 16.143659
0.000006 1.954899 16.130433
1.588582 4.785446 16.618079
1.588543 4.728170 16.486695
1.588562 4.865497 16.580411
1.588575 4.810739 16.489208
WTe2 (Type II Weyl semimetal)¶
to be continue
IrF4 (Nodal Chain metals)¶
to be continue
FeSi (Weyl point in Phonon system)¶
Citation¶
Please cite this paper when using WannierTools for your researchs:
@article{WU2017,
title = "WannierTools : An open-source software package for novel topological materials",
journal = "Computer Physics Communications",
volume = "224",
pages = "405 - 416",
year = "2018",
issn = "0010-4655",
doi = "https://doi.org/10.1016/j.cpc.2017.09.033",
url = "http://www.sciencedirect.com/science/article/pii/S0010465517303442",
author = "QuanSheng Wu and ShengNan Zhang and Hai-Feng Song and Matthias Troyer and Alexey A. Soluyanov",
keywords = "Novel topological materials, Topological number, Surface state, Tight-binding model"
}
Correspondence¶
Please report bugs to wuquansheng at gmail.com.
Licence¶
The WannierTools code is licensed under GPLv3. The licence text in the LICENSE file is included in the root directory of the WannierTools distribution.
Authors and contributions¶
WannierTools 2.x have been written by :
- QuanSheng Wu (EPFL, Switzerland)
- ShengNan Zhang (EPFL, Switzerland)
Contributors to the code include:
- Changming Yue (IOP, Beijing, China): symmetrization
- Yifei Guan (EPFL, Switzerland): Landau level
- Yi Liu (BNU, Beijing, China): Runge-Kutta integration
