前面我已经通过将一个紧束缚模型转换成WannierTools可计算的数据,研究了一下模型的拓扑性质,这里我想通过计算一下Bi$_2$Se$_3$这个材料的一些具体性质,因为这个材料是可以通过VASP计算得到其对应的能带及其它一些信息的,所以我可以结合VASP来完全重复这个材料具体信息,而且这个例子也是学习第一性计算较好的算例,所以就在这里仔细学习并记录一下.
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wt.in文件内容解析

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&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 0.0000    0.0000    0.5000
 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            ! Specify surface with two vectors, see doc
 1  0  0
 0  1  0


!> bulk band structure calculation flag
&CONTROL
BulkBand_calc            = T
BulkBand_points_calc     = T
DOS_calc                 = T
SlabBand_calc            = T
SlabBandWaveFunc_calc    = T
SlabBand_plane_calc      = T
WireBand_calc            = T
SlabSS_calc              = T
SlabArc_calc             = T
SlabQPI_calc             = T
Z2_3D_calc               = T
SlabSpintexture_calc     = T
Wanniercenter_calc       = T
/

&SYSTEM
NSLAB = 4               ! for thin film system
NSLAB1= 2               ! nanowire system 
NSLAB2= 2               ! nanowire system 
NumOccupied = 18        ! NumOccupied
SOC = 1                 ! soc
E_FERMI = 4.4195        ! e-fermi, a global shift of the energy levels
surf_onsite= 0.0        ! surf_onsite
/

&PARAMETERS
Eta_Arc = 0.001     ! infinite small value, like brodening 
E_arc = 0.0         ! energy level for contour plot of spectrum
OmegaNum = 400      ! omega number       
OmegaMin = -0.6     ! energy interval
OmegaMax =  0.5     ! energy interval
Nk1 = 10           ! number k points  odd number would be better
Nk2 = 10            ! number k points  odd number would be better
Nk3 = 10            ! number k points  odd number would be better
NP = 1              ! number of principle layers
Gap_threshold = 0.01 ! threshold for FindNodes_calc 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  0.50   ! 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

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

设置紧束缚哈密顿量

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&TB_FILE  ! 输入控制文件中共有4个这样的名字 TB_FILE, SYSTEM, CONTROL, PARAMETERS,分别用来控制不同内容
Hrfile = 'wannier90_hr.dat'  ! 紧束缚哈密顿量的位置
Package = 'VASP'             ! obtained from VASP, it could be 'VASP', 'QE', 'Wien2k', 'OpenMx'
/

设置体系的一些性质

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&SYSTEM
Nslab = 10  !Number of slabs for slab band, The default value is 10
Nslab1= 6   ! The thickness of nano ribbon
Nslab2= 6
NumOccupied = 18        ! 占据的Wannier能带的数目,这个设置一定要正确才行
SOC = 1                 ! SOC>0代表模型中考虑自旋轨道耦合,SOC=0则代表不考虑自旋轨道耦合
E_FERMI = 4.4195        ! real-valued, Fermi level for the given tight binding model
Bx= 0, By= 0, Bz= 0     ! Bx By Bz
surf_onsite= 0.0        ! real-valued, Additional onsite energy on the surface, you can set this to see how surface state changes
/

计算控制

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BulkBand_calc         = T  ! 计算体态能带	
BulkFS_calc           = F  ! 体系费米面计算
BulkGap_cube_calc     = F  ! Energy gap for a given k cube for bulk system	
BulkGap_plane_calc    = F  ! Energy gap for a given k plane for bulk system	
SlabBand_calc         = T  ! Band structure for 2D slab system(开边界能带计算)
WireBand_calc         = F  ! Band structure for 1D ribbon system(若为3D体系,则表示开两个方向边界进行计算)
SlabSS_calc           = T  ! Surface spectrum A(k,E) along a kline and energy interval for slab system(计算开边界时候的表面态)
SlabArc_calc          = F  ! Surface spectrum A(k,E0) for fixed energy E0 in 2D k-plane for slab system	(计算确定能量下的表面态)
SlabSpintexture_calc  = T  ! Spin texture in 2D k-plane for slab system(开边界表面态上的自旋分布计算)
wanniercenter_calc    = F  ! 计算Wannier Center的变化
BerryCurvature_calc   = F  ! 计算体系Berry曲率
/

参数设置

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E_arc = 0.0         ! 计算费米弧时候的能量
Eta_Arc = 0.001     ! infinite small value, like broadening(格林函数的小虚部)
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              ! 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 = 1.0 !This value is used when you do energy gap calculation like BulkGap_cube_calc=T
/

晶体结构信息设置

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LATTICE
Angstrom ! 长度单位
-2.069  -3.583614  0.000000     ! 元胞基矢
 2.069  -3.583614  0.000000
 0.000   2.389075  9.546667

原子位置

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ATOM_POSITIONS
5                               ! 元胞内有5个原子
Direct                          ! 原子位置的表示方式
Bi 0.3990    0.3990    0.6970   ! 每个原子的位置坐标
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

轨道投影

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PROJECTORS
 3 3 3 3 3          ! 每个原子的投影轨道数目
 Bi pz px py        ! 设置每个原子的投影轨道 
 Bi pz px py
 Se pz px py
 Se pz px py
 Se pz px py

表面计算设置

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SURFACE            ! 设置要研究的是哪个面上的性质
 1  0  0           ! a11, a12, a13
 0  1  0           ! a21 a22 a23

体态能带计算

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KPATH_BULK            ! 计算体态能带时,动量空间中路径的选择
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

特殊点能带计算

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KPOINTS_3D  !You can calculate the properties on some kpoints you specified in point mode
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

slab结构计算表面态

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KPATH_SLAB  ! 计算表面态时候的路径选择
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

2D平面上arc计算

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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

png

3D体BZ中的计算

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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

png

KCUBE_BULK

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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

png

Wannier Center计算

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WANNIER_CENTRES     ! copy from wannier90.wout(需要结合Wannier90来产生数据)
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

结果

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