wannierTools研究Topological Insulator
这里我想继续通过WannierTools来计算Topological insulator的一些性质,来让自己对输入文件中的一些参数有一个更加深刻的认识,并通过这个实例来学习新的一些控制参数的作用.
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Topological insulator
这个博客中学习的实例同样来自于源代码中examples文件夹中
首先解压文件得到这个体系的紧束缚模型的数据1
tar xzvf wannier90_hr.dat.tar.gz
wt.in已经准备好了,接下来就主要分析学习一下里面的参数设置
1 | &TB_FILE |
Results
将上面的两个文件内容准备好之后,就可以进行计算了1
mpirun -np 10 wt.x
计算完成之后对结果进行可视化处理1
gnuplot surfdos_l.gnu
Bi$_2$Se$_3$
这里对3D拓扑绝缘体Bi$_2$Se$_3$进行一些计算
首先解压紧束缚数据1
tar xzvf wannier90_hr.dat.tar.gz
接下来分析一下控制计算的wt.in文件1
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134&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 ! 计算体态能带
BulkBand_points_calc = T ! Flag for bulk energy band calculation for some k points
DOS_calc = T ! Flag for density of state calculation
SlabBand_calc = T ! Flag for 2D slab energy band calculation
SlabBandWaveFunc_calc = T ! Flag for 2D slab band wave function
SlabBand_plane_calc = T ! Flag for 2D slab energy band calculation
WireBand_calc = T ! Flag for 1D wire energy band calculation
SlabSS_calc = T ! Flag for surface state ARPES spectrum calculation
SlabArc_calc = T ! Flag for surface state fermi-arc calculation
SlabQPI_calc = T ! Flag for surface state QPI spectrum calculation in a given k plane in 2D BZ
Z2_3D_calc = T ! Flag for Z2 number calculations of 6 planes(强TI需要有4个indeces来判断)
SlabSpintexture_calc = T ! Flag for surface state spin-texture calculation(计算表面态上的spin分布变化)
Wanniercenter_calc = T ! Flag for Wilson loop calculation
/
&SYSTEM
NSLAB = 4 ! Number of slabs for 2d Slab system
NSLAB1= 2 ! Number of slabs for 1D wire system
NSLAB2= 2 ! Number of slabs for 1D wire system
NumOccupied = 18 !> Number of occupied bands for bulk unit cell
SOC = 1 ! A parameter to control soc; Soc=0 means no spin-orbit coupling; Soc>0 means spin-orbit coupling
E_FERMI = 4.4195 ! Fermi energy, search E-fermi in OUTCAR for VASP, set to zero for Wien2k
surf_onsite= 0.0 !> surface onsite energy shift
/
&PARAMETERS
Eta_Arc = 0.001 ! infinite small value, like brodening, used to calculate dos epsilon+i eta
E_arc = 0.0 ! energy level for contour plot of spectrum, Fermi energy for arc calculation
OmegaNum = 400 ! omega number
OmegaMin = -0.6 ! energy interval
OmegaMax = 0.5 ! energy interval
Nk1 = 101 ! number k points odd number would be better(如果这个数值过小,结果会非常粗糙)
Nk2 = 101 ! number k points odd number would be better
Nk3 = 101 ! number k points odd number would be better
NP = 1 ! number of principle layers
Gap_threshold = 0.01 ! threshold for FindNodes_calc output, threshold value for output the the k points data for Gap3D
/
KPATH_BULK ! k point path(动量空间能带计算路径)
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 ! 半开边界计算能带时的路径选择
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
KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane(2D半开边界计算时能带计算的位置选择)
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
将两个主要文件准备好之后,就可以开始计算了1
mpirun -np 2 wt.x &
对计算结果进行可视化1
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6gnuplot bulkek.gnu # 体态能带计算
gnuplot wanniercenter3D_Z2.gnu-tutorial # Wilson loop计算
gnuplot surfdos_l.gnu # 表面态密度计算
gnuplot arc_l.gnu # 计算费米弧
gnuplot spintext_l.gnu # 计算费米弧上的spin分布
gnuplot slabek.gnu # 计算边界态
上面就是这个实例的一些参数设置和计算得到的一些结果.
练习
在这里做个小练习,改动参数来计算一下不同表面上的能带以及谱函数,这里主要通过修改SURFACE这个参数下的内容来计算其它表面上的边界态以及能谱,将这个参数修改为1
2
3SURFACE ! Specify surface with two vectors, see doc
0 1 0
0 0 1
计算的结果如下
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