目录
计算指定k点的有效质量
BAND计算有效质量本身不需要计算能带，这和其他软件有所不同。其他软件的有效质量一般是从能带曲线，拟合出梯度而得到有效质量，因此是一个数值，也跟能带曲线在k空间的方向直接相关。BAND则是指定k点后，计算该k点附近各个方向的一些k点上，费米能级上下N条能带的值，因此得到的有效质量，对三维周期性体系（例如单晶硅）而言，类似椭球，存在三个轴，三个轴向各有一个值；对于二维周期性体系（例如石墨烯），则存在两个轴，BAND将会给出两个轴向的两个值。
计算设置
原本不需要计算能带、态密度，不过我们本例中，也勾选了这两项，作为对比：
一般而言，BAND的计算都需要将ｋ点设置为Very Good甚至以上：
关于能带的设置，下图所示数值，是设置能带曲线的细腻程度，数值越小，曲线越光滑细腻，不过一般而言0.01已经非常足够了：
设定要计算有效质量的k点坐标，用空格隔开x y z值：
其中
- Include N Bands above是指计算费米能级以上N条能带
- Include N Bands below是指计算费米能级以下N条能带
- Step size指拟合剃度，做差分时的间距
上面设置只计算费米能级上下各一条能带（上的有效质量）
结果查看
能带
SCM - BandStructure：
有效质量
SCM - Output 接近尾部，依次给出了4个k点，在两条能带上的有效质量：
E F F E C T I V E M A S S
Fermi energy -0.207568 Hartree -5.64821 eV
k-coordinates 0.000 0.000 0.000
fractional coords 0.000 0.000 0.000
Curvature for band index: 4
Energy wrt fermi level: -0.011368 Hartree -0.30935 eV
Energy: -0.218936 Hartree -5.95756 eV
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Step size: 0.001000 0.002000
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eigenvalues of band curvature -0.40428 -0.35443 -0.35327 -0.37782 -0.36537 -0.36507
effective mass (m0): -2.47351 -2.82141 -2.83069 -2.64678 -2.73692 -2.73919
eigenvectors:
eigenvector # 1 -0.557529 -0.582043 -0.591935 -0.557005 -0.582131 -0.592342
eigenvector # 2 -0.119314 -0.649455 0.750981 -0.119731 -0.649491 0.750883
eigenvector # 3 0.821538 -0.489320 -0.292645 0.821833 -0.489168 -0.292070
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Curvature for band index: 5
Energy wrt fermi level: 0.083703 Hartree 2.27768 eV
Energy: -0.123864 Hartree -3.37052 eV
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Step size: 0.001000 0.002000
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eigenvalues of band curvature 4.30233 4.30575 4.30600 4.33204 4.33289 4.33295
effective mass (m0): 0.23243 0.23225 0.23223 0.23084 0.23079 0.23079
eigenvectors:
eigenvector # 1 0.995717 0.076159 0.052419 0.995464 0.078022 0.054447
eigenvector # 2 0.020874 -0.737512 0.675011 0.020154 -0.732213 0.680777
eigenvector # 3 -0.090068 0.671026 0.735943 -0.092982 0.676592 0.730464
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k-coordinates 0.000 1.000 0.000
fractional coords 0.817 0.000 0.817
Curvature for band index: 4
Energy wrt fermi level: -0.060866 Hartree -1.65623 eV
Energy: -0.268433 Hartree -7.30444 eV
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Step size: 0.001000 0.002000
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eigenvalues of band curvature -3.81151 1.75287 1.89730 -3.81849 1.70969 1.95725
effective mass (m0): -0.26236 0.57049 0.52706 -0.26188 0.58490 0.51092
eigenvectors:
eigenvector # 1 0.000029 1.000000 0.000031 0.000014 1.000000 0.000016
eigenvector # 2 0.704358 -0.000042 0.709845 0.706707 -0.000021 0.707507
eigenvector # 3 0.709845 0.000002 -0.704358 0.707507 0.000001 -0.706707
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Curvature for band index: 5
Energy wrt fermi level: 0.048697 Hartree 1.32511 eV
Energy: -0.158871 Hartree -4.32309 eV
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Step size: 0.001000 0.002000
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eigenvalues of band curvature 0.21258 5.28351 5.28811 0.21186 5.28021 5.28941
effective mass (m0): 4.70421 0.18927 0.18910 4.72017 0.18939 0.18906
eigenvectors:
eigenvector # 1 0.000000 -1.000000 0.000000 0.000000 -1.000000 0.000000
eigenvector # 2 0.707098 0.000000 -0.707116 0.707111 0.000000 -0.707102
eigenvector # 3 0.707116 0.000000 0.707098 0.707102 0.000000 0.707111
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k-coordinates 0.000 0.000 1.000
fractional coords 0.817 0.817 0.000
Curvature for band index: 4
Energy wrt fermi level: -0.060866 Hartree -1.65624 eV
Energy: -0.268433 Hartree -7.30444 eV
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Step size: 0.001000 0.002000
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eigenvalues of band curvature -3.81123 1.75233 1.89731 -3.81842 1.70955 1.95725
effective mass (m0): -0.26238 0.57067 0.52706 -0.26189 0.58495 0.51092
eigenvectors:
eigenvector # 1 0.000028 0.000029 1.000000 0.000014 0.000015 1.000000
eigenvector # 2 0.706760 0.707454 -0.000041 0.707056 0.707158 -0.000020
eigenvector # 3 0.707454 -0.706760 0.000001 0.707158 -0.707056 0.000000
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Curvature for band index: 5
Energy wrt fermi level: 0.048697 Hartree 1.32511 eV
Energy: -0.158871 Hartree -4.32309 eV
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Step size: 0.001000 0.002000
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eigenvalues of band curvature 0.21258 5.28351 5.28811 0.21186 5.28021 5.28941
effective mass (m0): 4.70420 0.18927 0.18910 4.72017 0.18939 0.18906
eigenvectors:
eigenvector # 1 0.000000 0.000000 1.000000 0.000000 0.000000 1.000000
eigenvector # 2 -0.707089 0.707124 0.000000 -0.707104 0.707110 0.000000
eigenvector # 3 -0.707124 -0.707089 0.000000 -0.707110 -0.707104 0.000000
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k-coordinates 1.000 0.000 0.000
fractional coords 0.000 0.817 0.817
Curvature for band index: 4
Energy wrt fermi level: -0.060866 Hartree -1.65623 eV
Energy: -0.268433 Hartree -7.30444 eV
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Step size: 0.001000 0.002000
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eigenvalues of band curvature -3.81209 1.75403 1.89730 -3.81864 1.70997 1.95725
effective mass (m0): -0.26232 0.57011 0.52706 -0.26187 0.58480 0.51092
eigenvectors:
eigenvector # 1 -1.000000 -0.000029 -0.000030 -1.000000 -0.000015 -0.000015
eigenvector # 2 -0.000042 0.708274 0.705937 -0.000021 0.707276 0.706938
eigenvector # 3 -0.000001 -0.705937 0.708274 -0.000001 -0.706938 0.707276
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Curvature for band index: 5
Energy wrt fermi level: 0.048697 Hartree 1.32511 eV
Energy: -0.158871 Hartree -4.32309 eV
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Step size: 0.001000 0.002000
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eigenvalues of band curvature 0.21258 5.28351 5.28811 0.21186 5.28021 5.28941
effective mass (m0): 4.70421 0.18927 0.18910 4.72018 0.18939 0.18906
eigenvectors:
eigenvector # 1 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000
eigenvector # 2 0.000000 0.707087 -0.707127 0.000000 0.707111 -0.707103
eigenvector # 3 0.000000 0.707127 0.707087 0.000000 0.707103 0.707111
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例如最后一个k点：
- 坐标：1.000 0.000 0.000，在倒空间的分数坐标：0.000 0.817 0.817
- eigenvector # 1 1.000000 0.000000 0.000000方向的值：4.70421
- eigenvector # 2 0.000000 0.707087 -0.707127方向的值：0.18927
- eigenvector # 3 0.000000 0.707127 0.707087方向的值：0.18910
- 同时也增大差分间距进行了计算，其值列在右侧，差异不大