Irvsp: to obtain irreducible representations of electronic states in the VASP

https://doi.org/10.1016/j.cpc.2020.107760

开源程序“irvsp”，用于计算所有 230 个空间群的电子状态的不可约表示，并提供与 Vienna ab-initio Simulation Package 的接口。该代码由基于平面波的波函数 (WAVECAR) 和空间群算子（列在OUTCAR 中）提供，它们由 VASP 包生成。

该程序计算矩阵表示的迹线，并确定所有能带和三维布里渊区中所有 k 点的相应不可约表示。它还适用于双群的自旋轨道耦合 (SOC)。在拓扑量子化学理论建立之后，分析能带、它们的连通性和能带拓扑特别有用。此外，该代码也已扩展到（基于 Wannier 的）紧约束哈密顿量。

1. Obtain the wavefunctions at k-points

The pseudo-wavefunction is expanded in the plane waves:

2. Space group operators of a bulk

Read space group operators (SGO) from the OUTCAR

Primitive lattice vectors: (t1, t2, t3)

Primitive reciprocal lattice vectors: (g1, g2, g3)

The rotational matrix presentations Z can be obtained: 

3. Little group of a certain k-point 

Based on the integer matrices Z obtained in Step 2, program can  determine the IRs of the little group of a certain k-point

4. Character tables for k-little groups 

Provide two kinds of character tables (CRT) for all k-points. 

1. 32 point groups  

2. 230 space groups 

 eg. CRT for point group D3d, which is  used to determine the IRs for the energy  bands at Γ points 

eg. CRT for Γ-little group in SG166, which is used to determine  the IRs for the energy bands at Γ points 

5. Determination of irreducible representations 

2. Get the space group number and crystal structure (获取晶体结构的空间群) (phonopy --symmetry --tolerance 0.01 -c POSCAR) 

3. Replace the POSCAR with the POSCAR_std (得到优化的结构文件)

4. Use POSCAR_std to do DFT (VASP, QE ...) calculations (基于VASP做静态计算) 

5. Solve the decompositions of band representations with the output file (将输出文件上传至网站进行分析) 

Step 2 and 5 can be done online (http://tm.iphy.ac.cn/UnconvMat.html) 

Get the traces of electronic states from band structure calculation 

After obtaining the traces of electronic states

Get the irreducible representations of the candidate