IrRep: Symmetry eigenvalues and irreducible representations of ab initio band structures

We present IrRep – a Python code that calculates the symmetry eigenvalues of electronic Bloch states in crystalline solids and the irreducible representations under which they transform. As input it receives bandstructures computed with state-of-the-art Density Functional Theory codes such as VASP, Quantum Espresso, or Abinit, as well as any other code that has an interface to Wannier90. Our code is applicable to materials in any of the 230 space groups and double groups preserving time-reversal symmetry with or without spin-orbit coupling included, for primitive or conventional unit cells. This makes IrRep a powerful tool to systematically analyze the connectivity and topological classification of bands, as well as to detect insulators with non-trivial topology, following the Topological Quantum Chemistry formalism: IrRep can generate the input files needed to calculate the (physical) elementary band representations and the symmetry-based indicators using the CheckTopologicalMat routine of the Bilbao Crystallographic Server. It is also particularly suitable for interfaces with other plane-waves based codes, due to its flexible structure.我们推出IrRep——一款用于计算晶体固体中电子布洛赫态的对称本征值，以及这些态所属不可约表示的Python代码。该代码可接收由当前主流密度泛函理论（Density Functional Theory）程序（如VASP、Quantum Espresso或Abinit），以及任何可对接Wannier90的其他程序所计算得到的能带结构作为输入。我们的代码适用于所有230种空间群，以及无论是否包含自旋轨道耦合、满足时间反演对称性的双群所对应的材料，支持原胞或惯用原胞体系。这使得IrRep成为一款强大的工具，可按照拓扑量子化学（Topological Quantum Chemistry）形式体系，系统性分析能带的连通性与拓扑分类，同时能够检测具有非平庸拓扑性质的绝缘体：IrRep可生成所需输入文件，借助毕尔巴鄂晶体学服务器（Bilbao Crystallographic Server）的CheckTopologicalMat程序，计算（物理）基本能带表示与基于对称的拓扑指标。此外，由于其灵活的架构，IrRep也特别适配与其他基于平面波的程序进行对接。