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

TL;DR

IrRep is a Python tool that analyzes symmetry eigenvalues and irreducible representations of electronic band structures from ab initio calculations, aiding in topological classification and connectivity analysis of materials.

Contribution

It introduces a versatile Python code capable of extracting symmetry data from band structures computed by various DFT codes, supporting comprehensive topological analysis.

Findings

Supports all 230 space groups and double groups with time-reversal symmetry

Enables systematic topological classification of materials

Facilitates detection of topologically non-trivial insulators

Abstract

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.