ToMSGKpoint: A user-friendly package for computing symmetry transformation properties of electronic eigenstates of nonmagnetic and magnetic crystalline materials

TL;DR

ToMSGKpoint is a user-friendly Mathematica package that determines symmetry properties of electronic states in magnetic and nonmagnetic crystalline materials, facilitating topological material research without structure transformation complexities.

Contribution

It is the first package capable of analyzing (co)irreducible representations at various high-symmetry regions for any crystal structure, including magnetic cases, directly from ab initio wavefunctions.

Findings

Successfully applied to Bi2Se3, Na3Bi, and MnBi2Te4.

Supports analysis with or without spin-orbit coupling.

Streamlines symmetry analysis in topological material studies.

Abstract

The calculation of (co)irreducible representations of energy bands at high-symmetry points (HSPs) is essential for high-throughput research on topological materials based on symmetry-indicators or topological quantum chemistry. However, existing computational packages usually require transforming crystal structures into specific conventions, thus hindering extensive application, especially to materials whose symmetries are yet to be identified. To address this issue, we developed a Mathematica package, \texttt{ToMSGKpoint}, capable of determining the little groups and (co)irreducible representations of little groups of HSPs, high-symmetry lines (HSLs), and high-symmetry planes (HSPLs) for any nonmagnetic and magnetic crystalline materials in two and three dimensions, with or without considering spin-orbit coupling. To the best of our knowledge, this is the first package to achieve such functionality. The package also provides magnetic space group operations, supports the analysis of (co)irreducible representations of energy bands at HSPs, HSLs, and HSPLs using electronic wavefunctions obtained from \textit{ab initio} calculations interfaced with VASP. Designed for user convenience, the package generates results in a few simple steps and presents all relevant information in clear tabular format. Its versatility is demonstrated through applications to nonmagnetic topological insulator Bi$_2$Se$_3$ and Dirac semimetal Na$_3$Bi, as well as the antiferromagnetic topological material MnBi$_2$Te$_4$. Suitable for any crystal structure, this package can be conveniently applied in a streamlined study once magnetic space group varies with various symmetry-breakings caused by phase transitions.