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

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.

References in corpus (29)

• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Moire bands in twisted double-layer graphene
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Magnetic-field-induced quantized anomalous Hall effect in intrinsic magnetic topological insulator MnBi${}_2$Te${}_4$
• Topological quantum chemistry
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Prediction and observation of the first antiferromagnetic topological insulator
• The (High Quality) Topological Materials In The World
• Catalogue of Topological Electronic Materials
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Hexagonal Warping Effects in the Surface States of Topological Insulator Bi${}_2$Te${}_3$
• Observation of Fractionally Quantized Anomalous Hall Effect
• Experimental realization of an intrinsic magnetic topological insulator
• Antiferromagnetic topological insulators
• Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi${}_2$Se${}_3$
• High-throughput calculations of magnetic topological materials
• Irvsp: to obtain irreducible representations of electronic states in the VASP
• Catalogue of topological phonon materials
• Systematic investigation of emergent particles in type-III magnetic space groups
• Encyclopedia of emergent particles in type-IV magnetic space groups
• Exhaustive constructions of effective models in 1651 magnetic space groups
• Complete classification of band nodal structures
• SpaceGroupIrep: A package for irreducible representations of space group
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• MagneticKP: A package for quickly constructing $\mathbf{k}\cdot \mathbf{p}$ models of magnetic and non-magnetic crystals
• MSGCorep: A package for corepresentations of magnetic space groups