Diagnosis for topological semimetals in the absence of spin-orbital coupling

TL;DR

This paper introduces an automated, symmetry-based diagnostic scheme for identifying all topological band crossings in topological semimetals without relying on spin-orbital coupling, streamlining material predictions.

Contribution

The authors develop a novel, symmetry eigenvalue-based method to detect all topological band crossings at generic momenta in time-reversal symmetric systems without spin-orbital coupling.

Findings

Enables full automation and parallelization of topological band crossing detection.

Provides a comprehensive classification of crossings using symmetry eigenvalues.

Facilitates high-throughput numerical predictions of topological materials.

Abstract

Topological semimetals are under intensive theoretical and experimental studies. The first step of these studies is always the theoretical (numerical) predication of one of several candidate materials, starting from first principles. In these calculations, it is crucial that all topological band crossings, including their types and positions in the Brillouin zone, are found. While band crossings along high-symmetry lines, which are routinely scanned in numerics, are simple to locate, the ones at generic momenta are notoriously time-consuming to find, and may be easily missed. In this paper, we establish a theoretical scheme of diagnosis for topological semimetals where all band crossings are at generic momenta in systems with time-reversal symmetry and negligible spin-orbital coupling. The scheme only uses the symmetry (inversion and rotation) eigenvalues of the valence bands at high-symmetry points in the BZ as input, and provides the types, numbers and configurations of all topological band crossings, if any, at generic momenta. The nature of new diagnosis scheme allows for full automation and parallelizations, and paves way to high throughput numerical predictions of topological materials.