# Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines

## TL;DR

This paper classifies nonsymmorphic symmetry-enforced band crossings in trigonal materials with strong spin-orbit coupling, identifying Weyl points and nodal lines near the Fermi energy with potential experimental implications.

## Contribution

It provides a comprehensive classification of nonsymmorphic band degeneracies in trigonal materials, highlighting two types of Weyl crossings and identifying real materials exhibiting these features.

## Key findings

- Identification of accordion Weyl points in Cu2SrSnS4 and Te
- Discovery of Weyl nodal lines in Te16Si38
- Detailed ab-initio analysis of band structures and surface states

## Abstract

Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can enforce band crossings within high-symmetry lines or planes of the Brillouin zone. When these band degeneracies are close to the Fermi energy, they can give rise to a number of unusual phenomena: e.g., anomalous magnetoelectric responses, transverse Hall currents, and exotic surface states. In this paper, we present a comprehensive classification of such nonsymmorphic band crossings in trigonal materials with strong spin-orbit coupling. We find that in trigonal systems there are two different types of nonsymmorphic band degeneracies: (i) Weyl points protected by screw rotations with an accordion-like dispersion, and (ii) Weyl nodal lines protected by glide reflections. We report a number of existing materials, where these band crossings are realized near the Fermi energy. This includes Cu2SrSnS4 and elemental tellurium (Te), which exhibit accordion Weyl points; and the tellurium-silicon clathrate Te16Si38, which shows Weyl nodal lines. The ab-initio band structures and surface states of these materials are studied in detail, and implications for experiments are briefly discussed.