Topological band crossings in hexagonal materials

TL;DR

This paper classifies all possible nonsymmorphic topological band degeneracies in hexagonal materials with strong spin-orbit coupling, identifying materials with such features and discussing their surface states and experimental implications.

Contribution

It provides a comprehensive classification of nonsymmorphic band crossings in hexagonal materials, including symmetry analysis and identification of real materials exhibiting these features.

Findings

Identification of various nonsymmorphic band crossings in hexagonal materials.

Analysis of surface states associated with topological band crossings.

Discussion of experimental implications and potential device applications.

Abstract

Topological semimetals exhibit band crossings near the Fermi energy, which are protected by the nontrivial topological character of the wave functions. In many cases, these topological band degeneracies give rise to exotic surface states and unusual magneto-transport properties. In this paper, we present a complete classification of all possible nonsymmorphic band degeneracies in hexagonal materials with strong spin-orbit coupling. This includes (i) band crossings protected by conventional nonsymmorphic symmetries, whose partial translation is within the invariant space of the mirror/rotation symmetry; and (ii) band crossings protected by off-centered mirror/rotation symmetries, whose partial translation is orthogonal to the invariant space. Our analysis is based on (i) the algebraic relations obeyed by the symmetry operators and (ii) the compatibility relations between irreducible representations at different high-symmetry points of the Brillouin zone. We identify a number of existing materials where these nonsymmorphic nodal lines are realized. Based on these example materials, we examine the surface states that are associated with the topological band crossings. Implications for experiments and device applications are briefly discussed.