Existence of bulk chiral fermions and crystal symmetry

TL;DR

This paper uses group theory to identify conditions under which bulk chiral fermions can exist in nonmagnetic 3D crystals with weak spin-orbit coupling, providing tables for their systematic search.

Contribution

It systematically classifies space groups and symmetry points where bulk chiral fermions are possible or unavoidable, extending understanding of topological fermions in crystals.

Findings

Bulk chiral fermions are possible in specific space groups.

In some space groups, their existence is unavoidable.

The study provides tables to identify candidate materials.

Abstract

We consider the existence of bulk chiral fermions around points of symmetry in the Brillouin zone of nonmagnetic 3D crystals with negligible spin-orbit interactions. We use group theory to show that this is possible, but only for a reduced number of space groups and points of symmetry that we tabulate. Moreover, we show that for a handful of space groups the existence of bulk chiral fermions is not only possible but unavoidable, irrespective of the concrete crystal structure. Thus our tables can be used to look for bulk chiral fermions in a specific class of systems, namely that of nonmagnetic 3D crystals with sufficiently weak spin-orbit coupling. We also discuss the effects of spin-orbit interactions and possible extensions of our approach to Weyl semimetals, crystals with magnetic order, and systems with Dirac points with pseudospin 1 and 3/2. A simple tight-binding model is used to illustrate some of the issues.