Dirac Semimetals in Two Dimensions

TL;DR

This paper introduces symmetry-protected two-dimensional Dirac semimetals that maintain gapless Dirac cones at high-symmetry points, distinct from graphene, and explores their phases using symmetry considerations and tight-binding models.

Contribution

It demonstrates the existence of 2D Dirac semimetals protected by non-symmorphic symmetries and constructs explicit models for different phases, highlighting the role of symmetries in topological transitions.

Findings

Symmetry-protected Dirac points cannot exist singly in 2D.

Non-symmorphic symmetries enable stable 2D Dirac semimetals.

Breaking symmetries leads to topological insulators and Weyl semimetals.

Abstract

Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are \emph{not} gapped by spin-orbit interactions, and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases, and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of non-symmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases.