Deformation and Stability of Surface States in Dirac semimetals

TL;DR

This paper investigates the deformation and stability of surface states in Dirac semimetals, revealing conditions under which surface states persist or are destroyed, and clarifying the role of symmetries in their robustness.

Contribution

It demonstrates that certain surface states in Dirac semimetals are protected by non-generic symmetries and identifies scenarios where surface states can be completely eliminated without affecting the bulk.

Findings

Double Fermi arcs are not topologically protected in Dirac semimetals.

Extra particle-hole symmetry contributes to the robustness of surface states.

Surface states can be destroyed without breaking bulk symmetry or topology.

Abstract

The unusual surface states of topological semimetals have attracted a lot of attention. Recently, we showed [PNAS 113, 8648 (2016)] that for a Dirac semimetal (DSM) arising from band-inversion, such as Na$_3$Bi and Cd$_3$As$_2$, the expected double Fermi arcs on the surface are not topologically protected. Quite generally, the arcs deform into states similar to those on the surface of a strong topological insulator. Here we address two questions related to deformation and stability of surface states in DSMs. First, we discuss why certain perturbations, no matter how large, are unable to destroy the double Fermi arcs. We show that this is related to certain extra (particle-hole) symmetry, which is non-generic in materials. Second, we discuss situations in which the surface states are completely destroyed without breaking any symmetry or impacting the bulk Dirac nodes. We are not aware of any experimental or density functional theory (DFT) candidates for a material which is a bulk DSM without any surface states, but our results clearly show that this is possible.