Fermi arcs and surface criticality in dirty Dirac materials

TL;DR

This paper investigates how disorder affects surface states in Weyl and Dirac semimetals, revealing critical behaviors at the surface that depend on boundary conditions and disorder, with implications for understanding surface criticality in topological materials.

Contribution

It introduces a local self-consistent Born approximation to analyze surface states and uncovers surface criticality phenomena influenced by disorder and boundary conditions.

Findings

Surface criticality exists in Dirac semimetals and is smoothed out in Weyl semimetals.

Disorder modifies the local density of states and surface group velocity profiles.

Phase diagrams show distinct surface behaviors depending on boundary conditions and disorder strength.

Abstract

We study the effects of disorder on semi-infinite Weyl and Dirac semimetals where the presence of a boundary leads to the formation of either Fermi arcs/rays or Dirac surface states. Using a local version of the self-consistent Born approximation, we calculate the profile of the local density of states and the surface group velocity. This allows us to explore the full phase diagram as a function of boundary conditions and disorder strength. While in all cases we recover the sharp criticality in the bulk, we unveil a critical behavior at the surface of Dirac semimetals, which is smoothed out by Fermi arcs in Weyl semimetals.