Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator

TL;DR

This paper investigates how disorder affects the topological transition from a 2D Dirac semi-metal to an insulator, revealing an intermediate disordered semi-Dirac phase and characterizing the transition with analytical methods.

Contribution

It introduces a detailed analysis of disorder effects on the topological merging transition, identifying an intermediate disordered semi-Dirac phase and its properties.

Findings

Disorder smears the transition between phases.

An intermediate disordered semi-Dirac phase exists.

Transition behavior varies on either side of the semi-Dirac phase.

Abstract

We study the influence of disorder on the topological transition from a two-dimensional Dirac semi-metal to an insulating state. This transition is described as a continuous merging of two Dirac points leading to a semi-Dirac spectrum at the critical point. The latter is characterized by a dispersion relation linear in one direction and quadratic in the orthogonal one. Using the self-consistent Born approximation and renormalization group we calculate the density of states above, below and in the vicinity of the transition in the presence of different types of disorder. Beyond the expected disorder smearing of the transition we find an intermediate disordered semi-Dirac phase. On one side this phase is separated from the insulating state by a continuous transition while on the other side it evolves through a crossover to the disordered Dirac phase.