Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators

TL;DR

This paper investigates the density of states scaling at the transition from a Dirac semimetal to a diffusive metal in three-dimensional topological insulators, revealing universal scaling behavior and critical exponents distinct from conventional Anderson transitions.

Contribution

It introduces a novel single parameter scaling of the density of states at the semimetal-metal transition and estimates critical exponents that differ from traditional Anderson transition values.

Findings

Density of states follows a universal scaling function.

Critical exponents $ u$ and $z$ differ from conventional Anderson transition.

Scaling behavior observed at the tricritical point.

Abstract

The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of disordered $\mathbb{Z}_2$ topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent $\nu$ and the dynamical critical exponent $z$ are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed.