Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals

TL;DR

This paper investigates the phase transitions in three-dimensional disordered Dirac semimetals, revealing a rich phase diagram with semimetal, diffusive metal, and insulator phases, and characterizing the quantum critical points and multifractal properties.

Contribution

It provides a detailed numerical analysis of the quantum phase diagram, identifying three distinct phases and two quantum critical points in disordered Dirac semimetals, highlighting their multifractal nature.

Findings

Identification of three phases: semimetal, diffusive metal, insulator.

Existence of two quantum critical points with multifractal characteristics.

Phase diagram showing disorder-driven transitions at half-filling and doping.

Abstract

We study the quantum phase diagram of a three dimensional non-interacting Dirac semimetal in the presence of either quenched axial or scalar potential disorder, by calculating the average and the typical density of states as well as the inverse participation ratio using numerically exact methods. We show that as a function of the disorder strength a half-filled (i.e. undoped) Dirac semimetal displays three distinct ground states, namely an incompressible semimetal, a compressible diffusive metal, and a localized Anderson insulator, in stark contrast to a conventional dirty metal that only supports the latter two phases. We establish the existence of two distinct quantum critical points, which respectively govern the semimetal-metal and the metal-insulator quantum phase transitions and also reveal their underlying multifractal nature. Away from half-filling the (doped) system behaves as a diffusive metal that can undergo Anderson localization only, which is shown by determining the mobility edge and the phase diagram in terms of energy and disorder.