Quantum criticality between topological and band insulators in $(3+1)$-dimensions

TL;DR

This paper investigates the quantum critical behavior between topological and trivial insulators in 3+1 dimensions, analyzing the effects of Coulomb interaction and disorder on Dirac fermions and phase transitions.

Contribution

It provides a detailed analysis of the stability of the semi-metallic phase and the nature of phase transitions under disorder and interactions in Dirac fermion systems.

Findings

Semi-metallic phase remains stable up to a critical disorder strength.

Direct transition between insulators persists below critical disorder.

Beyond critical disorder, a transition to a diffusive metallic phase occurs.

Abstract

Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semi-metallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semi-metallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semi-metallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases. Our results are also applicable to even number of flavors of Dirac fermions, and the band inversion transition in various non-topological narrow gap semiconductors.