Nearly semi-elliptic relation between the minimal conductivity and Hall conductivity in unpaired Dirac fermions

TL;DR

This paper investigates the relationship between minimal and Hall conductivities in unpaired Dirac fermions, revealing a nearly semi-elliptic relation influenced by disorder and topological phase transitions, supported by experimental observations.

Contribution

It introduces a nearly semi-elliptic relation between conductivities in unpaired Dirac fermions and links disorder effects to topological phase transitions.

Findings

Disorder can induce a metal-insulator transition near charge neutrality.

Minimal conductivity coexists with half-quantized Hall conductivity in massless cases.

The relation aligns with experimental results in magnetic topological insulators.

Abstract

Electric conductivities may reveal the topological and magnetic properties of band structures in solids, especially for two-dimensional unpaired Dirac fermions. In this work, we evaluate the longitudinal and Hall conductivity for unpaired Dirac fermions in the framework of the self-consistent Born approximation and find a nearly semi-elliptic relation between the minimal conductivity and Hall conductivities in the Dirac fermions. Near the charge neutrality point, disorder may drive a metal-insulator transition, and enhance the longitudinal conductivity. For the massless case, the minimal conductivity $\sigma_{xx}^*$ coexists with the half-quantized Hall conductivity $e^2/2h$, forming an indicator for the parity anomalous semimetal. The relation signals a disorder-induced metallic phase that bridges two topologically distinct insulating phases, and agrees with the recent experimental observation in magnetic topological insulators.