Disordered topological quantum critical points in three-dimensional systems

TL;DR

This paper investigates how non-magnetic disorder affects three-dimensional topological quantum critical points, revealing conditions for their stability and analyzing the impact on quantum conductivity through a self-consistent phase diagram.

Contribution

It demonstrates the cancellation of backward scattering processes due to Berry phase effects and derives a phase diagram considering generic non-magnetic disorders.

Findings

Backward scattering mediated by chemical-potential impurities is canceled by T-reversal processes.

The absolute stability of TQCP requires preservation of the parity density.

The phase diagram shows different behaviors under various non-magnetic disorder potentials.

Abstract

Generic non-magnetic disorder effects onto those topological quantum critical points (TQCP), which intervene the three-dimensional topological insulator and an ordinary insulator, are investigated. We first show that, in such 3-d TQCP, any backward scattering process mediated by the chemical-potential-type impurity is always canceled by its time-reversal (T-reversal) counter-process, because of the non-trivial Berry phase supported by these two processes in the momentum space. However, this cancellation can be generalized into only those backward scattering processes which conserve a certain internal degree of freedom, i.e. the parity density, while the `absolute' stability of the TQCP against any non-magnetic disorders is required by the bulk-edge correspondence. Motivated by this, we further derive the self-consistent-Born phase diagram in the presence of generic non-magnetic disorder potentials and argue the behaviour of the quantum conductivity correction in such cases. The distinction and similarity between the case with only the chemical-potential-type disorder and that with the generic non-magnetic disorders are finally summarized.