Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors

TL;DR

This paper investigates how disorder affects phase transitions between metallic, insulating, and topological phases in three-dimensional topological insulators and superconductors, using numerical and field theory methods.

Contribution

It provides a numerical phase diagram for 3D topological insulators with disorder and develops a field theory framework for various symmetry classes.

Findings

Numerical phase diagram for AII class topological insulators with disorder.

Field theory analysis yields critical exponents and anomalous dimensions.

Topological superconductors characterized by integer invariants analyzed via non-linear sigma models.

Abstract

We discuss the effects of disorder in time-reversal invariant topological insulators and superconductors in three spatial dimensions. For three-dimensional topological insulator in symplectic (AII) symmetry class, the phase diagram in the presence of disorder and a mass term, which drives a transition between trivial and topological insulator phases, is computed numerically by the transfer matrix method. The numerics is supplemented by a field theory analysis (the large-$N_f$ expansion where $N_f$ is the number of valleys or Dirac cones), from which we obtain the correlation length exponent, and several anomalous dimensions at a non-trivial critical point separating a metallic phase and a Dirac semi-metal. A similar field theory approach is developed for disorder-driven transitions in symmetry class AIII, CI, and DIII. For these three symmetry classes, where topological superconductors are characterized by integer topological invariant, a complementary description is given in terms of the non-linear sigma model supplemented with a topological term which is a three-dimensional analogue of the Pruisken term in the integer quantum Hall effect.