Global phase diagram of a three dimensional dirty topological superconductor

TL;DR

This paper maps the phase diagram of a 3D topological superconductor with disorder, revealing a transition from topological insulators to a thermal metal phase, characterized by critical scaling of thermal conductance.

Contribution

It combines field theoretic and numerical methods to analyze how disorder affects phase transitions in 3D topological superconductors, identifying a disorder-induced thermal metallic phase.

Findings

Weak disorder does not affect the topological phase transition.

Strong disorder introduces an intervening thermal metallic phase.

Thermal conductance exhibits single parameter scaling at phase transitions.

Abstract

We investigate the phase diagram of a three-dimensional, time-reversal symmetric topological superconductor in the presence of charge impurities and random $s$-wave pairing. Combining complimentary field theoretic and numerical methods, we show that the quantum phase transition between two topologically distinct paired states (or thermal insulators), described by thermal Dirac semimetal, remains unaffected in the presence of sufficiently weak generic randomness. At stronger disorder, however, these two phases are separated by an intervening thermal metallic phase of diffusive Majorana fermions. We show that across the insulator-insulator and metal-insulator transitions, normalized thermal conductance displays single parameter scaling, allowing us to numerically extract the critical exponents across them. The pertinence of our study in strong spin-orbit coupled, three-dimensional doped narrow gap semiconductors, such as Cu$_x$Bi$_2$Se$_3$, is discussed.