Quantum phases of disordered three-dimensional Majorana-Weyl fermions

TL;DR

This paper investigates how disorder affects the phases of three-dimensional Majorana-Weyl fermions in a topological superconductor, revealing a transition from a thermal semimetal to a diffusive metal and identifying different insulating phases.

Contribution

It provides a detailed phase diagram of disordered 3D Majorana-Weyl fermions, showing the conversion of the thermal Hall semimetal into a diffusive metal and characterizing various insulating states.

Findings

Infinitesimal disorder converts ThSM into ThDM due to rare fluctuations.

Phase diagram includes ThDM and thermal insulators, with a crossover at finite energies.

Identifies two types of thermal insulators: trivial band insulator and Anderson insulator.

Abstract

The gapless Bogoliubov-de Gennes (BdG) quasiparticles of a clean three dimensional spinless $p_x+ip_y$ superconductor provide an intriguing example of a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions in class D of the Altland-Zirnbauer symmetry classification; such a phase can support a large anomalous thermal Hall conductivity and protected surface Majorana-Fermi arcs at zero energy. We study the effect of quenched disorder on such a topological phase with both numerical and analytical methods. Using the kernel polynomial method, we compute the average and typical density of states for the BdG quasiparticles; based on this, we construct the disordered phase diagram. We show for infinitesimal disorder, the ThSM is converted into a diffusive thermal Hall metal (ThDM) due to rare statistical fluctuations. Consequently, the phase diagram of the disordered model only consists of ThDM and thermal insulating phases. Nonetheless, there is a cross-over at finite energies from a ThSM regime to a ThDM regime, and we establish the scaling properties of the avoided quantum critical point which marks this cross-over. Additionally, we show the existence of two types of thermal insulators: (i) a trivial thermal band insulator (ThBI) [or BEC phase] supporting only exponentially localized Lifshitz states (at low energy), and (ii) a thermal Anderson insulator (AI) at large disorder strengths. We determine the nature of the two distinct localization transitions between these two types of insulators and ThDM.We also discuss the experimental relevance of our results for three dimensional, time reversal symmetry breaking, triplet superconducting states.