# Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor

## TL;DR

This paper investigates the effects of disorder on the surface states of higher-spin topological superconductors, revealing that disorder can stabilize and protect these states, leading to universal signatures in thermal and density of states measurements.

## Contribution

It demonstrates that nonmagnetic disorder enhances topological protection of Majorana surface states in spin-3/2 topological superconductors, revealing universal critical behavior and quantized thermal transport signatures.

## Key findings

- Disorder induces a stable surface conformal field theory in higher-spin TSCs.
- Universal signatures include power-law density of states and quantized thermal conductivity ratios.
- Disorder stabilizes conducting Majorana surface states, akin to the integer quantum Hall effect.

## Abstract

We study the Majorana surface states of higher-spin topological superconductors (TSCs) that could be realized in ultracold atomic systems or doped semimetals with spin-orbit coupling. As a paradigmatic example, we consider a model with p-wave pairing of spin-3/2 fermions that generalizes ${}^3\text{He-}B$. This model has coexisting linear and cubic dispersing Majorana surface bands. We show that these are unstable to interactions, which can generate a spontaneous surface thermal quantum Hall effect (TQHE). By contrast, nonmagnetic quenched disorder induces a surface conformal field theory (CFT) that is stable against weak interactions: topological protection is enhanced by disorder. Gapless surface states of higher-spin TSCs could therefore be robustly realized in solid state systems, where disorder is inevitable. The surface CFT is characterized by universal signatures that depend only on the bulk topological winding number, and include power-law scaling of the density of states, a universal multifractal spectrum of local density of states fluctuations, and a quantized ratio of the longitudinal thermal conductivity $\kappa_{xx}$ divided by temperature $T$. By contrast, $\kappa_{xx}/T$ for the clean surface without TQHE order would diverge as $T \rightarrow 0$. Since disorder stabilizes the conducting Majorana surface fluid and quantizes thermal transport, our results suggest a close analogy between bulk TSCs and the integer quantum Hall effect.