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

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.