We study the two-dimensional disordered topological superconductor with Hubbard interactions. When the magnitude of the pairing potential is tuned to special values, this interacting model is exactly solvable even when disorders are imposed on the potential term or coupling constants. The topology of this model is investigated in detail by the real space Chern number formula, which computes the topological index of disordered systems to high precisions. It is found that the disorders can drive the system from topological trivial phase to a non-trivial phase, which generalizes the topological Anderson phenomena to interacting models. The self-consistent Born approximation is also employed to understand the influence of the disorders on the parameters of the interacting topological superconductor. It provide an alternative way to understand the topological transitions at weak disordered region.We study the two-dimensional disordered topological superconductor with Hubbard interactions. When the magnitude of the pairing potential is tuned to special values, this interacting model is exactly solvable even when disorders are imposed on the potential term or coupling constants. The topology of this model is investigated in detail by the real space Chern number formula, which computes the topological index of disordered systems to high precisions. It is found that the disorders can drive the system from topological trivial phase to a non-trivial phase, which generalizes the topological Anderson phenomena to interacting models. The self-consistent Born approximation is also employed to understand the influence of the disorders on the parameters of the interacting topological superconductor. It provide an alternative way to understand the topological transitions at weak disordered region.

arXiv:2311.01730Nov 3, 20230 citations

Disorder-enhanced topological protection and universal quantum criticality in a spin- 32 topological superconductor

Sayed Ali Akbar Ghorashi, Seth Davis, Matthew S. Foster

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 $^{3}\mathrm{He}\ensuremath{-}B$. 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 they 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 ${\ensuremath{\kappa}}_{xx}$ divided by temperature $T$ . By contrast, ${\ensuremath{\kappa}}_{xx}/T$ for the clean surface without TQHE order would diverge as $T\ensuremath{\rightarrow}0$. 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.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 $^{3}\mathrm{He}\ensuremath{-}B$. 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 they 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 ${\ensuremath{\kappa}}_{xx}$ divided by temperature $T$. By contrast, ${\ensuremath{\kappa}}_{xx}/T$ for the clean surface without TQHE order would diverge as $T\ensuremath{\rightarrow}0$. 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.

arXiv:1701.02787Physical review. B./Physical review. BApr 3, 201729 citations

p

-wave pairing of spin-3/2 fermions that generalizes $^{3}\mathrm{He}\ensuremath{-}B$. 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 they 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 ${\ensuremath{\kappa}}_{xx}$ divided by temperature

T

. By contrast, ${\ensuremath{\kappa}}_{xx}/T$ for the clean surface without TQHE order would diverge as $T\ensuremath{\rightarrow}0$. 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.