Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors

Abstract

We consider the interplay of disorder and interactions upon the gapless surface states of 3D topological superconductors. The combination of topology and superconducting order inverts the action of time-reversal symmetry, so that extrinsic time-reversal invariant surface perturbations appear only as "pseudomagnetic" fields (abelian and non-abelian vector potentials, which couple to spin and valley currents). The main effect of disorder is to induce multifractal scaling in surface state wavefunctions. These critically delocalized, yet strongly inhomogeneous states renormalize interaction matrix elements relative to the clean system. We compute the enhancement or suppression of interaction scaling dimensions due to the disorder exactly, using conformal field theory. We determine the conditions under which interactions remain irrelevant in the presence of disorder for symmetry classes AIII and DIII. In the limit of large topological winding numbers (many surface valleys), we show that the effective field theory takes the form of a Finkel'stein non-linear sigma model, augmented by the Wess-Zumino-Novikov-Witten term. The sigma model incorporates interaction effects to all orders, and provides a framework for a controlled perturbative expansion; the inverse spin or thermal conductance is the small parameter. For class DIII we show that interactions are always irrelevant, while in class AIII there is a finite window of stability, controlled by the disorder. Outside of this window we identify new interaction-stabilized fixed points.

27 pages, 10 figures. v2: published version

References in corpus (13)

• Classification of topological insulators and superconductors in three spatial dimensions
• Anderson Transitions
• Electron transport in disordered graphene
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• Exact relations between multifractal exponents at the Anderson transition
• Graphene via large N I: Renormalization
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• The fate of topological-insulator surface states under strong disorder
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Andreev spectroscopy and surface density of states for a three-dimensional time-reversal invariant topological superconductor
• Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
• Disordered d-wave superconductors with interactions
• Metal-insulator transition in Hubbard-like models with random hopping

Cited by in corpus (18)

• Topology of crystalline insulators and superconductors
• Superconducting doped topological materials
• Superconductivity of disordered Dirac fermions in graphene
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Surface transport coefficients for three-dimensional topological superconductors
• Beating no-go theorems by engineering defects in quantum spin models
• Nematic superconductivity in Cu${}_x$Bi${}_2$Se${}_3$: The surface Andreev bound states
• Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry
• Spontaneous gap generation on the surface of weakly interacting topological insulators using nonmagnetic impurities
• Mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction
• Marginal CFT perturbations at the integer quantum Hall transition
• Generalized multifractality at spin quantum Hall transition
• Localized surfaces of three dimensional topological insulators
• Wiedemann-Franz-type relation between shot noise and thermal conduction of Majorana surface states in a three-dimensional topological superconductor
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Induced topological order at the boundary of 3D topological superconductors
• Marginally localized edges of time-reversal symmetric topological superconductors
• Mesoscopic fluctuations of the local density of states in interacting electron systems