Topological protection, disorder, and interactions: Survival at the surface of three-dimensional 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 wave functions. 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 nonlinear 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.

Surface transport coefficients for three-dimensional topological superconductors

“…Then we consider a large winding number (|ν| 1) expansion, using the WessZumino-Novikov-Witten Finkel'stein nonlinear sigma models (WZNW-FNLsMs) introduced in Ref. [11]. We find that the AA corrections to the spin (CI, AIII) or thermal (DIII) conductances are suppressed in the conformal limit for all three TSC classes, to the lowest nontrivial order in 1/|ν|.…”

“…For classes CI and AIII, η(r) is a complex-valued Dirac spinor; the U(1) charge is the conserved spin projection along the z-spin axis [7,11]. The U(1) current encodes the z-spin density and associated spin current…”

“…Without interactions, the ratio of the thermal conductivity to temperature is also universal in the limit T → 0 [7,11]. These results are insufficient to establish universal transport, however, because interactions usually induce Altshuler-Aronov (AA) conductance corrections in the presence of disorder [15].…”

“…In a 3D TSC, the physics is uniquely different, owing to the anomalous form that TRS assumes at the surface [7,10,11]. Nonmagnetic disorder couples only to the color or spin currents of the |ν|-fold degenerate Majorana quasiparticle bands [7,11].…”

Mesoscopic fluctuations of the local density of states in interacting electron systems

“…The second scenario with instability due to attractive interaction in the Cooper channel has been in the focus of theoretical research during last decade [34][35][36][37][38][39][40][41]. It was found that in some range of parameters multifractality favours the superconducting instability which results in enhanced superconducting transition temperature T c in comparison with the clean case.…”