Interaction-Mediated Surface-State Instability in Disordered Three-Dimensional Topological Superconductors with Spin SU(2) Symmetry

We show that arbitrarily weak interparticle interactions destabilize the surface states of 3D topological superconductors with spin SU(2) invariance (symmetry class CI) in the presence of nonmagnetic disorder. The conduit for the instability is disorder-induced wave function multifractality. We argue that time-reversal symmetry breaks spontaneously at the surface, so that topologically protected states do not exist for this class. The interaction-stabilized surface phase is expected to exhibit ferromagnetic order, or to reside in an insulating plateau of the spin quantum Hall effect.

Figure 1

Phase portrait sketch for the surface physics of a 3D time-reversal invariant, spin SU(2) symmetric topological superconductor. The vertical axis is the interaction strength $U$ [Eq. (10)], while the horizontal axis measures nonmagnetic disorder. Although the noninteracting system has a disorder-stabilized phase with delocalized (“protected”) surface states (II), it is destroyed by arbitrarily weak interactions [Eq. (11)]. Instead, at zero temperature, we expect that the surface exhibits broken spin symmetry [$U>0\Rightarrow (\mathrm{III})$], or the spin quantum Hall effect [$U<0\Rightarrow (\mathrm{IV})$]. In either scenario, interactions break time-reversal symmetry spontaneously.