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 non-magnetic disorder. The conduit for the instability is disorder-induced wavefunction 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.Comment: v2: 5+3 pages, 1 figure; expanded introduction, added background on topological superconductors and multifractality, technical details relegated to sup info (published version

Relaxation and persistent oscillations of the order parameter in the non-stationary BCS theory

We determine the limiting dynamics of a fermionic condensate following a sudden perturbation for various initial conditions. We demonstrate that possible initial states of the condensate fall into two classes. In the first case, the order parameter asymptotes to a constant value. The approach to a constant is oscillatory with an inverse square root decay. This happens, e.g., when the strength of pairing is abruptly changed while the system is in the paired ground state and more generally for any nonequilibrium state that is in the same class as the ground state. In the second case, the order parameter exhibits persistent oscillations with several frequencies. This is realized for nonequilibrium states that belong to the same class as excited stationary states. Our classification of initial states extends the concept of excitation spectrum to nonequilibrium regime and allows one to predict the evolution without solving equations of motion.Comment: 8 pages, 4 figure