Hall conductivity as bulk signature of topological transitions in superconductors

Abstract

Topological superconductors (TSCs) may undergo transitions between phases with different topological numbers which are related to the presence of gapless (Majorana) edge states. In a TSC the charge Hall conductivity, σxy, is not quantized and evolves continuously between different topological phases. Here we show that in two-dimensional Z-TSC the derivatives of σ_xy display sharp features signaling the topological transitions. We consider in detail the case of a triplet superconductor with p-wave symmetry in the presence of Rashba spin-orbit coupling and externally applied Zeeman spin splitting. We generalize to the cases where the normal system is already topologically non-trivial.