Anomalous electromagnetic response of superconducting Rashba systems in trivial and topological phases

Two-dimensional electron systems with spin-orbit coupling in the proximity of a superconductor and a magnetic insulator have recently been considered as promising candidates to realize topological superconducting phases. Here we discuss electromagnetic response properties of these systems. Breaking of time-reversal symmetry leads to an anomalous Hall effect with a characteristic non-monotonic gate voltage dependence and a Hall conductivity that can change a sign as temperature is varied. The imaginary part of the Hall conductivity at finite frequency, which shows up for example in the Kerr rotation or photoabsorption, can distinguish different topological phases. In addition, we demonstrate the existence magnetoelectric effects associated with the Hall effect; in-plane electric fields induce a parallel magnetization and in-plane time-dependent magnetic fields induce parallel electric current.