Magnetoelectric effects in superconducting nanowires with Rashba spin-orbit coupling

Recent experiments in semiconductor nanowires with a spin-orbit coupling and proximity-induced superconductivity exhibit signatures of Majorana bound states predicted to exist in the topological phase. In this Letter we predict that these nanowire systems exhibit unconventional magnetoelectric effects showing a sharp crossover behavior at the topological phase transition. We find that magnetic fields with a component parallel to the spin-orbit field can give rise to currents in equilibrium. Surprisingly, also fields perpendicular to the spin-orbit field may induce currents and can be employed in adiabatic charge pumping. The perpendicular field magnetoelectric effect may be regarded as a manifestation of the anomalous Hall effect in one dimension. We discuss how the predicted phenomena could be observed in experiments and employed in probing the topological phase transition.