Anomalous Hall effect in superconductors with spin-orbit interaction

Abstract

We calculate the anomalous Hall conductance of superconductors with spin-orbit (SO) interaction and with either uniform or local magnetization. In the first case, we consider a uniform ferromagnetic ordering in a spin-triplet superconductor, whereas, in the second case, we consider a conventional s-wave spin-singlet superconductor with a magnetic impurity (or a diluted set of magnetic impurities). In the latter case, we show that the anomalous Hall conductance can be used to track the quantum-phase transition that occurs when the spin coupling between the impurity and the electronic spin density exceeds a certain critical value. In both cases, we find that, for large SO coupling, the superconductivity is destroyed and the Hall conductance oscillates strongly.