Anomalous Hall effect in chiral superconductors from impurity superlattices

Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one-loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this work, we consider the effect of impurities embedded in chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effective theory whose anomalous Hall effect can be studied with ease. We demonstrate that the occurrence of the Hall effect depends on the superlattice geometry and the parity of the chiral pairing. In particular, due to the composite particle-hole character of the subgap states, the Hall conductance arises at the one-loop level of the current-current correlator in our effective model. Generalized to random impurities, our theory sheds new light on the physics of impurity-induced anomalous Hall conductivity in chiral superconductors.