Time-reversal-odd-bilinears: Key to the anomalous Hall effect in chiral superconductors

Motivated by the observation of the polar Kerr effect in e.g. UPt₃ and Sr₂RuO₄, we consider the origin of the anomalous Hall conductivity in a clean chiral superconductor. Using a generic model of a two-band system, we demonstrate that the existence of the anomalous Hall conductivity is guaranteed if one can construct a "time-reversal-odd-bilinear" from the pairing potential. In particular, this confirms the importance of interband pairing in generating the anomalous Hall conductivity. We illustrate this result with a toy model of a chiral p-wave superconductor.