Origin of the anomalous Hall effect in two-band chiral superconductors

We consider the origin of anomalous Hall effect in a general model clean two-band chiral superconductor. Within Kubo formalism we derive an analytic expression for high-frequency ac conductivity valid close to critical temperature. This involves two distinct gauge-invariant time-reversal-odd bilinear (TROB) functions involving pairing potential and its Hermitian conjugate. argue that existence at least one these TROBs generically implies nonzero conductivity. The allow us clarify roles intra- interband pairing, provide straightforward criterion superconducting state exhibit effect. briefly exemplify our results with calculations $p$-wave strontium ruthenate $d$-wave on honeycomb lattice.