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The physics of a planar chiral $p\pm i p$ superconductor is studied forvarious vortex configurations. The occurrence of vortex quasi-particle boundstates is exposed together with their ensuing collective properties, such assub-gap bands induced by inter-vortex tunneling. A general method todiagonalize the Hamiltonian of a superconductor in the presence of a vortexlattice is developed, that employs only smooth gauge transformations. Itrenders the Hamiltonian to be periodic (thus allowing the use of a Blochtheorem) and enables the treatment of systems with vortices of finite radii.The pertinent anomalous charge response $c_{xy}$ is calculated (using theStreda formula), and reveals that it contains a quantized contribution. This isattributed to the response to the nucleation of vortices, from which we deducethe system's quantum phase.

How vortex bound states affect the Hall conductivity of a chiral $p\pm i p$ superconductor