  The physics of a planar chiral $p\pm i p$ superconductor is studied for
various vortex configurations. The occurrence of vortex quasi-particle bound
states is exposed together with their ensuing collective properties, such as
sub-gap bands induced by inter-vortex tunneling. A general method to
diagonalize the Hamiltonian of a superconductor in the presence of a vortex
lattice is developed, that employs only smooth gauge transformations. It
renders the Hamiltonian to be periodic (thus allowing the use of a Bloch
theorem) and enables the treatment of systems with vortices of finite radii.
The pertinent anomalous charge response $c_{xy}$ is calculated (using the
Streda formula), and reveals that it contains a quantized contribution. This is
attributed to the response to the nucleation of vortices, from which we deduce
the system's quantum phase.
