The physics of a planar chiral $p\pm ip$ superconductor is studied for various vortex configurations. The occurrence of vortex quasiparticle bound states is exposed together with their ensuing collective properties, such as subgap bands induced by intervortex 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 the 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.

• Received 17 April 2018

DOI:https://doi.org/10.1103/PhysRevB.98.104511