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Majorana quasiparticles localized in vortex cores of a chiral p-wavesuperconductor hybridize with one another to form bands in a vortex lattice. Webegin by solving a fully microscopic theory describing all quasiparticle bandsin a chiral p-wave superconductor in magnetic field, then use this solution tobuild localized Wannier wavefunctions corresponding to Majorana quasiparticles.A low-energy tight-binding theory describing the intervortex hopping of theseis then derived, and its topological properties---which depend crucially on thesigns of the imaginary intervortex hopping parameters---are studied. We showthat the energy gap between the Majorana bands may be either topologicallytrivial or nontrivial, depending on whether the Chern number contributions fromthe Majorana bands and those from the background superconducting condensate addconstructively or destructively. This topology directly affects thetemperature-dependent thermal Hall conductivity, which we also calculate.

Majorana bands, Berry curvature, and thermal Hall conductivity in the vortex state of a chiral p-wave superconductor