Characterizations of topological superconductors: Chern numbers, edge states and Majorana zero modes

Abstract

The topological properties in topological superconductors are usually characterized by bulk Chern numbers, edge-state spectra, and Majorana zero modes. Whether they are equivalent or inequivalent is not well understood. Here, we investigate this issue with a focus on a checkerboard-lattice model combining the Chern insulator and chiral p-wave superconductivity. Multiple topologically superconducting phases with Chern numbers up to N = 4 are produced.Weexplicitly demonstrate the mismatch between the Chern numbers, edge states, and Majorana zero modes in this two-dimensional topological-superconductor model. The intrinsic reason is that some edge states in the superconducting phases inherited from the Chern-insulator phase are not protected by particle-hole symmetry.Wefurther check the mismatches in vortex states. Our results therefore clarify these different but complementary topological features and suggest that further considerations are required to characterize various topological superconductors.