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

Abstract

The topological properties in topological superconductors are usually characterized by the 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 focus on a checkerboard-lattice model combining the Chern insulator and chiral $p$-wave superconductivity. Multiple topologically superconducting phases with Chern numbers up to $\mathcal{N}=4$ are produced. We explicitly 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 the particle-hole symmetry. We further 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.

arXiv comment14 pages, 5 figures

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Cited by in corpus (7)

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• Surface spectra of Weyl semimetals through self-adjoint extensions
• Single-quasiparticle eigenstate thermalization
• Superconductor Vortex Spectrum Including Fermi Arc States in Time-Reversal Symmetric Weyl Semimetals
• Fermi arc criterion for surface Majorana modes in superconducting time-reversal symmetric Weyl semimetals