On the bulk boundary correspondence and the existence of Majorana bound states on the edges of 2D topological superconductors

Abstract

The bulk-boundary correspondence establishes a connection between the bulk topological index of an insulator or superconductor, and the number of topologically protected edge bands or states. For topological superconductors in two dimensions the first Chern number is related to the number of protected bands within the bulk energy gap, and is therefore assumed to give the number of Majorana band states in the system. Here we show that this is not necessarily the case. As an example we consider a hexagonal-lattice topological superconductor based on a model of graphene with Rashba spin orbit coupling, proximity induced s-wave superconductivity, and a Zeeman magnetic field. We explore the full Chern number phase diagram of this model, extending what is already known about its parity. We then demonstrate that despite the high Chern numbers that can be seen in some phases these do not strictly always contain Majorana bound states.

arXiv comment8 pages, 7 figures

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Cited by in corpus (13)

• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure
• Pinning of Andreev bound states to zero energy in two-dimensional superconductor-semiconductor Rashba heterostructures
• Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
• Dimerization-induced topological superconductivity in a Rashba nanowire
• Topological superconductivity in Fibonacci quasicrystals
• Surface spectra of Weyl semimetals through self-adjoint extensions
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Topological Phases in Nodeless Tetragonal Superconductors
• Non-centrosymmetric superconductors on honeycomb lattice
• Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Quantum theory for edge current and noise in two-dimensional topological superconductors