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

Abstract

7 pages, 7 figuresInternational audienceThe 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

Non‐Centrosymmetric Superconductors on Honeycomb Lattice

“…In this work, we aim for the edge states of topologically non‐trivial superconducting states in graphene‐based system in the form of zigzag nanoribbon (ZNR). Note that, zigzag and armchair nanoribbons both can host topologically non‐trivial superconducting states on hexagonal lattice . We consider ZNR here for simplicity.…”

Zero-energy Andreev bound states in iron-based superconductor Fe(Te,Se)

“…Since the first model of MBSs in one-dimensional (1D) p-wave superconductor (SC) was proposed by Kitaev [13,14] many scenarios for generating MBSs have been put forward, e.g. in semiconductor nanowires with strong spin-orbit coupling and Zeeman field [15][16][17][18][19][20][21][22][23], in carbon-based materials [24][25][26][27][28][29][30], in magnetic atomic chains [31][32][33][34][35][36][37][38][39][40], in topological insulator (TI) nanowires [41][42][43], in two-dimensional (2D) ferromagnetic insulator-semiconductor heterostructures [44][45][46][47][48][49][50][51], and in three-dimensional (3D) strong TIs coupled to conventional s-wave SCs [52][53][54][55][56][57]. Some of the above models have been reported to be realized experimentally [20-23, 30, 38-40, 58-73], enri...…”

Topological phases in nodeless tetragonal superconductors

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