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

Nicholas Sedlmayr (1, 2) , Vardan Kaladzhyan (3, 4) , Clément Dutreix (5, 6) , Cristina Bena (3)

1 Department of Physics, Rzeszów University of Technology
2 Department of Physics and Astronomy [East Lansing]
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681
4 LPS - Laboratoire de Physique des Solides
5 LOMA - Laboratoire Ondes et Matière d'Aquitaine
6 ENS de Lyon - École normale supérieure de Lyon

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.

Keywords: Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

Domains: Physics [physics]; Condensed Matter [cond-mat]

Nicholas Sedlmayr, Vardan Kaladzhyan, Clément Dutreix, Cristina Bena. Bulk boundary correspondence and the existence of Majorana bound states on the edges of 2D topological superconductors. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2017, 96 (18), pp.184516 (1-7). ⟨10.1103/PhysRevB.96.184516⟩. ⟨cea-01626934⟩