Majorana quasiparticles in spin-singlet superconductors with underlying sublattices

C. Dutreix

Published 2017-03-07Version 1

Majorana boundary quasiparticles may naturally emerge in a spin-singlet superconductor with Rashba spin-orbit interactions, when a Zeeman magnetic field breaks time-reversal symmetry. Their existence and robustness against adiabatic changes is deeply related, via a bulk-edge correspondence, to topological properties of the band structure. As it does in the quantum spin Hall effect, the spin-orbit ensures the existence of a gapped phase without inducing any topological transitions. The present work nonetheless shows that this spin-flip process may additionally be responsible for topological transitions, provided the superconducting system has an underlying sublattice structure, as it appears in a dimerized Peierls chain, graphene, and phosphorene. These systems, which belong to the Bogoliubov-de Gennes class D, are found to have an extra symmetry that plays the role of the parity. It enables us to characterize the topology of the particle-hole symmetric band structure in terms of band inversions. The topological phase diagrams this leads to are then obtained analytically and exactly. They reveal that, because of the underlying sublattice structure, the existence of topological superconducting phases requires a minimum doping fixed by the strength of the Rashba spin-orbit. Majorana boundary quasiparticles are then predicted to emerge when the Fermi level lies in the vicinity of the bottom (top) of the conduction (valence) band in semiconductors like the dimerized Peierls chain and phosphorene. In the case of (stretched) graphene, which is semimetallic, it turns out that the Majorana quasiparticles cannot emerge at zero and low doping, that is when the Fermi energy is close to the Dirac points. It is nevertheless possible to obtain such boundary quasiparticles when the Fermi level lies in the vicinity of the van Hove singularities.