# Topological spin-singlet superconductors with underlying sublattice structure

## TL;DR

This paper investigates how sublattice structures and spin-orbit interactions in certain superconductors can induce topological phases supporting Majorana quasiparticles, with exact phase diagrams and doping conditions identified.

## Contribution

It reveals the role of sublattice structure and Rashba spin-orbit coupling in topological transitions and Majorana quasiparticle emergence in spin-singlet superconductors.

## Key findings

- Topological phase diagrams are derived analytically and exactly.
- Majorana quasiparticles emerge near band edges at specific doping levels.
- Sublattice structure imposes a minimum doping requirement for topological phases.

## Abstract

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. The present paper shows that the spin-orbit may be responsible for topological transitions when 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 the characterization of 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 finally predicted to emerge when the Fermi level lies in the vicinity of the bottom (top) of the conduction (valence) band in semiconductors such as the dimerized Peierls chain and phosphorene. In a two-dimensional topological superconductor based on (stretched) graphene, which is semimetallic, Majorana quasiparticles cannot emerge at zero and low doping, that is, when the Fermi level is close to the Dirac points. Nevertheless, they are likely to appear in the vicinity of the van Hove singularities.