Topological spin-singlet superconductors with underlying sublattice structure

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.

References in corpus (24)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus
• Merging of Dirac points in a two-dimensional crystal
• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• A new magnetic field dependence of Landau levels on a graphene like structure
• Topological spin-current in non-centrosymmetric superconductors
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Intercalant-independent transition temperature in superconducting black phosphorus
• Electron-doped phosphorene: A potential monolayer superconductor
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Giant spin orbit interaction due to rotating magnetic fields in graphene nanoribbons
• Helical States in Curved Bilayer Graphene
• Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability
• Masses and Majorana fermions in graphene

Cited by in corpus (8)

• Suppression of the overlap between Majorana fermions by orbital magnetic effects in semiconducting-superconducting nanowires
• On the bulk boundary correspondence and the existence of Majorana bound states on the edges of 2D topological superconductors
• Prevalence of trivial zero-energy sub-gap states in non-uniform helical spin chains on the surface of superconductors
• Majorana bound states in a superconducting Rashba nanowire in the presence of antiferromagnetic order
• Dimerization-induced topological superconductivity in a Rashba nanowire
• Strain manipulation of Majorana fermions in graphene armchair nanoribbons
• Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer
• Trivial and Non-trivial Superconductivity in dsDNA