Superconducting pairing symmetry and spin-orbit coupling in proximitized graphene

Graphene has been shown to exhibit unusual topological phases upon proximity to different dichalcogenide substrates [1]. However, the effect of these perturbations in the presence of superconducting correlations has not been explored. We study the effect of different superconducting symmetry pairings over a range of chemical potential. We analyze the symmetry and identify the topological characteristics of the resulting quasiparticle spectrum at the mean field level.
Interestingly, the system with nearest neighbor spin-singlet superconductivity order parameter may exhibit inverted bands in the quasiparticle band structure, reminiscent of the electronic bands [1]. As the system parameters change, the corresponding edge states in such phase appear after a transition to a regime that closes the bulk bandgap. As we will show, however, both gapped phases belong to a topologically trivial regime, as the results of their invariant number Z2 indicate.
Our results also show that the phases in a time-reversal-invariant 2D-superconductor are not dependent on the magnitude of the singlet and triplet order parameter, and/or the chemical potential, as the topological invariant number remains unchanged.
[1] A. M. Alsharari et al., Phys. Rev. B 98, 195129 (2018).