Abstract
Graphene may exhibit different topological phases as a result of proximity to different substrates. We study the effect of superconductivity in such systems using the effective Bogolyubov-de Gennes Hamiltonian with different superconducting pairing order parameters. We analyze the topological phase transition and symmetry class of the system in different parameter regimes. A particularly interesting situation occurs when nearest-neighbor spin-singlet superconducting pairing is present in phases of proximitized graphene that exhibit either inverted band or quantum spin Hall behavior. Both superconducting phases show similar characteristics in the low-energy range, including the appearance of robust edge states, and are neighboring phases across a transition that closes the quasiparticle gap as the chemical potential changes. Detailed construction and analysis of the existence and nature of edge states are presented in different system regimes.