  Superconductivity in graphene-based systems has recently attracted much
attention, as either intrinsic behavior or induced by proximity to a
superconductor may lead to interesting topological phases and symmetries of the
pairing function. A prominent system considers the pairing to have chiral
symmetry. The question arises as to the effect of possible spin-orbit coupling
on the resulting superconducting quasiparticle spectrum. Utilizing a
Bogolyubov-de Gennes (BdG) Hamiltonian, we explore the interplay of different
interaction terms in the system, and their role in generating complex Berry
curvatures in the quasiparticle spectrum, as well as non-trivial topological
behavior. We demonstrate that the topology of the BdG Hamiltonian in these
systems may result in the appearance of edge states along the zigzag edges of
nanoribbons in the appropriate regime.
