Superconductivity in monolayer and few-layer graphene. II. Topological edge states and Chern numbers

We study the emergence of electronic edge states in superconducting monolayer, bilayer, and trilayer graphene for both spin-singlet and spin-triplet superconducting order parameters. We focus mostly on the gapped chiral p + ip'- and d + id'-wave superconducting states that show a nonzero Chern number and a corresponding number of edge states. For the p + ip'-wave state, we observe a rich phase diagram for the Chern number when tuning the chemical potential and the superconducting order parameter amplitude, which depends strongly on the number of layers and their stacking and is also modified by trigonal warping. At small parameter values, compared to hopping energy, we observe a region whose Chern number is unique to rhombohedrally stacked graphene and is independent of the number of layers. Our results can be understood in relation not only to the superconducting order parameter winding as expected but also to the normal state band structure. This observation establishes the importance of the normal state characteristics for understanding the topology in superconducting graphene systems.