Exotic topological phenomena in chiral superconducting states on doped quantum spin Hall insulators with honeycomb lattices

We conduct a theoretical investigation of the topological phenomena associated with chiral superconducting pairing states induced in a doped Kane-Mele model on a honeycomb lattice. Through numerical analysis, we obtain exotic phase diagrams for both the d+id and p+ip superconducting states. In the case of the d+id pairing state, high Chern number states with C=4 emerge. The Chern number decreases as the spin-orbit coupling is introduced. For the p+ip pairing state, additional phase transition lines are present in the overdoped region near the Van Hove singularity point, leading to the emergence of high Chern number phases with C=6. We further verify these high Chern number phases through the bulk-edge correspondence. To understand the origin of the exotic topological phase diagrams in the chiral superconducting state, we examine the electronic structure at the phase transition lines. This investigation provides insight into the complex interplay between chiral superconductivity and topological properties, potentially paving the way for the discovery of new materials with unique topological properties.