Exotic Topological Phenomena in Chiral Superconducting States on Doped Quantum Spin Hall Insulators with Honeycomb Lattices

We have conducted 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 have obtained exotic phase diagrams for both the $d+id$ and $p+ip$ superconducting states. In the case of the $d+id$ pairing state, higher Chern number states with $\left| C \right| = \pm 4$ 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 higher Chern number phases with $\left| C \right| = \pm 6$. These higher Chern number phases are further verified through the bulk-edge correspondence. To understand the origin of the exotic topological phase diagrams in the chiral superconducting state, we have examined 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.