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We have conducted a theoretical investigation of the topological phenomenaassociated with chiral superconducting pairing states induced in a dopedKane-Mele model on a honeycomb lattice. Through numerical analysis, we haveobtained exotic phase diagrams for both the $d+id$ and $p+ip$ superconductingstates. In the case of the $d+id$ pairing state, higher Chern number stateswith $\left| C \right| = \pm 4$ emerge. The Chern number decreases as thespin-orbit coupling is introduced. For the $p+ip$ pairing state, additionalphase transition lines are present in the overdoped region near the Van Hovesingularity point, leading to the emergence of higher Chern number phases with$\left| C \right| = \pm 6$. These higher Chern number phases are furtherverified through the bulk-edge correspondence. To understand the origin of theexotic topological phase diagrams in the chiral superconducting state, we haveexamined the electronic structure at the phase transition lines. Thisinvestigation provides insight into the complex interplay between chiralsuperconductivity and topological properties, potentially paving the way forthe discovery of new materials with unique topological properties.

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