Detailed analysis of topological edge and corner states in valley-Hall-like photonic Kagome insulators

Valley-Hall-like second-order photonic topological insulators in Kagome-lattice photonic crystals with C_3v point-group symmetry are elaborately analyzed. Different from conventional valley-Hall photonic topological insulators, the calculation results show the topological invariant of the Kagome insulators is more suitable to be described by quantized electric polarization rather than valley Chern numbers. Topological edge states are thoroughly investigated at almost all the possible zigzag-type and armchair-type interfaces between photonic crystals with different topological phases, presenting important features of valley-Hall phase such as robust transport with little backscattering. Zero-dimensional corner states in most available oblique corners with different angles formed by zigzag-type or armchair-type edges are also detailly studied, showing the second-order topological insulator signature. This work provides a guidance for the practical realization of topological waveguides and high-Q cavities with Kagome photonic crystals.