Higher-order hybrid adiabatic topological states in photonic crystals

Topological photonics has established itself as a formidable platform with the potential to emulate relativistic phenomena predicted by condensed matter field theory. In this letter, we reveal an exotic form of higher-order topological states in an insulator/semimetal hybrid system; we have called them adiabatic orbital corner states. This class of topological states arises by introducing an adiabatic variation of the mass term in the Dirac Hamiltonian, which is directly related to the perturbation in the structural parameters of a kagome photonic lattice. The adiabatic variation presented here involves a smooth and natural spatial transition from an external trivial normal insulator phase, through the nontrivial semimetal phase to the nontrivial higher-order topological insulator phase. We have found that through this distribution of topological phases, the corner states in the higher-order insulator phases hybridize with the Dirac states existing in the semimetal phase, forming hybridized corner states analogous to various atomic orbitals. Due to the occurrence of different phases in the finite model analyzed, we have resorted to the spectral localizer theory, which allowed us to identify the topological nature of the hybrid states. These results could lead the way in investigating pseudorelativistic orbitals in topological photonic systems and future explorations of exotic collective modes arising from hybrid topological lattices.