Finance

Combinatorics

Physics

Topology (electrical circuits)

Mathematics

Topological order

Boundary (topology)

Photonic crystal

Topological quantum number

Symmetry protected topological order

Topological insulator

Mathematical analysis

Physical chemistry

Topological entropy in physics

Order (exchange)

Economics

Chemistry

Polarization (electrochemistry)

Photonics

Condensed matter physics

Quantum mechanics

Quantum

Physical review. B./Physical review. B

Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have not yet been found in photonic crystals. Here, we propose a type of two-dimensional second-order photonic crystals with zero-dimensional corner states and one-dimensional boundary states for optical frequencies. All of these states are topologically nontrivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily fabricated structure of the photonic crystals, different topological phases can be realized straightforwardly. Our study can be generalized to higher dimensions and provides a platform for higher-order photonic topological insulators and semimetals.

Second-order photonic topological insulator with corner states