Abstract

Significance Topological insulators are first discovered in electronic systems. A key factor is the Kramers doublet for the spin-1/2 electrons under fermionic time-reversal symmetry T f 2 = − 1 . Unlike electrons, photons are massless bosons with spin-1. Therefore, the Kramers degeneracy theorem cannot readily apply to photons under the bosonic time-reversal symmetry. So far, there has been no coherent physical explanation for the symmetry protection mechanism behind the photonic topological insulator. Here, we design a photonic topological insulator that violates the bosonic time-reversal symmetry but complies with a fermionic-like pseudo time-reversal symmetry. The analyses and results, through comprehensive investigations on the properties of edge states, validate that the topological edge states are, in fact, protected by the fermionic-like pseudo time-reversal symmetry T p ( T p 2 = − 1 ).