Fractional Topological Numbers at Photonic Edges and Corners

Topological phases of matter feature exotic edge states. However, the fractional topological numbers at edges, although predicted long ago by Jackiw and Rebbi, remain elusive in topological photonic systems. Here we report on the observation of fractional topological numbers at the topological edges and corners in one- and two-dimensional photonic crystals. The fractional topological numbers are determined via measurements of the photonic local density of states. In one-dimensional photonic crystals, we witness a rapid change of the fractional topological number at the edges rising from 0 to 1/2 when the photonic band gap experiences a topological transition, confirming the well-known prediction of Jackiw and Rebbi. In two-dimensional systems, we discover that the fractional topological number in the corner region varies from 0 to 1/2 and 1/4 in phases with different photonic band gaps. Our study paves the way toward topological manipulation of fractional quantum numbers in photonics.