Vectorial Bulk-Boundary Correspondence for 3D Photonic Chern Insulators

摘要

In 2D Chern insulators, the topology of the bulk states is captured by a topologicalinvariant, the Chern number. The scalar bulk-boundary correspondence(sBBC) relates the change in Chern number across an interface with thenumber of 1D chiral edge modes at the interface. However, 3D Chern insulators(3D CIs) can be characterized by a Chern vector C = (C_x ,C_y ,C_z ) anda more general vector bulk-boundary correspondence (vBBC) is needed tocorrectly predict the propagation of the surface modes. In this work the possibleinterfaces between 3D photonic Cis are explored, focusing on possiblechanges in Chern vector orientation. To formulate a 3D Vbbc, a link is derivedbetween the Chern vector discontinuity across an interface and the windingof the surface equifrequency loops on the boundary. Last, it is demonstratedhow to correctly predict the number and the propagation direction of topologicalphotonic surface modes in 3D Cis.