Vectorial Bulk-Boundary Correspondence for 3D Photonic Chern Insulators

TL;DR

This paper develops a vectorial bulk-boundary correspondence for 3D photonic Chern insulators, enabling accurate prediction of surface mode propagation based on Chern vector discontinuities.

Contribution

It introduces a 3D vector bulk-boundary correspondence linking Chern vector changes to surface mode behavior in photonic CIs, extending 2D concepts.

Findings

Derived a link between Chern vector discontinuity and surface loop winding.

Formulated a 3D vBBC to predict surface mode number and direction.

Demonstrated correct prediction of topological surface modes in 3D CIs.

Abstract

In 2D Chern insulators (2D CI), the topology of the bulk states is captured by a topological invariant, the Chern number. The scalar bulk-boundary correspondence (sBBC) relates the change in Chern number across an interface with the number of 1D chiral edge modes at the interface. However, 3D Chern insulators (3D CI) can be characterized by a Chern vector C = (Cx, Cy, Cz) and a more general vector bulk-boundary correspondence (vBBC) is needed to correctly predict the propagation of the surface modes. In this work the possible interfaces between 3D photonic CIs are explored, focusing on possible changes in Chern vector orientation. To formulate a 3D vBBC, a link is derived between the Chern vector discontinuity across an interface and the winding of the surface equifrequency loops on the boundary. Lastly, it is demonstrated how to correctly predict the number and the propagation direction of topological photonic surface modes in 3D CIs.