Raghu and Haldane's photonic bulk-edge correspondence

Let a two-dimensional photonic crystal have a boundary and bulk band gaps. In each bulk band gap, consider the left- and right-moving boundary modes, and let the bulk Chern number be the Chern number associated with the positive-frequency bands below that gap. Raghu and Haldane's photonic bulk-edge correspondence. The difference between the number of left- and right-moving boundary modes in a bulk band gap is a topologically protected quantity equal to the bulk Chern number associated with the positive-frequency bands below the gap. This conjecture connects bulk topological invariants of photonic crystals with robust, unidirectional edge transport; the supplied source context attributes it to Raghu and Haldane and describes its experimental confirmation, but does not provide a precise resolution status for the formulation given here.