Bulk–boundary correspondence
A change of bulk topology across an interface requires gap-crossing boundary states under suitable assumptions.
$$N_{\mathrm R}-N_{\mathrm L}=\Delta C$$
What this means
A change of bulk topology across an interface requires gap-crossing boundary states under suitable assumptions.
Deep dive: mathematical and physical mechanism
Across an interface between two 2D Chern insulators, the net number of chiral edge channels equals the difference in Chern numbers. Edge spectra interpolate between bulk bands, reflecting the obstruction to a globally trivial interpolation.
How it appears in quantum phenomena
Chiral electronic edge states and one-way photonic edge channels.
Assumptions, caveats and limitations
Boundary protection assumes the bulk gap and relevant symmetries or conservation laws persist.
Connect the ideas
For context, see the Topological Band Theory topic guide and the reading references.