Topological edge-state contributions to high-order harmonic generation in finite flakes

Edge states play a major role in the electron dynamics of topological insulators as they are the only conducting part in such materials. In this work we consider the Haldane model for a two-dimensional topological insulator, subjected to an intense laser field. We compare the numerically simulated high-harmonic generation (HHG) in the bulk of the Haldane model to HHG in corresponding finite flakes with edge states present, and explain the differences. In particular, peaks for energies below the bulk band gap appear in the spectra for the finite flakes. The positions of these peaks show a strong dependence on the size of the flakes, which can be explained using the dispersion relation for the edge states.