High-order harmonic generation from Su-Schrieffer-Heeger chains with edge states: Three-step processes and their interference

With high-order harmonic generation (HHG) from Su-Schrieffer-Heeger (SSH) chains considered as a paradigm example, the mechanism of HHG in the presence of edge states (ESs) is clarified from the perspective of the underlying three-step processes and their interference. This is done by analyzing the HHG contributions from the states of different types, with the energy of the ESs possibly being modified within the band gap. The ES energy shift introduces asymmetry in the transitions between the ESs and the two bands; in such a generic setting, it is found that the ES-induced HHG plateau can be either attributed to the contribution from the initially occupied ES alone, or alternatively understood as a consequence of interfering contributions from the ES and the valence band. On the basis of the three-step processes, it is shown that the ES-induced plateau can be described with semiclassical trajectories for the electron-hole dynamics in real space. This work also demonstrates the possibility of the ES-induced HHG being outweighed by the interband HHG for long chains, underlining the importance of the length scale of the system for observing the ES-induced HHG enhancement in practice.