Topological effects in high-harmonic generation from finite and bulk solids

We investigate theoretically how the harmonic emission changes when the illuminated condensed-matter system undergoes a topological phase transition. We start with two-band bulk systems (examples being the Su-Schrieffer-Heeger chain, the Haldane or the Qi-Wu-Zhang models) and derive an explicit equation for the velocity of the laser-driven electrons, including all topological terms [1] that are often swept under the rug by approximations in treatments based on the semi-conductor Bloch equations. We find that the helicity of the harmonics changes through a topological phase transition; however, not all harmonics change their helicity in the same way. We continue with thin, hexagonal nanoribbons where four bands play a role and a flip of the helicity is observed at a certain harmonic order that depends on the Haldane-like next-nearest neighbor hopping [2]. Finally, we discuss the difference between finite and bulk systems. Despite the ubiquitous “bulk-boundary correspondence” the presence of topologically protected edge currents in finite systems affect the laser-driven electron dynamics and thus harmonic generation.

[1] Daniel Moos, Christoph Jürß, Dieter Bauer, Phys. Rev. A (accepted) [arXiv:2007.13434]
[2] Christoph Jürß, Dieter Bauer, Phys. Rev. A 102, 043105 (2020) [arXiv:2006.16037]