High-harmonic generation to probe multifractality, mobility edges, and topological properties in one-dimensional quasiperiodic systems.

We show that high-harmonic spectroscopy offers an advanced avenue for probing electronic properties of quasicrystals beyond the linear response regime. Focusing on Aubry-André-Harper (AAH) chains, we extract the multifractal spectrum from the harmonic emission intensity—an essential indicator of the spatial distribution of electronic states in quasicrystals. Additionally, we address the detection of mobility edges, vital energy thresholds that demarcate localized and extended eigenstates within generalized AAH models. The precise identification of these mobility edges sheds light on the metal-insulator transition and the behavior of electronic states near these boundaries. Furthermore, we demonstrate that this technique can unravel some of the topological properties of the system. Merging high-harmonic spectroscopy with the AAH model provides a powerful framework for understanding the nature of states in quasicrystals for an extremely wide energy range not captured within linear response studies, thereby offering valuable insights for guiding future experimental investigations.