Unraveling Multifractality and Mobility Edges in Quasiperiodic Aubry-Andr\'e-Harper Chains through High-Harmonic Generation

TL;DR

This paper demonstrates that high-harmonic spectroscopy can effectively probe the complex electronic properties of quasicrystals, revealing multifractal spectra and mobility edges in the Aubry-André-Harper model, advancing understanding of localization phenomena.

Contribution

It introduces high-harmonic spectroscopy as a novel tool to analyze multifractality and mobility edges in quasiperiodic systems, providing insights beyond traditional linear response methods.

Findings

High-harmonic spectra reveal multifractal characteristics of electronic states.

Identification of mobility edges in the AAH model through harmonic analysis.

Enhanced understanding of metal-insulator transitions in quasicrystals.

Abstract

Quasicrystals are fascinating and important because of their unconventional atomic arrangements, which challenge traditional notions of crystalline structures. Unlike regular crystals, they lack translational symmetry and generate unique mechanical, thermal, and electrical properties, holding promise for numerous applications. In order to probe the electronic properties of quasicrystals, tools beyond linear response transport measurements are needed, since all spectral regions can be affected by the non-periodic geometry. Here we show that high-harmonic spectroscopy offers an advanced avenue for this goal. Focusing on the quasiperiodic 1D Aubry-Andr\'e-Harper (AAH) model, we leverage high-harmonic spectroscopy to delve into their intricate characteristics: By carefully analyzing emitted harmonic intensities, we extract the multifractal spectrum -- 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. Merging high-harmonic spectroscopy with the AAH model provides a powerful framework for understanding the interplay between localization and extended states in quasicrystals for an extremely wide energy range not captured within linear response studies, thereby offering valuable insights for guiding future experimental investigations.