Temperature-induced optical enhancement near a localization transition

Quasiperiodic systems are an intermediate class of systems between periodic crystals and disordered systems, famously exhibiting metal-insulator transitions (MITs) even in one dimension. While their transport properties have been studied extensively, a systematic analysis of the finite-frequency optical conductivity near the critical point has been lacking. In this work, we carry out a detailed study of the optical conductivity in the paradigmatic Aubry-Andr\'e model. We find that the zero-temperature low-frequency optical signal is strongly restructured by the quasiperiodic potential, exhibiting an optical gap that closes discontinuously as the system approaches the MIT. Most strikingly, we uncover a mechanism for a strong enhancement of the low-frequency finite temperature optical conductivity at certain resonant frequencies. This enhancement stems from the thermal activation of Pauli-blocked transitions between strongly resonant van Hove singularities. This mechanism provides new insight into finite-frequency transport in quasiperiodic systems and a new pathway for manipulating optical properties near a localization transition. Furthermore, our findings establish the optical response as a powerful, experimentally accessible tool for probing non-trivial quasiperiodicity effects.