Resonant metallic states in driven quasiperiodic lattices

TL;DR

This paper demonstrates that weak periodic driving in a quasiperiodic lattice can induce resonant coupling of localized states, creating extended metallic states that enable ballistic transport, with effects controllable by tuning frequencies.

Contribution

It introduces a mechanism for resonant delocalization in driven quasiperiodic systems, extending the Aubry-Andre model into a dynamic regime with controllable metallic states.

Findings

Resonant driving creates extended metallic eigenstates from localized ones.

Size of metallic states grows linearly with system size.

Wave packets exhibit ballistic spreading when overlapping with resonant states.

Abstract

We consider a quasiperiodic Aubry-Andre (AA) model and add a weak time-periodic and spatially quasiperiodic perturbation. The undriven AA model is chosen to be well in the insulating regime. The spatial quasiperiodic perturbation extends the model into two dimensions in reciprocal space. For a spatial resonance which reduces the reciprocal space dynamics to an effective one-dimensional two-leg ladder case, the ac perturbation resonantly couples certain groups of localized eigenstates of the undriven AA model and turns them into extended metallic ones. Slight detuning of the spatial and temporal frequencies off resonance returns these states into localized ones. We analyze the details of the resonant metallic eigenstates using Floquet representations. In particular, we find that their size grows linearly with the system size. Initial wave packets overlap with resonant metallic eigenstates and lead to ballistic spreading.