Floquet mobility edges and transport in a periodically driven generalized Aubry-Andr\'e model

TL;DR

This paper explores how a periodic electric field influences the spectral and transport properties of the generalized Aubry-Andr model, revealing controllable Floquet mobility edges and diverse transport regimes.

Contribution

It uncovers the emergence of two distinct Floquet mobility edges in the driven GPD model and demonstrates their control via drive parameters, with detailed spectral and transport analysis.

Findings

Discovery of two Floquet mobility edges: DL and ML in different regimes.

Control of mobility edges through electric field amplitude and frequency.

Observation of superdiffusive to ballistic transport in the bounded regime.

Abstract

We investigate the effect of a periodic electric field drive on the generalized Aubry-Andr\'e model, also known as the Ganeshan-Pixley-Das Sarma (GPD) model, which is well known as a host of mobility edges. Our study of the Floquet spectrum of the driven GPD model uncovers the emergence of two distinct Floquet mobility edges, a delocalized--localized (DL) edge in the bounded regime, and a multifractal--localized (ML) edge in the unbounded regime. Using analytical results derived from Avila's global theory applied to the high frequency effective Hamiltonian, together with numerical diagnostics such as the fractal dimension and inverse participation ratio, we demonstrate that these mobility edges can be effectively controlled by the amplitude and frequency of the electric field drive. We also identify drive-induced localization at specific values of the driving parameters, corresponding to dynamical localization points in the absence of quasiperiodic potential. Furthermore, the dynamical study of the periodically driven GPD model demonstrates superdiffusive to almost ballistic transport in the bounded regime corresponding to the DL edges, whereas subdiffusive transport is observed in the unbounded regime associated with the ML edges. We also analyze deviations from the high-frequency effective description by explicitly examining the low-frequency driving regime, where significant and counterintuitive deviations in both spectral properties and transport behavior are observed. Our study highlights the interplay of a quasiperiodic potential and a periodically varying electric field drive as a powerful mechanism to engineer mobility edges and control transport in systems with rich spectral features.