Mott, Floquet, and the response of periodically driven Anderson insulators

TL;DR

This paper explores the complex response of periodically driven Anderson insulators across different regimes, extending Mott's linear response theory to long times and strong fields, and mapping out a detailed phase diagram.

Contribution

It introduces a comprehensive phase diagram for driven Anderson insulators, identifying four distinct response regimes beyond traditional linear response theory.

Findings

Identification of four regimes: linear, non-linear, near-adiabatic, and dissipative.

Extension of Mott's theory to long times and strong fields.

Characterization of the response behavior across different regimes.

Abstract

We consider periodically driven Anderson insulators. The short time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times---which is the physics of Floquet late time states---and strong electric fields. This results in a `phase diagram' in the frequency-field strength plane, in which we identify four distinct regimes. These are: a linear response regime dominated by pre-existing Mott resonances, which exists provided Floquet saturation is not reached within a period; a non-linear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to pre-existing resonances; and finally an enhanced dissipative regime.