Kubo formula for Floquet states and photoconductivity oscillations in a 2D electron gas

TL;DR

This paper develops a theoretical model using Floquet states and a Kubo-like formula to explain microwave-induced resistance oscillations and zero-resistance states in high-mobility 2D electron gases under magnetic fields.

Contribution

It introduces a non-perturbative Floquet-based formalism for photoconductivity, incorporating impurity effects and predicting new negative-resistance states at high microwave power.

Findings

Reproduces the observed oscillation period and phase in magnetoresistance.

Shows negative dissipation occurs only in very high mobility samples.

Predicts multi-photon processes leading to new resistance states at specific ratios.

Abstract

The recent discovery of the microwave induced vanishing resistance states in a two dimensional electron system (2DES) is an unexpected and surprising phenomena. In these experiments the magnetoresistance of a high mobility 2DES under the influence of microwave radiation of frequency $\omega$ at moderate values of the magnetic field, exhibits strong oscillations with zero-resistance states (ZRS) governed by the ratio $\omega /\omega_c$, where $\omega_c$ is the cyclotron frequency. In this work we present a model for the photoconductivity of a two dimensional electron system (2DES) subjected to a magnetic field. The model includes the microwave and Landau contributions in a non-perturbative exact way, impurity scattering effects are treated perturbatively. In our model, the Landau-Floquet states act coherently with respect to the oscillating field of the impurities, that in turn induces transitions between these levels. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. We study the effects of both short-range and long-range disorder on the photoconductivity. Our calculation yields a magnetoresistance oscillatory behavior with the correct period and phase. It is found that, in agreement with experiment, negative dissipation can only be induced in very high mobility samples. We analyze the dependence of the results on the microwave power and polarization. For high-intensity radiation multi-photon processes take place predicting new negative-resistance states centered at $ \omega / \omega_c=1/2$, and $ \omega / \omega_c= 3/2$.