Kubo formula for Floquet states and photoconductivity oscillations in a two-dimensional electron gas

The recent discovery of the microwave-induced vanishing resistance states in a two-dimensional electron system (2DES) is an unexpected and surprising phenomenon. In these experiments the magnetoresistance of a high mobility 2DES under the influence of microwave radiation of frequency ω at moderate values of the magnetic field exhibits strong oscillations with zero-resistance states (ZRS) governed by the ratio ω∕ωc, where ωc is the cyclotron frequency. In this work we present a model for the photoconductivity of a 2DES subjected to a magnetic field. The model includes the microwave and Landau contributions in a nonperturbative, exact way, while 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, multiphoton processes take place predicting negative-resistance states centered at ω∕ωc=1/2 and ω∕ωc=3/2.