Fractional minima in the conductivity of the quantum-Hall-system under microwaves

Abstract

We analyse theoretically the conductivity of a quantum Hall system exposed to microwave radiation. We find that whenever microwave frequency and cyclotron frequency are commensurate, there is a {\em resonance} in the longitudinal conductivity. This resonance has the form of the derivative of a Lorentz function; precisely at the center of the resonance, the microwave induced conductivity vanishes. Between the resonances there are maxima and minima, the depths and precise positions of which depend on the microwave amplitude and the scattering rate of the impurities. We demonstrate the existence of these resonances by a microscopic, analytical calculation of the conductivity in lowest order in the microwave intensity and show here that the conductivity is independent of the microwave polarization, linear or circular. We then discuss the general case and predict minima in the longitudinal conductivity corresponding to fractional values of the microwave frequency divided by the cyclotron frequency.