Towards a synchronization theory of microwave-induced zero-resistance states

Abstract

We develop a synchronization theory for the dynamics of two-dimensional electrons under a perpendicular magnetic field and microwave irradiation showing that dissipative effects can lead to the synchronization of the cyclotron phase with the driving microwave phase at certain resonant ratios between microwave and cyclotron frequencies. We demonstrate two important consequences of this effect: the stabilization of skipping orbits along the sample edges and the trapping of the electrons on localized short-ranged impurities. We then discuss how these effects influence the transport properties of ultrahigh-mobility two-dimensional electron gas and propose mechanisms by which they lead to microwave-induced zero-resistance states. Our theoretical analysis shows that the classical electron dynamics along the edge and around circular disk impurities is well described by the Chirikov standard map providing a unified formalism for those two rather different cases. We argue that this work will provide the foundations for a full quantum synchronization theory of zero-resistance states for which a fully microscopic detailed theory still should be developed.