Period and phase of microwave-induced resistance oscillations and zero-resistance states in two-dimensional electron systems

We present phenomenological analysis of the period and the phase of microwave-induced resistance oscillations (MIRO) and ``zero-resistance'' states (ZRS) recently observed in two-dimensonal electron systems. While MIRO are found to be well described by a ``1/4-cycle shift,'' we find that as MIRO evolve into ZRS with increasing magnetic field B, the phase becomes progressively smaller, decreasing roughly as $1/B.$ As a result, both maxima and minima in the ZRS regime form periodic in $1/B$ sequences, without a 1/4-cycle shift. A simple model based on oscillatory density of states is found to provide a unified description of the period/phase of MIRO/ZRS and leads to an interpretation of previously reported fine structures in terms of multiphoton processes.