Domain patterns in the microwave-induced zero-resistance state

It has been proposed that the microwave-induced "zero-resistance" phenomenon, observed in a GaAs two-dimensional electron system at low temperatures in moderate magnetic fields, results from a state with multiple domains, in which a large local electric field E(r) is oriented in different directions. We explore here the questions of what may determine the domain arrangement in a given sample, what do the domains look like in representative cases, and what may be the consequences of domain-wall localization on the macroscopic dc conductance. We consider both effects of sample boundaries and effects of disorder, in a simple model, which has a constant Hall conductivity, and is characterized by a Lyapunov functional.