Steady states of a microwave-irradiated quantum-Hall gas

We consider effects of a long-wavelength disorder potential on the zero conductance state (ZCS) of the microwave-irradiated 2D electron gas. Assuming a uniform Hall conductivity, we construct a Lyapunov functional and derive stability conditions on the domain structure of the photogenerated fields. We solve the resulting equations for a general one-dimensional and certain two-dimensional disorder potentials, and find nonzero conductances, photovoltages, and circulating dissipative currents. In contrast, weak white-noise disorder does not destroy the ZCS, but induces mesoscopic current fluctuations.