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 photo-generated fields. We solve the resulting equations for a general one-dimensional and certain two-dimensional disorder potentials, and find non-zero conductances, photo-voltages, and circulating dissipative currents. In contrast, weak white noise disorder does not destroy the ZCS, but induces mesoscopic current fluctuations. 
Assa Auerbach (Technion), Ilya Finkler and Bertrand I. Halperin   (Harvard), Amir Yacoby (Weizmann)