Steady States of a Microwave Irradiated Quantum Hall Gas

TL;DR

This paper investigates how long-wavelength disorder affects the zero conductance state in microwave-irradiated 2D electron gases, revealing stability conditions, domain structures, and the persistence of ZCS under weak disorder.

Contribution

It introduces a Lyapunov functional approach to analyze the stability and domain structure of the ZCS considering disorder effects, providing new insights into the behavior of irradiated quantum Hall systems.

Findings

Non-zero conductances and photo-voltages in disordered systems

Disorder induces mesoscopic current fluctuations without destroying ZCS

Stability conditions for domain structures derived from Lyapunov functional

Abstract

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.