Hysteretic phenomena in a 2DEG in the quantum Hall effect regime, studied in a transport experiment

The nonequilibrium state of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime, manifested in the hysteresis of magnetoresistance of a 2DEG with a constriction, has been experimentally studied. The large amplitude of the hysteresis enabled us to make the consistent phenomenological description of the hysteresis. We performed minor loop measurements, recovered the anhysteretic curve, and studied the time dependence. We showed that the hysteresis has significant phenomenological similarities with that of magnetization of ferromagnets, showing multistability, jumps of relaxation, and having the anhysteretic curve. The difference is manifested itself in an unusual inverted (anti-coercive) behavior of the hysteresis. The time relaxation of the hysteresis has fast and slow regimes, similar to that of non-equilibrium magnetization of a 2DEG in QHE regime pointing to their common origin. We studied the dependence of the hysteresis loop area on the lithographic width of the constriction and found the threshold value of width $\sim$1.35 $\mu$m. This points to the edge nature of the nonequilibrium currents (NECs) and allows us to determine the width of the NECs area ($\sim$0.5 $\mu$m). We suggest the qualitative picture of the observed hysteresis, based on non-equilibrium redistribution of the electrons among the Landau level states and assuming huge imbalance between the population of bulk and edge electronic states.