We investigated experimentally non-equilibrium state of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime, studying the hysteresis of magnetoresistance of a 2DEG with a constriction. The large amplitude of the hysteresis e
nabled us to make the consistent phenomenological description of the hysteresis. We studied the dependence on the magnetic field sweep prehistory (minor loop measurements), recovered the anhysteretic curve, and studied the time dependence of the magnetoresistance. We showed that the hysteresis of magnetoresistance of a 2DEG in the QHE regime has significant phenomenological similarities with the hysteresis of magnetization of ferromagnetic materials, showing multistability, jumps of relaxation, and having the anhysteretic curve. Nevertheless, we revealed the crucial difference, manifested itself in an unusual inverted (anti-coercive) behavior of the magnetoresistance 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 beyond which the hysteresis is not observed. This points to the edge nature of the non-equilibrium 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.
Influence of forced mechanical vibrations of a suspended single-electron transistor on electron tunneling through the quantum dot limited by the Coulomb blockade is investigated. It is shown that mechanical oscillations of the quantum dot lead to the
Coulomb blockade breakdown, shown in sharp resonant peaks in the transistor conductance dependence on the excitation frequency at values corresponding to the mechanical oscillations eigen modes. Physical mechanism of the observed effect is considered. It is presumably connected with oscillations of the mutual electrical capacitances between the quantum dot and surrounding electrodes.
