Nonstationary phenomena in Si MOSFETs in the quantum hall effects regime

We report the observation of nonstationary hysteresis phenomena in charging of Si MOSFET at a quantizing magnetic field. In these experiments (Pudalovet al 1984; Pudalov and Semenchinsky 1985) the charging currentJ g of the capacitance gate-2D-layer was measured while sweeping of the magnetic fieldH or a gate voltageV g at a constant rate. The numerical integration of the measured valuesJ g with respect to time gave the dependences of change inQ s vsV g or vsH. At low temperatureTQ s(V g) near those integer values of Landau level fillingν=n s/n H=2, 4, 6, 8, 12, which correspond to the most deep minima inρ xx and flat plateaux inρ xy. Heren s is the 2D electron density,n H being Landau level degeneracy number,ρ xx andρ xy —the resistivity tensor components. The inherent feature of the curveQ s(V g) is the hysteresis: at increasingV g the chargeQ s is less than the equilibrium value, while at decreasingV g the charge exceeds the equilibrium one. The maximum difference of charges at an increase and decrease ofV g grows-rapidly at loweringT and atT=0.42 K amounts to ∼10% of the full charge confined by one Landau level (n H.e.S). It is worth to note that such behaviour ofQ s(V g) does not influence the values ofρ xy (with accuracy of ∼ 10−5) and the shape ofρ xy plateaux andρ xx-minima. Measurements at various sweep rates dV g/dt demonstrated that if the sweep rate is lower, the hysteresis region is narrower and the deviation of chargesQ s from its equilibrium value is smaller. By extrapolating the dependence of hysteresis loop width on dV g/dt, the ultimate sweep rate may be estimated, for which a hysteresis will completely disappear. Thus, for instance, atT=0.42 K andν=4 it will occur when the time interval of one Landau level fillingτ H will be equal to 100 years. A similar hysteresis in 2D-layer charge occurs in varying magnetic field also, when the gate voltage is disconnected with the battery and hence the charge in MOSFET is maintained constant. This hysteresis loop rapidly vanishes at temperatures >1 K. The long relaxation time of a nonequilibrium charge in 2D-layer can be connected phenomenologically with small drift velocities of electrons along the potential gradient due to a small value of conductivityσ xx. This relaxation time may be estimated asτ∼C/σ xx whereC is the electrical capacitance of MOSFET area with a nonequilibrium charge. The value ofτ∼109 s givesσ xx a −18 Ohm−1/□, i.e.ρ xx−11 Ohm/□. Simultaneously with nonequilibrium charge relaxation in 2D-layer there arise circular Hall currents decaying with the same rate. In conclusion, we observed and investigated nonequilibrium charging of 2D-layer in quantum Hall effect regime. To explain the phenomenon we supposed that circular Hall currents is comparable to the eddy currents excited in a superconducting ring.