| Summary: | Torque magnetometry techniques have been employed to study the quantum Hall effect in several AIGaAs/GaAs-heterostructure two-dimensional electron gas samples at filling factors between 1 and 4. Two magnetometers were employed to acquire measurements for three samples an existing instrument was used to acquire data for two samples and a novel instrument has been developed in which the output signal sensitivity is increased by 700% during experiments on a third sample. The third sample was also illuminated in situ. The samples exhibit breakdown-like behaviour in two forms. The first is the saturation of the magnetic moment peak size with respect to increasing sweep rate. A simple charge-up model, which treats the charge density of the sample in terms of a capacitance around the edge of the sample, was used to analyse experimental data. Temperature dependence of the longitudinal conductivity is analysed with respect to a published model of Polyakov and Shklovskii. The charge-up time constant, rc (10--105) seconds, decreased with increasing temperature and was found to follow a straight line when plotted on a logarithmic scale against temperature. Characteristic temperatures extracted from the data lie in the range T0 * (0.2--2.0) Kelvin. Decay time measurements were performed to acquire the decay time constant rd. Two regimes of decay were observed, the first exhibiting a time constant of the order of several seconds followed by a second phase with a much larger time constant many minutes or hours. The second form of breakdown was demonstrated as a type of noisy breakdown clearly observed at filling factor 2 in two samples. This noise, of the form of sudden jumps followed by more gradual growth, was interpreted using an edge charge-up model and is thought to be consistent with the sand-pile model of the theory of self-organised criticality. As a result the frequency of occurrence of noisy jumps as a function of their particular size is seen to follow a power law. Time constants of individual noise jumps were found to lie mainly in the range (1--10) seconds.
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