A. J. Matthews

A low-temperature high-sensitivity torsion balance magnetometer with in situ stator adjustment

Torsion balance magnetometry can be used as a versatile probe of two-dimensional electron systems. We have developed a highly sensitive magnetometer, utilizing capacitive proximity detection of the rotor position, for use at temperatures below 10 mK. The instrument incorporates two piezo-electric linear motors to enable the stator positions to be adjusted in situ at base temperature. The magnetometer responsivity is inversely proportional to the square of the rotor–stator separation and the novel linear motor technique, accompanied by effective vibration isolation and optimized capacitance bridge electronics, achieves a resolution 6.5×10−12 N m Hz−1/2. This resolution, together with the low temperatures attainable, allows for experiments that probe the family of quantum fluid states responsible for the fractional quantum Hall effect, even at filling factors greater than one.

BREAKDOWN OF THE QUANTUM HALL EFFECTS IN HOLE SYSTEMS AT HIGH INDUCED CURRENTS

The magnetisation of two dimensional hole systems in the quantum Hall regime has been studied using a highly-sensitive torsion balance magnetometer. In a time varying magnetic field eddy currents are induced which become large around integer and fractional filling factors where ρxx takes a very low value. The sweep rate and temperature dependence of these induced currents are in good agreement with the model of quantum Hall effect breakdown proposed recently by Matthews et al. This model also allows comparison between the energy gap at different filling factors and so provides a measurement of the fractional quantum Hall effect energy gap, Δ1/3, and the spin split energy gap, g*μBB.

Current breakdown of the integer and fractional quantum Hall effects detected by torque magnetometry

We have developed a novel technique that enables measurements of the breakdown of both the integer and fractional quantum Hall effects in a two-dimensional electron system without the need to contact the sample. The critical Hall electric fields that we measure are significantly higher than those reported by other workers, and support the quasi-elastic inter-Landau-level tunnelling model of breakdown. Comparison of the fractional quantum Hall effect results with those obtained on the integer quantum Hall effect allows the fractional quantum Hall effect energy gap to be determined and provides a test of the composite-fermion theory. The temperature dependence of the critical current gives an insight into the mechanism by which momentum may be conserved during the breakdown process.

Induced currents, frozen charges and the quantum Hall effect breakdown

Puzzling results obtained from torque magnetometry in the quantum Hall effect regime are presented, and a theory is proposed for their explanation. Magnetic moment saturation, which is usually attributed to the quantum Hall effect breakdown, is shown to be related to the charge redistribution across the sample.

High‐Current Breakdown of the Quantum Hall Effect

We have recently developed a model for the high‐current breakdown of the integer quantum Hall effect, as measured in contactless experiments using a highly‐sensitive torsion balance magnetometer. The model predicts that, for low‐mobility samples, the critical current for breakdown should decrease linearly with temperature. This prediction is verified experimentally with the addition of a low‐temperature (< ∼ 300 mK) saturation of the critical current. This saturation is consistent with quasi‐elastic inter‐Landau‐level scattering when the maximum electric field in the sample reaches a large enough value. Here we extend this model to ‘nearly’ integer filling factors to show how the model may account for the shape of the magnetisation signal.

Breakdown of the Quantum Hall Effects in Hole Systems at High Induced Currents

The magnetisation of two dimensional hole systems in the quantum Hall regime has been studied using a highly‐sensitive torsion balance magnetometer. In a time varying magnetic field eddy currents are induced which become large around integer and fractional filling factors where ρxx takes a very low value. The sweep rate and temperature dependence of these induced currents are shown to be in good agreement with the model of quantum Hall effect breakdown proposed recently by Matthews et al. This model also allows comparison between the energy gap at different filling factors and so provides a measurement of the fractional quantum Hall effect energy gap, Δ1/3.

HIGH-CURRENT BREAKDOWN OF THE QUANTUM HALL EFFECT

We have recently developed a model for the high-current breakdown of the integer quantum Hall effect, as measured in contactless experiments using a highly-sensitive torsion balance magnetometer. The model predicted that, for low-mobility samples, the critical current for breakdown should decrease linearly with temperature. This prediction was verified experimentally with the addition of a low-temperature (≲ 300 mK) saturation of the critical current. This saturation is consistent with quasi-elastic inter-Landau-level scattering when the maximum electric field in the sample reaches a large enough value. In this paper we extend this model to nearly integer filling factors to show how the model may account for the shape of the magnetisation signal.