De Haas-van Alphen ͑dHvA͒ oscillations are observed for Landau levels ͑LLs͒ with filling factors between 4 and 52, at temperatures in the range 50 mK to 1 K, in experiments on high-mobility GaAs/͑Al, Ga͒As heterojunctions. The oscillations become sawtooth-shaped at low filling factors, and theoretical fits to the data, assuming the two-dimensional electron gas to be a non-interacting Fermi system, show the shape of LLs to be close to a ␦ function. The small residual width ͑ϳ0.4 meV or less͒ fits equally well to either a Gaussian or a Lorentzian density-of-states model. In almost all cases, a constant background density of states has to be included to obtain a satisfactory fit. Weak odd-filling-factor dHvA peaks are detected at high fields, from which a g-factor enhancement of 15 can be inferred. Comparison of the scattering time derived from the fits before and after illumination, with the momentum relaxation time derived from transport, reveals a counterintuitive behavior in the bulk-modulation-doped sample.

We report experimental demonstration of the feasibility of reaching temperatures below 1 mK using cryogen-free technology. Our prototype system comprises an adiabatic nuclear demagnetization stage, based on hyperfineenhanced nuclear magnetic cooling, integrated with a commercial cryogenfree dilution refrigerator and 8 T superconducting magnet. Thermometry was provided by a current-sensing noise thermometer. The minimum temperature achieved at the experimental platform was 600 µK. The platform remained below 1 mK for over 24 h, indicating a total residual heat-leak into the experimental stage of 5 nW. We discuss straightforward improvements to the design of the current prototype that are expected to lead to enhanced performance. This opens the way to widening the accessibility of temperatures in the microkelvin regime, of potential importance in the application of strongly correlated electron states in nanodevices to quantum computing.

We describe the design and performance of a series of fast, precise current sensing noise thermometers. The thermometers have been fabricated with a range of resistances from 1.290 Ω down to 0.2 mΩ. This results in either a thermometer that has been optimised for speed, taking advantage of the improvements in superconducting quantum interference device (SQUID) noise and bandwidth, or a thermometer optimised for ultra-low temperature measurement, minimising the system noise temperature. With a single temperature calibration point, we show that noise thermometers can be used for accurate measurements over a wide range of temperatures below 4 K. Comparisons with a melting curve thermometer, a calibrated germanium thermometer and a pulsed platinum nuclear magnetic resonance thermometer are presented. For the 1.290 Ω resistance we measure a 1 % precision in just 100 ms, and have shown this to be independent of temperature.

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We have observed induced currents associated with the fractional quantum Hall effect (FQHE) in a contactless two-dimensional electron gas subjected to a sweeping magnetic field. Their currentvoltage characteristics exhibit pronounced nonlinearities caused by the breakdown of the FQHE at high currents. Our results support the inter-Landau-level-scattering model of breakdown and provide a new local probe of the FQHE energy gaps at n 1͞3 and 2͞3. They are also consistent with the compositefermion picture but yield an effective mass significantly smaller than previously reported values.[S0031-9007(98)07588-7] PACS numbers: 73.40.Hm, 73.20.Dx Since its discovery, the integer quantum Hall effect (IQHE) has been the subject of considerable research activity. In early measurements [1], the IQHE was found to break down under the application of high currents. A variety of models [2][3][4][5] has been proposed to explain the origin and mechanism for the breakdown, but this remains a matter of great debate. The fractional quantum Hall effect [6] (FQHE) is phenomenologically very similar to the IQHE, despite its quite different physical origin as a many-body effect. This similarity has led to attempts to describe the FQHE in similar terms to the IQHE, the most elegant of these being the composite-fermion (CF) scheme proposed by Jain [7]. In this Letter we use a novel contactless measurement of current breakdown in the FQHE which enables direct comparison of breakdown in the IQHE and FQHE, providing a new local probe of the FQHE energy gap and a test of the CF picture.Current breakdown of the IQHE has been investigated thoroughly in GaAs-(Al,Ga)As heterojunctions and has been used to study the current distribution in transport samples. In the initial measurements of breakdown [1,5,8], critical current densities of between 0.5 and 2 Am 21 were reported, corresponding to critical Hall fields of the order of 10 4 V m 21 , inferred assuming a uniform current distribution. In subsequent measurements [9], on constricted Hall bars (with widths of the order 1 mm rather than 300 400 mm), the critical current densities measured gave critical Hall fields of 4.6 3 10 5 V m 21 . Investigation of current breakdown of the quantum Hall effect has recently been extended to fractional filling factors by Takamasu et al. [10], who report critical fields of the order 5 3 10 3 V m 21 for Landau-level filling factors n 1 and 1 3 , with linear dependence on magnetic field for the integers n 1 to 6, and on effective magnetic field B ‫ء‬ jB 2 B 1͞2 j for the fractions. The variation of critical Hall field with sample width in these measurements suggests that neither the current density nor the Hall field is uniform across the Hall bar.MacDonald et al. [11] derived a self-consistent equation describing the charge, current, and Hall-voltage distributions in a two-dimensional electron gas (2DEG) and demonstrated that the current is strongly weighted towards the edges of the sheet, with typically 80% of the Hall voltage dropped within 10 mm of the edges...