A. Usher

Odd and even fractionally quantized states in GaAs-GaAlAs heterojunctions

Fractional quantization at values ν = pq has been observed in two ultra high mobility heterojunctions. For the N = 0 Landau level the set of fractions corresponding to q = 3, 5 and 7 has been observed for both spin states, while for the N = 1 Landau level even fractions are observed at 14, 12 and 34. Both the temperature and electron concentration dependence of the resistivity minima at fractional occupancies have been studied.

Magnetization studies of Landau level broadening in two-dimensional electron systems

We have used a torque magnetometer to measure de Haas - van Alphen oscillations in the magnetization of two-dimensional electrons in GaAs/AlGaAs heterostructures and multiple-quantum-well systems for temperatures ranging from 0.125 K to 4.2 K and in magnetic fields of up to 15 T. Our results indicate that for high magnetic fields the density of states can be described by a series of Lorentzian-broadened Landau levels with a broadening that is independent of the magnetic field, B, and Landau level index, n. However, at low magnetic fields the Lorentzian-broadened density of states becomes indistinguishable from a Gaussian one with a broadening that is proportional to . The high-field behaviour of the Landau level line-shape is shown to differ appreciably from the low-field case as reported by other workers using both magnetization and other experimental methods. The reliability of this and other experimental techniques is discussed.

Contactless detection of current breakdown of the quantum Hall effect

Abstract Contactless measurements have been made, using a torque magnetometer, of the size and decay times of the eddy currents induced in a high mobility two-dimensional electron system, as the magnetic field is swept through the magnetoresistance minima associated with the quantum Hall effect. The currents show a highly non-linear dependence on the sweep rate, suggestive of the breakdown of nearly-dissipationless current flow. Comparison of the critical current at which breakdown occurs in our experiments with previously reported values indicates that the majority of the current flows close to the edge of our sample. The observation of a rapid initial decay followed by a much slower one (of the order of hours at the lowest temperatures) upon stopping the field sweep is further evidence that the quantum Hall effect is initially destroyed by the large eddy current; after a short time the current density drops below the critical value and the nearly dissipationless state returns.

The decay of induced eddy currents in a two-dimensional electron system

Large long-lived eddy currents are induced in a two-dimensional electron system as the magnetic field is swept through the almost dissipationless states associated with the quantum Hall effect. We have measured the temperature dependence of the decay times of these currents in a GaAs/AlGaAs single heterostructure, using a torque magnetometer at dilution refrigerator temperatures. At Landau-level filling factor nu = 4, the decay time is less than a minute at T = 40 mK, whereas at nu = 1 and 2 we observe a decay time of about four hours which follows a short initial decay of the order of minutes. We discuss the possible mechanisms for decay of the currents and conclude that the energy is stored predominantly in the Hall electric field between the edge and the centre of the sample. At T = 40 mK we estimate a 2D resistivity of the order of 10 -14 ohms per square for nu = 1 and 10 -11 ohms per square for nu = 4.

Experimental tests of fractional quantum hall effect theory

Abstract The predicted effect of disorder on the hierarchical model of the FQHE, the extension of the FQHE to the N =1 Landau level and the Laughlin scaling diagram are examined in a range of experiments. A new method of obtaining the ground state energy gaps by analysis of the widths of fractional resistivity minima is outlined and preliminary data are presented that point to a method for the experimental determination of quasi-particle charge.

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.

Low‐temperature mobility of two‐dimensional electrons in (Ga,In)As–(Al,In)As heterojunctions

We report an investigation of the scattering mechanisms affecting the two‐dimensional electron system in modulation‐doped Ga0.47In0.53As–Al0.48In0.52As single heterojunctions. Low‐temperature magnetotransport measurements were used to determine the dependence of the electron mobility μ on the density Ns of the two‐dimensional carriers. For Ns≤4×1011 cm−2, we find that μ increases with Ns, leveling off as Ns is further increased. This behavior is a clear indication that, contrary to some theoretical predictions, μ is chiefly limited by ionized‐impurity scattering in this regime. We develop a theoretical model of the scattering mechanisms present in our systems whose results agree with our experiments. We find that alloy and interface‐roughness scattering become important only when Ns≥5×1011 cm−2.

Decay of long-lived quantum Hall induced currents in 2D electron systems

The decay of quasi-persistent circulating currents in the dissipationless quantum Hall regime has been observed. The currents induced by a time-varying magnetic field flow within a two-dimensional electron system (2DES) embedded in a GaAs–(Al,Ga)As heterojunction. The associated magnetic moment is measured using a highly sensitive magnetometer. The currents are observed to continue circulating for many hours after the magnetic field sweep is stopped indicating a very low sheet resistivity. Two distinct current decay regimes are observed, consisting of an initial exponential decay lasting a few tens of seconds followed by a much slower power-law decay. The presence of the fast initial decay, during which the current falls typically to half of its original value, indicates that the system is initially quite dissipative because the quantum Hall effect (QHE) has broken down due to the large induced current. As the current decays, the quasi-dissipationless QHE state recovers, resulting in the much slower decay, which the data suggest will persist for at least several days, much longer than has previously been suggested. The power-law form of the long decay suggests multiple relaxation paths for the system to return to equilibrium, each having a different characteristic time constant. This can equivalently be thought of as a resistivity which gradually falls with current.

Influence of the long-lived quantum Hall potential on the characteristics of quantum devices

Hysteretic effects are reported in magneto-transport experiments on lateral quantum devices. The effects are characterized by two vastly different relaxation times (minutes and days). It is shown that the observed phenomena are related to long-lived eddy currents. This is confirmed by torsion-balance magnetometry measurements of the same two-dimensional electron gas (2DEG) material. These observations show that the induced quantum Hall potential at the edges of the 2DEG reservoirs influences transport through the devices, and have important consequences for the transport properties of all lateral devices, subjected to quantizing magnetic fields.

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.