J. E. F. Frost

One-dimensional transport and the quantisation of the ballistic resistance

The authors present experimental results, and a supporting theory, showing that a one-dimensional system in which transport is ballistic possesses a quantised resistance, h/2ie2, where i is the number of occupied 1D sub-bands and the spin degeneracy is two. A short narrow channel is defined in the 2DEG of a GaAs-AlGaAs heterojunction and as the width of the system is changed, the sub-bands pass through the Fermi energy and the resistance jumps between quantised values. The value of the quantised resistance is derived and the accuracy of the quantisation is discussed. The effect can be strong at temperatures approximately 0.1 K, with up to 17 sub-bands being observed. The action of a transverse magnetic field is to depopulate the sub-bands and form hybrid levels; a parallel field lifts the spin degeneracy and brings about a further quantisation of resistance at values h/2(i+1/2)e2.

High-frequency single-electron transport in a quasi-one-dimensional GaAs channel induced by surface acoustic waves

We report on an experimental investigation of the direct current induced by transmitting a surface acoustic wave (SAW) with frequency 2.7 GHz through a quasi-one-dimensional (1D) channel defined in a GaAs - AlGaAs heterostructure by a split gate, when the SAW wavelength was approximately equal to the channel length. At low SAW power levels the current reveals oscillatory behaviour as a function of the gate voltage with maxima between the plateaux of quantized 1D conductance. At high SAW power levels, an acoustoelectric current was observed at gate voltages beyond pinch-off. In this region the current displays a step-like behaviour as a function of the gate voltage (or of the SAW power) with the magnitude corresponding to the transfer of one electron per SAW cycle. We interpret this as due to trapping of electrons in the moving SAW-induced potential minima with the number of electrons in each minimum being controlled by the electron - electron interactions. As the number of electrons is reduced, the classical Coulomb charging energy becomes the Mott - Hubbard gap between two electrons and finally the system becomes a sliding Mott insulator with one electron in each well.

Addition of the one-dimensional quantised ballistic resistance

The authors present experimental results showing that the quantised nature of the ballistic resistance in narrow channels is preserved when the electrons pass ballistically through two narrow constrictions. As the width of each narrow channel is varied independently, the resistance of the pair is equal to the resistance of the narrowest; this is explained by the conservation of quantum (sub-band) number. The absolute quantisation is not as accurate as observed in a single constriction and is modified by an anomalous resistance whose origin the authors discuss.

Crosslinked PMMA as a high-resolution negative resist for electron beam lithography and applications for physics of low-dimensional structures

We present a novel technique which employs crosslinked PMMA as a high-resolution negative resist for electron beam lithography. The technique allows the patterning of submicrometre features in an insulating layer, thus simplifying the fabrication process of various multilayer devices. We demonstrate this by reference to specific devices and present simple experimental results which prove the usefulness of the technique.

Electrostatically defined heterojunction rings and the Aharonov–Bohm effect

Micron‐sized loops of high‐mobility two‐dimensional electron gas have been made on GaAs‐AlGaAs heterostructures using a novel split‐gate technique. Aharonov–Bohm oscillations of amplitude up to 20% of the device resistance have been observed at very low temperatures (T<100 mK), together with h/2e oscillations which appear to be due to interference between pairs of time‐reversed paths near B=0. The h/e period is found to vary by ∼25% with magnetic field, possibly as a result of the formation of edge states. In the quantum Hall effect, plateaus in Rxx are seen at high B due to variations in carrier concentration across the ring, which may cause backscattering of some edge states.

Magnetic-field-induced insulator-quantum Hall-insulator transition in a disordered two-dimensional electron gas

We present low-temperature transport measurements on the two-dimensional electron gas in delta -doped GaAs which undergoes an insulator-quantum Hall-insulator transition as the magnetic field is increased. Both low- and high-held transitions are marked by peaks in sigma xx and the temperature-independent critical value of sigma xy of 0.5e2/h per spin. We map out the phase diagram versus disorder and magnetic field and study the temperature dependence of sigma xx throughout. In the quantum Hall region we observe Mott variable range hopping and, around the high-field transitions, scaling via a single parameter: z=(B-B*)T-0.45. The functional dependence on z above this transition is fitted by recent network percolation calculations.

The transition from one- to zero-dimensional ballistic transport

The authors present results on the quantum conduction properties of a one-dimensional channel, 0.7 mu m long and 0.3 mu m wide, containing two potential barriers. The barriers are 0.5 mu m apart and 0.18 mu m wide and are defined by a gate on a high-mobility GaAs-AlGaAs heterojunction. The device behaves like a one-dimensional ballistic point contact with two narrow barriers in the middle. Reducing the width by electrostatic squeezing reveals quasi-periodic peaks in the resistance due to the resonance. At higher temperatures the effect of the barriers is removed so that the peaks disappear leaving the quantised plateaus associated with a one-dimensional ballistic point contact. A magnetic field removes the structure when the level broadening becomes comparable to the level separation.

Ballistic transport in one dimension: additional quantisation produced by an electric field

Experimental evidence is presented for the appearance of new plateaux in the differential conductance of a ballistic 1D channel in the high DC bias regime. In zero magnetic field, the authors observe steps in the differential conduction of e2/h, as opposed to the conventional value of 2e2/h for a spin-degenerate 1D subband. The new plateaux are found to be at quantised values to an accuracy of a few per cent and are described well by a model that assumes the bias is dropped symmetrically in the 1D channel. In addition, all the plateaux disappear with increasing DC voltage bias which can be explained in terms of an enhancement of the tunnelling probability. The same effects persist in a transverse magnetic field and the authors are able to calculate subband spacings as a function of the applied magnetic field.

Direct experimental determination of the tunnelling time and transmission probability of electrons through a resonant tunnelling structure

A sharp step-like structure, which is seen in the current-voltage characteristic of a laterally confined AlGaAs/GaAs resonant tunnelling structure, is a novel manifestation of a quantum effect arising when one-dimensional wires feed electrons into a zero-dimensional quantum box. The authors can analyse the data to deduce a tunnelling time, an inelastic scattering time and the transmission probability for electrons in this system. The height of the current steps, Delta I, gives the electron tunnelling time, taue, via Delta I=e/2 taue, while the differential conductance gives the peak transmission probability, T0, via G approximately (e2/h)T0. The authors must invoke inelastic scattering to explain the low value of T0 approximately 9% obtained from the data, and so they find that tunnelling in their structure is sequential.

The growth and physics of high mobility two-dimensional hole gases

Abstract Modulation-doped p-type GaAs-Al x Ga 1−x As heterojunctions have been grown by molecular beam epitaxy (MBE) on the (311)A GaAs surface using silicon as the acceptor. Two-dimensional hole gases with mobilities as high as 570,000 cm 2 V −1 s −1 at 50 mK have been obtained. It is shown that the sample mobility is dependent upon the direction of orientation of the fabricated Hall bar on the MBE wafer which could be due to the anisotropic nature of the Fermi surface in p-type systems. Experimental results on the fractional quantum Hall effect (FQHE) in these high mobility hole gases are also presented.