D. C. Peacock

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.

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.

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.

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.

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.

One-dimensional quantised ballistic resistors in parallel configuration

The authors have defined, in parallel configuration, two split gate devices 0.3 mu m long by 0.3 mu m wide with a centre-to-centre separation of 0.5 mu m on a high mobility heterojunction. At low temperatures, when the phase coherence length is longer than the channel length, the conduction through each one is ballistic and shows steps in conductance of 2e2/h. If the phase coherence length is also greater than the channel separation, transport through both channels is no longer independent, but instead the channels act co-operatively, leading to coherent steps in the conductance of 4e2/h; this can be seen even if the channels do not have the same widths. The device shows Aharonov-Bohm oscillators in resistance of amplitude 10%, arising from a current circulating via edge states through both channels, indicating that the electron wavefunctions is indeed coherent through both.

Resonant magneto-transport through a lateral quantum box in a semiconductor heterostructure

The authors have investigated magneto-transport through a lateral quantum box defined by a patterned Schottky barrier on a GaAs-AlGaAs heterojunction. As the size of the box, and the reflecting barrier potential, are varied, edge states are successively reflected with a consequent change in the value of the plateaux of resistance. Superimposed on a plateau are modulations of resistance having both electrical and magnetic origin. Resonant transport, with an increase in transmission ratio to unity, (corresponding to oscillations in resistance at, or above, the plateaux values), occurs when an integer number of wavelengths fit into the box perimeter and are rapidly modulated by flux quantisation of the Aharonov-Bohm type. In addition, resonance can arise when an incident wave tunnels through the barriers via a circulating, trapped, edge current. This behaviour brings in an extra mode of current and causes the resistance to drop below the value of a plateau in contrast to the previously mentioned resonance arising from transport above the barrier.

Transport in a superlattice of 1D ballistic channels

The authors have fabricated a 2D array of 1D narrow channels in a square lattice configuration on a high mobility GaAs/GaAlAs heterostructure. When a gate voltage is applied the underlying two-dimensional electron gas is depleted creating 4000 dots, of size 0.2 mu m, leaving a grid-like conducting path of quasi one-dimensional channels that are linked every 0.5 mu m. For low values of magnetic field the Hall voltage measured on either side of the device is quenched across its entire width of 25 mu m. The longitudinal magneto-resistance reveals Aharonov-Bohm oscillations with a flux period of h/e for magnetic fields up to 0.4 T. The conductance versus gate voltage shows structure that is consistent with Bragg reflections of the electron waves when the one-dimensional subband wavelength at the Fermi energy, in the direction of current flow, is equal to one superlattice period. Dips in the conductance when this criteria is met show a ln T temperature dependence, similar in origin to a 2D quantum interference. A magnetic field quenches these dips when the cyclotron orbit is comparable with the superlattice period.

The one dimensional quantised ballistic resistance in GaAs/AlGaAs heterojunctions with varying experimental conditions

Abstract The quantisation of the one-dimensional ballistic resistance has been investigated in “split-gate” high electron mobility structures where the gates define a narrow quasi-one-dimensional channel in an otherwise two-dimensional electron gas. Various authors have made theoretical predictions about the effects on this quantisation of device geometry and experimental conditions. We present new experimental data from a series of such structures, and focus on two phenomena: length-dependent resonances in the resistance and the possibility of negative differential resistance.