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We present a comprehensive study of the dependence of fractal conductance fluctuations (FCF) on semiconductor billiard parameters. We find that the fractal dimension depends solely on an empirical parameter that quantifies the resolution of the discrete energy level spectrum of the billiard. We have also investigated the effect of profile softness using billiards formed in a double two-dimensional electron gas heterostructure and find that FCF are robust to the changes in profile softness achieved.

The variation of the magnetoconductance of two quantum dot arrays fabricated on GaAs/AlGaAs with temperature and sample current was used to extract carrier heating values at various magnetic fields. These measurements yielded a power law dependence of the electron temperature with the sample current and we study its variation with magnetic field. The power law exponent for the energy-relaxation time for both the dot arrays stays nearly constant over the entire magnetic field range.

The influence of temperature and drive current on the Shubnikov-de Haas oscillations is studied as a means to investigate the nature of the electron–phonon interaction in an etched InGaAs quantum wire. The temperature dependence of the energy-relaxation time, and the current dependence of the electron temperature, appear consistent with an energy relaxation process that is dominated by three-dimensional electron–phonon scattering. A deviation from this behavior is found in measurements performed at 1.6 K, however, and simple estimates suggest that this may be associated with the increased importance at low temperatures of phonon confinement in the etched wire.

The nonlinear conductivity of an array of quantum dots, formed by split-gates on a GaAs/AlGaAs heterostructure, is studied. Previously, this array was shown to exhibit a gate bias-induced localization behavior at low temperatures, similar to the insulating state found in 2D systems. Here, we study the effect of source–drain bias potential on the heating of the electron system in the dots. We find that the scaling of conductance with this bias voltage can be described by an equation similar to that for temperature. In addition, we determine the effective temperature and energy-relaxation time. This relaxation time appears to decay as T−3/2 at higher temperatures, but shows a saturation at low temperatures.

We report geometry-induced fractal behaviour analogous to fractional Brownian motion in the low-field magneto-conductance fluctuations of a mesoscopic semiconductor billiard. Such fractal behaviour was recently predicted to be due to the trajectory trapping behaviour of the mixed (regular/chaotic) phase space generated by the soft-walled nature of the billiard potential profile. Hence, our results constitute a possible experimental observation of the infinite hierarchical nature of this mixed phase space. Preliminary investigations into the effects of temperature and gate bias, which directly control electron coherence and billiard potential profile, are presented.

We study theoretically and experimentally a nominally stadium shaped quantum billiard, a device in which the classical dynamics is expected to be chaotic. Using self-consistent solutions for the confining potential in our calculations, we find, in agreement with experiment, that the magnetotransport is dominated by a periodic oscillations, characteristic of regular orbits in the structure, indicating the stability of non-chaotic classical trajectories.

We study the magnetic field dependence of the correlation field ΔB c and amplitude δg of the conductance fluctuations, observed in the low-temperature magnetoresistance of a quasi-ballistic split-gate wire. With increasing the fields, there exists a crossover from diffusive to ballistic motions in the quasi-ballistic transport. Scattering processes have been discussed by analyzing a linear field dependence of ΔB c above the crossover. The crossover behaviors are considered to be a precursor effect on the formation of the edge channel accompanied with a rapid increase of inelastic scattering length l in .

We study carrier scattering processes in GaAs/AlGaAs quantum wires by a correlation field analysis of the conductance fluctuations observed in their low temperature magnetoresistance. In the diffusive transport regime, the magneto-resistance at low magnetic fields shows universal conductance fluctuations (UCF) and the correlation field Bc is field independent. However, at higher fields, where the Landau level quantization is resolved, Bc is found to increase as a power law of the magnetic field. We compare our results with recent theoretical predictions for the diffusive nature and also with our own semi-classical explanations for the dynamical transport.

We are studying quantum interference effects in narrow GaAs/AlGaAs wires of the quasi-ballistic regime, where the wire dimensions are comparable to or less than the phase coherence length of electron transport. By analysing the auto-correlation function of the universal conductance fluctuations in low field magnetoresistances, we obtained the wire-width and the magnetic field dependences of the correlation field and observed phase-coherence behaviors of electron waves. Estimating the boundary correlation field as ω c τ = 1, we can discuss a mean free path in the split-gated wire. Such a boundary field analysis indicates a possibility of determination of the microscopic mean free path of quantum narrow wires.

We have analysed the variation of the amplitude of the magnetoconductivity peaks of the 2DEG in GaAs/AlGaAs heterojunctions as a function of Landau level index number. We interpret our observations in terms of a scattering change as the magnetic field is varied and the size of the orbit dimensions relative to the scale of long-range potential fluctuations. Furthermore, the experimental values of the conductivity peaks are compared with theoretical predictions. Agreement is possible over a limited range of magnetic field and only when a low areal density of scatterers is used.

One of the key parameters for the observation of quantum interference effects in mesoscopic systems is the phase-breaking time τ φ . While there have been many measurements of this important phase-breaking time in diffusive mesoscopic structures, there have been relatively few studies of phase breaking in zero-dimensional structures. Here, a saturation of the phase-breaking time at low temperatures is found, with a decay at higher temperatures generally of the form of T −2/3 . Variation with dot size suggests a scaling in which the phase-breaking interaction is described by the total number of electrons N = nA within the dot.

In order to clarify the quantum interference effect in quasi-ballistic narrow wires of GaAs/AlGaAs, we have studied magnetic field dependence of the correlation field of the universal condactance fluctuations in the magnetoresistance and discussed localization effect of the electron wave in the wire.

Transient heat pulse techniques allow specific heat ( C ) and thermal conductivity (κ) to be determined from a single measurement. We have developed a new numerical fitting technique to analyse such data, which improves the accuracy of results obtained from heat pulse calorimetry. In this paper we present two further improvements to this technique which compensate for the finite duration of the heat pulse injected into the sample and any distortion of the temperature response caused by measurement time constants.