J. P. Bird

Geometry-induced fractal behaviour in a semiconductor billiard

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

Is There a Magnetic-Field-Induced Breakdown in the Universality of Conductance Fluctuations?

Over the past few years, there have been many reports of the breakdown of universality in conductance fluctuations in mesoscopic systems when a high magnetic field is applied, particularly in the case of quantum wires. Normally, conductance fluctuations are described by a single scaling parameter-the coherence length l Φ . The increase in the magnetic coherence length B c is generally attributed to a decrease in l Φ which is not observed in the amplitude of the fluctuations. Worse, in high mobility material, the fluctuations seem to increase in amplitude, which is also inconsistent with a decrease in l Φ . Here, we argue that (1) the wire behavior is governed by surface scattering, (2) there is a formation of edge states in the high magnetic field, and (3) a breakdown of diffusive transport and transition to quasi-ballistic transport in the edge states in high-mobility material. The transition to high field behavior occurs when the cyclotron orbit at the Fermi surface becomes smaller than the width, so that proper treatment of the amplitude of the fluctuations and of the magnetic correlation length remains in keeping with theoretically expected behavior without loss of universality.

Application of narrow band-gap materials in nanoscale spin filters

We develop a simple analytical model to study the influence of different material systems on the operation of a quantum-point-contact spin filter. Such a device has been predicted to allow for local control of the spin polarization in a semiconductor, and for direct electrical detection of the induced spin polarization. Narrow band-gap semiconductors, such as InAs and InSb, are predicted to exhibit excellent spin-filter characteristics, due to their large g-factor values, and enhanced subband splittings. As a practical step towards the realization of such a spin filter, the electrical properties of InGaAs quantum wires are investigated.

Zero field magnetoresistance peaks in open quantum dots: weak localization or a fundamental property?

Performing numerical simulations of open quantum dots, we reproduce the zero field resistance peaks seen experimentally, a phenomenon previously attributed to weak localization. Our results show however that these peaks can have a different origin, involving conductance resonances that reflect the underlying spectrum. Even with ensemble averaging, we find that the shape of the resistance peak can be more of a probe of these resonances than of the dynamics of the dot.

The influence of environmental coupling on phase breaking in open quantum dots

Abstract Studies of the phase breaking time in open quantum dots reveal a value of the order of a few tens of picoseconds at low resistances, which increases by as much as one order of magnitude as the quantum point contact leads are narrowed to support just a few modes. In addition, the value of the phase breaking time in the high resistance regime shows considerable device dependent variations, indicative of a sensitivity of phase coherence to device dependent disorder. In order to account for these observations, we suggest an interpretation of phase breaking which invokes the discrete nature of the level spectrum in the open dots and which emphasizes the role of the quantum point contacts in selectively exciting dot eigenstates.

Scale factor mapping of statistical and exact self-similarity in billiards

We investigate the fractal magnetotransport properties of mesoscopic billiards. Employing three geometries, we find the self-similarity to be either statistical or exact. We use a correlation analysis to investigate the relationship between these two families of scaling behaviours.

Quantum transport in ballistic quantum dots

Carriers in small 3D quantum boxes take us from unintentional qquantum dots in MOSFETs (arising from the doping fluctuations) tto single-electron quantum dots in semiconductor hheterostructures. In between these two extremes are the realm of oopen, ballistic quantum dots, in which the transport can be quite regular. Several issues must be considered in treating the transport in these dots, among which are: (1) phase coherence within the dot; (2) the transition between semi-classical and fully quantum transport, (3) the role of the contacts, vis-a-vis the fabricated boundaries, and (4) the actual versus internal boundaries. In this paper, we discuss these issues, including the primary observables in experiment, the intrinsic nature of oscillatory behavior in magnetic field and dot size, and the connection to semi-classical transport emphasizing the importance of the filtering by the input (and output) quantum point contacts.

Stability of regular orbits in ballistic quantum dots

Abstract 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.

Geometry-induced fractal behaviour:: fractional Brownian motion in a ballistic mesoscopic billiard

Abstract 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.