Semiclassical theory of transport in a random magnetic field

We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({\bf r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({\bf r})$ and its mean value $\bar{B}$. For $\bar{B}=0$, the governing parameter is $\alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $\alpha\ll 1$ the Drude theory applies, at $\alpha\gg 1$ most particles drift adiabatically along closed contours and are localized in the adiabatic approximation. The conductivity is then determined by a special class of trajectories, the "snake states", which percolate by scattering at the saddle points of $B({\bf r})$ where the adiabaticity of their motion breaks down. The external field also suppresses the diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to a weak violation of the adiabaticity of the cyclotron rotation, yielding an exponential drop of the conductivity at large $\bar{B}$. In the regime $\alpha\gg 1$ the crossover between the snake-state percolation and the percolation of the drift orbits with increasing $\bar{B}$ has the character of a phase transition (localization of snake states) smeared exponentially weakly by non-adiabatic effects. The ac conductivity also reflects the dynamical properties of particles moving on the fractal percolation network. In particular, it has a sharp kink at zero frequency and falls off exponentially at higher frequencies. We also discuss the nature of the quantum magnetooscillations. Detailed numerical studies confirm the analytical findings. The shape of the magnetoresistivity at $\alpha\sim 1$ is in good agreement with experimental data in the FQHE regime near $\nu=1/2$.Comment: 22 pages REVTEX, 14 figure

Variation of elastic scattering across a quantum well

The Drude scattering times of electrons in two subbands of a parabolic quantum well have been studied at constant electron sheet density and different positions of the electron distribution along the growth direction. The scattering times obtained by magnetotransport measurements decrease as the electrons are displaced towards the well edges, although the lowest-subband density increases. By comparing the measurements with calculations of the scattering times of a two-subband system, new information on the location of the relevant scatterers and the anisotropy of intersubband scattering is obtained. It is found that the scattering time of electrons in the lower subband depends sensitively on the position of the scatterers, which also explains the measured dependence of the scattering on the carrier density. The measurements indicate segregation of scatterers from the substrate side towards the quantum well during growth.Comment: 4 pages, 4 figure

Dephasing time of composite fermions

We study the dephasing of fermions interacting with a fluctuating transverse gauge field. The divergence of the imaginary part of the fermion self energy at finite temperatures is shown to result from a breakdown of Fermi's golden rule due to a faster than exponential decay in time. The strong dephasing affects experiments where phase coherence is probed. This result is used to describe the suppression of Shubnikov-de Haas (SdH) oscillations of composite fermions (oscillations in the conductivity near the half-filled Landau level). We find that it is important to take into account both the effect of dephasing and the mass renormalization. We conclude that while it is possible to use the conventional theory to extract an effective mass from the temperature dependence of the SdH oscillations, the resulting effective mass differs from the $m^\ast$ of the quasiparticle in Fermi liquid theory.Comment: 14 pages, RevTeX 3.0, epsf, 1 EPS figur

Percolation-type description of the metal-insulator transition in two dimensions

A simple non-interacting-electron model, combining local quantum tunneling and global classical percolation (due to a finite dephasing time at low temperatures), is introduced to describe a metal-insulator transition in two dimensions. It is shown that many features of the experiments, such as the exponential dependence of the resistance on temperature on the metallic side, the linear dependence of the exponent on density, the $e^2/h$ scale of the critical resistance, the quenching of the metallic phase by a parallel magnetic field and the non-monotonic dependence of the critical density on a perpendicular magnetic field, can be naturally explained by the model.Comment: 4 pages, 4 figure

Two-species percolation and Scaling theory of the metal-insulator transition in two dimensions

Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two dimensions [1]. Here, based upon that model, a two-species-percolation scaling theory is introduced and compared to the experimental data. The two species in this model are, on one hand, the ``metallic'' point contacts, whose critical energy lies below the Fermi energy, and on the other hand, the insulating quantum point contacts. It is shown that many features of the experiments, such as the exponential dependence of the resistance on temperature on the metallic side, the linear dependence of the exponent on density, the $e^2/h$ scale of the critical resistance, the quenching of the metallic phase by a parallel magnetic field and the non-monotonic dependence of the critical density on a perpendicular magnetic field, can be naturally explained by the model. Moreover, details such as the nonmonotonic dependence of the resistance on temperature or the inflection point of the resistance vs. parallel magnetic are also a natural consequence of the theory. The calculated parallel field dependence of the critical density agrees excellently with experiments, and is used to deduce an experimental value of the confining energy in the vertical direction. It is also shown that the resistance on the ``metallic'' side can decrease with decreasing temperature by an arbitrary factor in the degenerate regime ($T\lesssim E_F$).Comment: 8 pages, 8 figure

Collapse of Spin-Splitting in the Quantum Hall Effect

It is known experimentally that at not very large filling factors $\nu$ the quantum Hall conductivity peaks corresponding to the same Landau level number $N$ and two different spin orientations are well separated. These peaks occur at half-integer filling factors $\nu = 2 N + 1/2$ and $\nu = 2 N + 3/2$ so that the distance between them $\delta\nu$ is unity. As $\nu$ increases $\delta\nu$ shrinks. Near certain $N = N_c$ two peaks abruptly merge into a single peak at $\nu = 2N + 1$. We argue that this collapse of the spin-splitting at low magnetic fields is attributed to the disorder-induced destruction of the exchange enhancement of the electron $g$-factor. We use the mean-field approach to show that in the limit of zero Zeeman energy $\delta\nu$ experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for $N_c$ in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures $N_c = 0.9 d n^{5/6} n_i^{-1/3},$ where $d$ is the spacer width, $n$ is the density of the two-dimensional electron gas, and $n_i$ is the two-dimensional density of randomly situated remote donors.Comment: 14 pages, compressed Postscript fil

Apparent Metallic Behavior at B = 0 of a two-dimensional electron system in AlAs

We report the observation of metallic-like behavior at low temperatures and zero magnetic field in two dimensional (2D) electrons in an AlAs quantum well. At high densities the resistance of the sample decreases with decreasing temperature, but as the density is reduced the behavior changes to insulating, with the resistance increasing as the temperature is decreased. The effect is similar to that observed in 2D electrons in Si-MOSFETs, and in 2D holes in SiGe and GaAs, and points to the generality of this phenomenon

Thermodynamic Signature of a Two-Dimensional Metal-Insulator Transition

We present a study of the compressibility, K, of a two-dimensional hole system which exhibits a metal-insulator phase transition at zero magnetic field. It has been observed that dK/dp changes sign at the critical density for the metal-insulator transition. Measurements also indicate that the insulating phase is incompressible for all values of B. Finally, we show how the phase transition evolves as the magnetic field is varied and construct a phase diagram in the density-magnetic field plane for this system.Comment: 4 pages, 4 figures, submitted to Physical Review Letters; version 1 is identical to version 2 but didn't compile properl

Supervised exercise training as an adjunctive therapy for venous leg ulcers: study protocol for a randomised controlled trial

Background: Venous leg ulcers are common, chronic wounds that are painful and reduce quality of life. Compression therapy is known to assist in the healing of venous leg ulceration. Supervised exercise training that targets an improvement in calf muscle pump function might be a useful adjunctive therapy for enhancing ulcer healing and other aspects of physical and mental health. However, the evidence of exercise for individuals with venous ulcers is sparse. Here, we describe the protocol for a study that aims to assess the feasibility of undertaking a randomised controlled trial of a supervised exercise programme in people who are receiving compression for venous ulceration. Methods/Design: This is a randomised, controlled, assessor-blinded, two-centre, feasibility trial with two parallel groups. Eighty adults who are receiving lower-limb compression for a venous leg ulcer will be randomly assigned to receive usual care (compression only) or usual care plus a 12-week supervised exercise programme. Participants in the exercise group will be invited to undertake three, 60-minute sessions of supervised exercise each week, and each session will involve a combination of treadmill walking, upright cycling and strength and flexibility exercises for the lower limbs. Participants will be assessed before randomisation and 3, 6 and 12 months after randomisation. Primary outcomes include rates of recruitment, retention and adherence. Secondary outcomes include time to ulcer healing, proportion of participants healed, percentage and absolute change in ulcer size, health-related quality of life (EQ-5D-5L and VEINES-QOL/Sym), lower-limb cutaneous microvascular function (laser Doppler flowmetry coupled with iontophoresis) and physical fitness (30-second sit-to-stand test, chair sit and reach test, 6-minute walk test and ankle range of motion). The costs associated with the exercise programme and health-care utilisation will be calculated. We will also complete interviews with a sub-sample of participants to explore their experiences of having a venous ulcer and the acceptability of the exercise intervention and study procedures. Discussion: Data from this study will be used to refine the supervised exercise programme, investigate the acceptability of the intervention and study design and determine the most appropriate outcome measures, thereby providing estimates of the factors needed to design an adequately powered trial across several centres

Visual Evoked Potentials Change as Heart Rate and Carotid Pressure Change

The relationship between cardiovascular activity and the brain was explored by recording visual evoked potentials from the occipital regions of the scalp during systolic and diastolic pressure (Experiment I) and during fast and slow heartbeats at systolic and diastolic pressure (Experiment II). Visual evoked potentials changed significantly as heart rate and carotid pressure fluctuated normally, and these changes were markedly different in the right and left cerebral hemispheres. Evoked potentials recorded from the right hemisphere during various cardiac events differed significantly, whereas those recorded from the left did not. In both experiments, differences in the right hemisphere were due primarily to the P1 component, which was larger at diastolic than at systolic pressure. The present findings are consistent with formulations from behavioral studies suggesting that baroreceptor activity can influence sensory intake, and suggest that hemispheric specialization may play an important role in the relationship between cardiac events, the brain and behavior.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73146/1/j.1469-8986.1982.tb02579.x.pd