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

Quantum magneto-oscillations in a two-dimensional Fermi liquid

Quantum magneto-oscillations provide a powerfull tool for quantifying Fermi-liquid parameters of metals. In particular, the quasiparticle effective mass and spin susceptibility are extracted from the experiment using the Lifshitz-Kosevich formula, derived under the assumption that the properties of the system in a non-zero magnetic field are determined uniquely by the zero-field Fermi-liquid state. This assumption is valid in 3D but, generally speaking, erroneous in 2D where the Lifshitz-Kosevich formula may be applied only if the oscillations are strongly damped by thermal smearing and disorder. In this work, the effects of interactions and disorder on the amplitude of magneto-oscillations in 2D are studied. It is found that the effective mass diverges logarithmically with decreasing temperature signaling a deviation from the Fermi-liquid behavior. It is also shown that the quasiparticle lifetime due to inelastic interactions does not enter the oscillation amplitude, although these interactions do renormalize the effective mass. This result provides a generalization of the Fowler-Prange theorem formulated originally for the electron-phonon interaction.Comment: 4 pages, 1 figur

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

Supervised exercise training as an adjunct therapy for venous leg ulcers: a randomised controlled feasibility trial

Background Venous leg ulcers (VLUs) are typically painful and heal slowly. Compression therapy offers high healing rates; however, improvements are not usually sustained. Exercise is a low‐cost, low‐risk and effective strategy for improving physical and mental health. Little is known about the feasibility and efficacy of supervised exercise training used in combination with compression therapy patients with VLUs. Objectives To assess the feasibility of a 12‐week supervised exercise programme as an adjunct therapy to compression in patients with VLUs. Methods This was a two‐centre, two‐arm, parallel‐group, randomized feasibility trial. Thirty‐nine patients with venous ulcers were recruited and randomized 1 : 1 either to exercise (three sessions weekly) plus compression therapy or compression only. Progress/success criteria included exercise attendance rate, loss to follow‐up and patient preference. Baseline assessments were repeated at 12 weeks, 6 months and 1 year, with healing rate and time, ulcer recurrence and infection incidents documented. Intervention and healthcare utilization costs were calculated. Qualitative data were collected to assess participants’ experiences. Results Seventy‐two per cent of the exercise group participants attended all scheduled exercise sessions. No serious adverse events and only two exercise‐related adverse events (both increased ulcer discharge) were reported. Loss to follow‐up was 5%. At 12 months, median ulcer healing time was lower in the exercise group (13 vs. 34·7 weeks). Mean National Health Service costs were £813·27 for the exercise and £2298·57 for the control group. Conclusions The feasibility and acceptability of both the supervised exercise programme in conjunction with compression therapy and the study procedures is supported

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

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

On the Theory of Metal-Insulator Transitions in Gated Semiconductors

It is shown that recent experiments indicating a metal-insulator transition in 2D electron systems can be interpreted in terms of a simple model, in which the resistivity is controlled by scattering at charged hole traps located in the oxide layer. The gate voltage changes the number of charged traps which results in a sharp change in the resistivity. The observed exponential temperature dependence of the resistivity in the metallic phase of the transition follows from the temperature dependence of the trap occupation number. The model naturally describes the experimentally observed scaling properties of the transition and effects of magnetic and electric fields.Comment: 4 two-column pages, 4 figures (included in the text

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