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P. Woelfle

Publications and source records attributed to P. Woelfle.

At least 37 records · Page 2Linked to original sources
arXiv2001

Magnetotransport in 2D lateral superlattices with smooth disorder: Quasiclassical theory of commensurability oscillations

Commensurability oscillations in the magnetoresistivity of a two-dimensional electron gas in a two-dimensional lateral superlattice are studied in the framework of quasiclassical transport theory. It is assumed that the impurity scattering is of small-angle nature characteristic for currently fabricated high-mobility heterostructures. The shape of the modulation-induced magnetoresistivity $Δρ_{xx}$ depends on the value of the parameter $γ\equiv η^2 ql/4$, where $η$ and $q$ are the strength and the wave vector of the modulation, and $l$ is the transport mean free path. For $γ\ll 1$, the oscillations are described, in the regime of not too strong magnetic fields $B$, by perturbation theory in $η$ as applied earlier to the case of one-dimensional modulation. At stronger fields, where $Δρ_{xx}$ becomes much larger than the Drude resistivity, the transport takes the advection-diffusion form (Rayleigh-Bénard convection cell) with a large Péclet number, implying a much slower ($\propto B^{3/4}$) increase of the oscillation amplitude with $B$. If $γ\gg 1$, the transport at low $B$ is dominated by the modulation-induced chaos (rather than by disorder). The magnetoresistivity drops exponentially and the commensurability oscillations start to develop at the magnetic fields where the motion takes the form of the adiabatic drift. Conditions of applicability, the role of the type of disorder, and the feasibility of experimental observation are discussed.

cond-mat.dis-nn↗
arXiv2000

Magnetotransport in lateral superlattices with small-angle impurity scattering: Low-field magnetoresistance

An analytical study of the low-field magnetoresistance of a two-dimensional electron gas subject to a weak periodic modulation is presented. We assume small-angle impurity scattering characteristic for high-mobility semiconductor heterostructures. It is shown that the condition for existence of the strong low-field magnetoresistance induced by so-called channeled orbits is $η^{3/2}ql\gg 1$, where $η$ and $q$ are the strength and the wave vector of the modulation, and $l$ is the transport mean free path. Under this condition, the magnetoresistance scales as $η^{7/2}$.

cond-mat.dis-nn↗
arXiv2000

Superfluid Helium 3: Link between Condensed Matter Physics and Particle Physics

The discovery of the superfluid phases of Helium 3 in 1971 opened the door to one of the most fascinating systems known in condensed matter physics. Superfluidity of Helium 3, originating from pair condensation of Helium 3 atoms, turned out to be the ideal testground for many fundamental concepts of modern physics, such as macroscopic quantum phenomena, (gauge-)symmetries and their spontaneous breakdown, topological defects, etc. Thereby the superfluid phases of Helium 3 enriched condensed matter physics enormously. In particular, they contributed significantly - and continue to do so - to our understanding of various other physical systems, from heavy fermion and high-Tc superconductors all the way to neutron stars, particle physics, gravity and the early universe. A simple introduction into the basic concepts and questions is presented.

cond-mat↗
arXiv2000

Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance

We study long-range correlations of equilibrium current densities in a two-dimensional mesoscopic system with the time reversal invariance broken by a random or homogeneous magnetic field. Our result is universal, i.e. it does not depend on the type (random potential or random magnetic field) or correlation length of disorder. This contradicts recent sigma-model calculations of Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well as for the renormalization of the conductivity. We show explicitly that the new term in the sigma-model derived by TS&E and claimed to lead to delocalization does not exist. The error in the derivation of TS&E is traced to an incorrect ultraviolet regularization procedure violating current conservation and gauge invariance.

cond-mat.mes-hall↗
arXiv2000

Vortex in a d-wave superconductor at low temperatures

A systematic perturbation theory is developed to describe the magnetic field-induced subdominant $s$- and $d_{xy}$-wave order parameters in the mixed state of a $d_{x^2-y^2}$-wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field $H_{c1}\ltsim H\ll H_{c2}$ from $T_c$ down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of subdominant $d_{xy}$ pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.

cond-mat.supr-con↗
arXiv2000

Comment on "Antilocalization in a 2D Electron Gas in a Random Magnetic Field"

In a recent Letter, Taras-Semchuk and Efetov reconsider the problem of electron localization in a random magnetic field in two dimensions. They claim that due to the long-range nature of the vector potential correlations an additional term appears in the effective field theory ($σ$-model) of the problem, leading to delocalization at the one-loop level. This calls into question the results of earlier analytical studies, where the random magnetic field problem was mapped onto the conventional unitary-class $σ$-model, implying that the leading quantum correction is of two-loop order and of a localizing nature. We show in this Comment, however, that the new term in fact does not exist and was erroneously obtained by Taras-Semchuk and Efetov because of an inconsistent treatment violating gauge invariance.

cond-mat.dis-nn↗
arXiv2000

Free Energy and Magnetic Penetration Depth of a $d$-Wave Superconductor in the Meissner State

We investigate the free energy and the penetration depth of a quasi-two-dimensional d-wave superconductor in the presence of a weak magnetic field by taking account of thermal, nonlocal and nonlinear effects. In an approximation in which the superfluid velocity $v_s$ is assumed to be slowly varying, the free energy is calculated and compared with available results in several limiting cases. It is shown that either nonlocal or nonlinear effects may cut off the linear-$T$ dependence of both the free energy and the penetration depth in all the experimental geometries. At extremely low $T$, the nonlocal effects will also generically modify the linear $H$ dependence of the penetration depth ("nonlinear Meissner effect") in most experimental geometries, but for supercurrents oriented along the nodal directions, the effect may be recovered. We compare our predictions with existing experiments on the cuprate superconductors.

cond-mat.supr-con↗
arXiv2000

Acoustoelectric current and pumping in a ballistic quantum point contact

The acoustoelectric current induced by a surface acoustic wave (SAW) in a ballistic quantum point contact is considered using a quantum approach. We find that the current is of the "pumping" type and is not related to drag, i.e. to the momentum transfer from the wave to the electron gas. At gate voltages corresponding to the plateaus of the quantized conductance the current is small. It is peaked at the conductance step voltages. The peak current oscillates and decays with increasing SAW wavenumber for short wavelengths. These results contradict previous calculations, based on the classical Boltzmann equation.

cond-mat.mes-hall↗
arXiv1999

Zero-frequency anomaly in quasiclassical ac transport: Memory effects in a two-dimensional metal with a long-range random potential or random magnetic field

We study the low-frequency behavior of the {\it ac} conductivity $σ(ω)$ of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a non-analytic $\propto|ω|$ correction to ${\rm Re} σ$, which corresponds to a $1/t^2$ long-time tail in the velocity correlation function. This contribution is induced by return processes neglected in Boltzmann transport theory. The prefactor of this $|ω|$-term is positive and proportional to $(d/l)^2$ for RP, while it is of opposite sign and proportional to $d/l$ in the weak RMF case, where $l$ is the mean free path and $d$ the disorder correlation length. This non-analytic correction also exists in the strong RMF regime, when the transport is of a percolating nature. The analytical results are supported and complemented by numerical simulations.

cond-mat.mes-hall↗
arXiv1999

Conductance distribution of disordered quasi one-dimensional wires

We determine analytically the distribution of conductances of quasi one-dimensional disordered electron systems, neglecting electron-electron interaction, for all strengths of disorder. We find that in the crossover region between the metallic and insulating regimes, P(g) is highly asymmetric, given by ``one-sided'' log-normal distribution. For larger disorder, the tail of the log-normal distribution is cut-off for g > 1 by a Gaussian.

cond-mat.mes-hall↗
arXiv1999

Current noise in a irradiated point contact

We propose a new approach to calculate current and current correlations in a ballistic quantum point contact interacting with a classical field. The approach is based on the concept of scattering states for a time dependent Hamiltonian neglecting electron-electron interaction. Using this approach we calculated the spectra of the current noise in a biased point contact irradiated by a weak random field. For typical radiation frequencies νless than the temperature T and the bias voltage V we find a narrow peak of width νon top of a broad background of width \max (T,eV).

cond-mat.mes-hall↗
arXiv1999

Strong magnetoresistance induced by long-range disorder

We calculate the semiclassical magnetoresistivity $ρ_{xx}(B)$ of non-interacting fermions in two dimensions moving in a weak and smoothly varying random potential or random magnetic field. We demonstrate that in a broad range of magnetic fields the non-Markovian character of the transport leads to a strong positive magnetoresistance. The effect is especially pronounced in the case of a random magnetic field where $ρ_{xx}(B)$ becomes parametrically much larger than its B=0 value.

cond-mat.dis-nn↗
arXiv1999

Weiss oscillations in the presence of small-angle impurity scattering

We calculate the magnetoresistivity of a two-dimensional electron gas in the presence of a periodic potential within classical transport theory, using realistic models of impurity scattering. The magnetooscillations induced by geometric resonance of the cyclotron orbits in the periodic grating, known as Weiss oscillations, are shown to be affected strongly by the small-angle scattering processes dominant in conventional semiconductor heterostructures. Our results are in full agreement with experimental findings.

cond-mat.dis-nn↗
arXiv1999

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 $α=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $α\ll 1$ the Drude theory applies, at $α\gg 1$ 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 $α\gg 1$ 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 $α\sim 1$ is in good agreement with experimental data in the FQHE regime near $ν=1/2$.

cond-mat.mes-hall↗
arXiv1998

Is the nonlinear Meissner effect unobservable?

We examine the effects of nonlocal electrodynamics for a d-wave superconductor on the field dependence of the magnetic penetration depth. The linear field dependence predicted in the local limit, commonly known as the nonlinear Meissner effect, is instead found to be quadratic, $δλ\sim H^2$ for fields below a crossover scale $H^*$. This crossover is shown to be geometry dependent and for most orientations of the screening currents is of the same order as or greater than $H_{c1}$, implying that the nonlinear Meissner effect can not be observed. For special orientations where the current flows along the nodal directions, however, the nonlinear Meissner effect may be recovered.

cond-mat.supr-con↗
arXiv1998

Non-adiabatic scattering of a classical particle in an inhomogeneous magnetic field

We study the violation of the adiabaticity of the electron dynamics in a slowly varying magnetic field. We formulate and solve exactly a non-adiabatic scattering problem. In particular, we consider scattering on a magnetic field inhomogeneity which models scatterers in the composite-fermion theory of the half-filled Landau level. The calculated non-adiabatic shift of the guiding center is exponentially small and exhibits an oscillatory behavior related to the "self-commensurability" of the drifting cyclotron orbit. The analytical results are complemented with a numerical simulation.

cond-mat↗
arXiv1998

Velocity shift of surface acoustic waves due to interaction with composite fermions in a modulated structure

We study the effect of a periodic density modulation on surface acoustic wave (SAW) propagation along a 2D electron gas near Landau level filling $ν=1/2$. Within the composite fermion theory, the problem is described in terms of fermions subject to a spatially modulated magnetic field and scattered by a random magnetic field. We find that a few percent modulation induces a large peak in the SAW velocity shift, as has been observed recently by Willett et al. As further support of this theory we find the dc resistivity to be in good agreement with recent data of Smet et al.

cond-mat.mes-hall↗