Fractional Aharonov-Bohm effect in mesoscopic rings

We study the effects of correlations on a one dimensional ring threaded by a uniform magnetic flux. In order to describe the interaction between particles, we work in the framework of the U $\infty$ Hubbard and $t$-$J$ models. We focus on the dilute limit. Our results suggest the posibility that the persistent current has an anomalous periodicity $\phi_{0}/p$, where $p$ is an integer in the range $2\leq p\leq N_{e}$ ($N_{e}$ is the number of particles in the ring and $\phi_{0}$ is the flux quantum). We found that this result depends neither on disorder nor on the detailed form of the interaction, while remains the on site infinite repulsion.Comment: 14 pages (Revtex), 5 postscript figures. Send e-mail to: [email protected]

Direct measurement of the phase coherence length in a GaAs/GaAlAs square network

The low temperature magnetoconductance of a large array of quantum coherentloops exhibits Altshuler-Aronov-Spivak oscillations which periodicitycorresponds to 1/2 flux quantum per loop.We show that the measurement of the harmonics content in a square networkprovides an accurate way to determine the electron phase coherence length$L\_{\phi}$ in units of the lattice length without any adjustableparameters.We use this method to determine $L\_{\phi}$ in a network realised from a 2Delectron gas (2DEG) in a GaAS/GaAlAs heterojunction. The temperaturedependence follows a power law $T^{-1/3}$ from 1.3 K to 25 mK with nosaturation, as expected for 1D diffusive electronic motion andelectron-electron scattering as the main decoherence mechanism.Comment: Additional experimental data in version

Quantum oscillations in mesoscopic rings and anomalous diffusion

We consider the weak localization correction to the conductance of a ring connected to a network. We analyze the harmonics content of the Al'tshuler-Aronov-Spivak (AAS) oscillations and we show that the presence of wires connected to the ring is responsible for a behaviour different from the one predicted by AAS. The physical origin of this behaviour is the anomalous diffusion of Brownian trajectories around the ring, due to the diffusion in the wires. We show that this problem is related to the anomalous diffusion along the skeleton of a comb. We study in detail the winding properties of Brownian curves around a ring connected to an arbitrary network. Our analysis is based on the spectral determinant and on the introduction of an effective perimeter probing the different time scales. A general expression of this length is derived for arbitrary networks. More specifically we consider the case of a ring connected to wires, to a square network, and to a Bethe lattice.Comment: 17 pages, 7 eps figure

What is the Thouless Energy for Ballistic Systems?

The Thouless energy, \Ec characterizes numerous quantities associated with sensitivity to boundary conditions in diffusive mesoscopic conductors. What happens to these quantities if the disorder strength is decreased and a transition to the ballistic regime takes place? In the present analysis we refute the intuitively plausible assumption that \Ec loses its meaning as an inverse diffusion time through the system at hand, and generally disorder independent scales take over. Instead we find that a variety of (thermodynamic) observables are still characterized by the Thouless energy.Comment: 4 pages REVTEX, uuencoded file. To appear in Physical Review Letter

Spectral statistics of disordered metals in the presence of several Aharonov-Bohm fluxes

The form factor for spectral correlations in a diffusive metal is calculated in the presence of several Aharonov-Bohm fluxes. When the fluxes $\phi$ are equal, the correlations are universal functions of $n g^2 \phi$ where $g$ is the dimensionless conductance and $n$ is the number of applied fluxes. This explains recent flux dependence of the correlations found numerically at the metal-insulator transition.Comment: 3 pages, Latex, 1 figure, to appear in Phys. Rev. B Rapid Com

Boundary scattering and weak localization of electrons in a magnetic field

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Resistivity due to a Domain Wall in Ferromagnetic Metal

The resistivity due to a domain wall in ferromagnetic metallic wire is calculated based on the linear response theory. The interaction between conduction electrons and the wall is expressed in terms of a classical gauge field which is introduced by the local gauge transformation in the electron spin space. It is shown that the wall contributes to the decoherence of electrons and that this quantum correction can dominate over the Boltzmann resisitivity, leading to a decrease of resisitivity by nucleation of a wall. The conductance fluctuation due to the motion of the wall is also investigated. The results are compared with recent experiments.Comment: 9 pages, 3 figure

Dephasing of a particle in a dissipative environment

The motion of a particle in a ring of length L is influenced by a dirty metal environment whose fluctuations are characterized by a short correlation distance $\ell << L$. We analyze the induced decoherence process, and compare the results with those obtained in the opposing Caldeira-Leggett limit ($\ell >> L$). A proper definition of the dephasing factor that does not depend on a vague semiclassical picture is employed. Some recent Monte-Carlo results about the effect of finite temperatures on "mass renormalization" in this system are illuminated.Comment: 18 pages, 2 figures, some textual improvements, to be published in JP

Non-linear sigma model study of magnetic dephasing in a mesoscopic spin glass

We propose a nonlinear sigma model for the description of quantum transport in a mesoscopic metallic conductor with magnetic impurities frozen in a spin glass phase. It accounts for the presence of both the corresponding scalar and magnetic random potentials. In a spin glass, this magnetic random potential is correlated between different realizations. As the strength of the magnetic potential is varied, this model describes the crossover between orthogonal and unitary universality classes of the nonlinear sigma model. We apply this technique to the calculations of the correlation of conductance between two frozen spin configurations in terms of dephasing rates for the usual low energy modes of weak localization theory.Comment: 6 pages, 2 figure

Functionals of the Brownian motion, localization and metric graphs

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\"odinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and conclusion added. Several references adde