5 research outputs found
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
Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network
We investigate weak localization in metallic networks etched in a two
dimensional electron gas between mK and mK when electron-electron
(e-e) interaction is the dominant phase breaking mechanism. We show that, at
the highest temperatures, the contributions arising from trajectories that wind
around the rings and trajectories that do not are governed by two different
length scales. This is achieved by analyzing separately the envelope and the
oscillating part of the magnetoconductance. For K we find
\Lphi^\mathrm{env}\propto{T}^{-1/3} for the envelope, and
\Lphi^\mathrm{osc}\propto{T}^{-1/2} for the oscillations, in agreement with
the prediction for a single ring \cite{LudMir04,TexMon05}. This is the first
experimental confirmation of the geometry dependence of decoherence due to e-e
interaction.Comment: LaTeX, 5 pages, 4 eps figure
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 in units of the
lattice length without any adjustableparameters.We use this method to determine
in a network realised from a 2Delectron gas (2DEG) in a GaAS/GaAlAs
heterojunction. The temperaturedependence follows a power law 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
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
Dimensional crossover in quantum networks: from macroscopic to mesoscopic Physics
4 pagesWe report on magnetoconductance measurements of metallic networks of various sizes ranging from 10 to plaquettes, with anisotropic aspect ratio. Both Altshuler-Aronov-Spivak (AAS) periodic oscillations and Aharonov-Bohm (AB) periodic oscillations are observed for all networks. For large samples, the amplitude of both oscillations results from the incoherent superposition of contributions of phase coherent regions. When the transverse size becomes smaller than the phase coherent length , one enters a new regime which is phase coherent (mesoscopic) along one direction and macroscopic along the other, leading to a new size dependence of the quantum oscillations