Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders

Abstract

We have studied the quantum oscillations of the conductance for arrays of connected mesoscopic metallic rings, in the presence of an external magnetic field. Several geometries have been considered: a linear array of rings connected with short or long wires compared to the phase coherence length, square networks and hollow cylinders. Compared to the well-known case of the isolated ring, we show that for connected rings, the winding of the Brownian trajectories around the rings is modified, leading to a different harmonics content of the quantum oscillations. We relate this harmonics content to the distribution of winding numbers. We consider the limits where coherence length $L_{\phi }$ is small or large compared to the perimeter $L$ of each ring constituting the network. In the latter case, the coherent diffusive trajectories explore a region larger than $L$, whence a network dependent harmonics content. Our analysis is based on the calculation of the spectral determinant of the diffusion equation for which we have a simple expression on any network. It is also based on the hypothesis that the time dependence of the dephasing between diffusive trajectories can be described by an exponential decay with a single characteristic time ${\tau }_{\phi }$ (model A) . At low temperature, decoherence is limited by electron-electron interaction, and can be modelled in a one-electron picture by the fluctuating electric field created by other electrons (model B). It is described by a functional of the trajectories and thus the dependence on geometry is crucial. Expressions for the magnetoconductance oscillations are derived within this model and compared to the results of model A. It is shown that they involve several temperature-dependent length scales.

35 pages, revtex4, 25 figures (34 pdf files)

References in corpus (8)

• Functionals of the Brownian motion, localization and metric graphs
• Direct measurement of the phase coherence length in a GaAs/GaAlAs square network
• Dephasing due to electron-electron interaction in a diffusive ring
• Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network
• Quantum oscillations in mesoscopic rings and anomalous diffusion
• Effect of connecting wires on the decoherence due to electron-electron interaction in a metallic ring
• On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach
• Al'tshuler-Aronov correction to the conductivity of a large metallic square network

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• Thermal noise and dephasing due to electron interactions in non-trivial geometries
• Ergodic vs diffusive decoherence in mesoscopic devices
• Möbius transformations and electronic transport properties of large disorderless networks
• Four-terminal resistances in mesoscopic networks of metallic wires: Weak localisation and correlations
• Transport and Dephasing in a Quantum Dot: Multiply Connected Graph Model