Quantum interference and Coulomb interaction in arrays of tunnel junctions

Abstract

We study the electronic properties of an array of small metallic grains connected by tunnel junctions. Such an array serves as a model for a granular metal. Previous theoretical studies of junction arrays were based on models of quantum dissipation which did not take into account the diffusive motion of electrons within the grains. We demonstrate that these models break down at sufficiently low temperatures: for a correct description of the screening properties of a granular metal at low energies the diffusive nature of the electronic motion within the grains is crucial. We present both a diagrammatic and a functional integral approach to analyse the properties of junction arrays. In particular, a new effective action is obtained which enables us to describe the array at arbitrary temperature. In the low temperature limit, our theory yields the correct, dynamically screened Coulomb interaction of a normal metal, whereas at high temperatures the standard description in terms of quantum dissipation is recovered.

14 pages, 7 figures

References in corpus (2)

• Magnetoresistance of Granular Superconducting Metals in a Strong Magnetic Field
• Weak Charge Quantization as an Instanton of Interacting sigma-model

Cited by in corpus (37)

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• Transport properties of granular metals at low temperatures
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• Transition from insulating to a non-insulating temperature dependence of the conductivity in granular metals
• Universal Description of Granular Metals at Low Temperatures: Granular Fermi Liquid
• Anomalous Hall effect in granular ferromagnetic metals and effects of weak localization
• Thermal transport in a granular metal array
• Electron Transport in Granular Metals
• Thermal transport in granular metals
• Charge relaxation resistance in the Coulomb blockade problem
• Inelastic electron transport in granular arrays
• Hall Transport in Granular Metals and Effects of Coulomb Interactions
• Tunneling density of states of granular metals
• Weak Localization in Metallic Granular Media
• Rings and boxes in dissipative environments
• Coulomb Blockade and Super Universality of the Theta-Angle
• Effects of fluctuations and Coulomb interaction on the transition temperature of granular superconductors
• Relaxation dynamics of the electron distribution in the Coulomb blockade problem
• Suppression of superconductivity in granular metals
• The problem of "macroscopic charge quantization" in single-electron devices
• Granulated superconductors:from the nonlinear sigma model to the Bose-Hubbard description
• Electron transport in two-dimensional arrays
• Superconducting Fluctuation Corrections to the Thermal Current in Granular Metals
• Optical conductivity of a granular metal at not very low temperatures
• Localization and Capacitance Fluctuations in Disordered Au Nano-junctions
• Temperature and magnetic-field dependence of the quantum corrections to the conductance of a network of quantum dots
• Mesoscopic charging effects in the $\sigma$-model for granular metals
• Coulomb blockade in metallic grains at large conductance
• Out-of-Equilibrium Admittance of Single Electron Box Under Strong Coulomb Blockade
• Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals
• Coulomb staircase in an asymmetrically coupled quantum dot
• Two-instanton approximation to the Coulomb blockade problem
• Plasmon assisted transport through disordered array of quantum wires
• Fluctuation Spectroscopy in Granular Superconductors with Application to Boron-doped Nanocrystalline Diamond
• Phononless thermally activated transport through a disordered array of quantum wires
• Mesoscopic electron transport and atomic gases, a review of Frank W. J. Hekking's scientific work