Effective charging energy for a regular granular metal array

Abstract

We study the Ambegaokar-Eckern-Schön (AES) model for a regular array of metallic grains coupled by tunnel junctions of conductance $g$ and calculate both paramagnetic and diamagnetic terms in the Kubo formula for the conductivity. We find analytically, and confirm by numerical path integral Monte Carlo methods, that for $0<g<4$ the conductivity obeys an Arrhenius law $\sigma (T)\sim \exp [-E^{\ast }(g)/T]$ with an effective charging energy $E^{\ast }(g)$ when the temperature is sufficiently low, due to a subtle cancellation between $T^2$ inelastic-cotunneling contributions in the paramagnetic and diamagnetic terms. We present numerical results for the effective charging energy and compare the results with recent theoretical analyses. We discuss the different ways in which the experimentally observed $\sigma (T)\sim \exp [-\sqrt{T_0/T}]$ law could be attributed to disorder.

5 pages, 3 figures, ReVTeX; added estimates of effective charging energies and discussion of effects of disorder

References in corpus (6)

• Coulomb effects in granular materials at not very low temperatures
• Transition from insulating to a non-insulating temperature dependence of the conductivity in granular metals
• Electron Transport in Granular Metals
• Granular systems in the Coulomb blockade regime
• Magnetic droplets in a metal close to a ferromagnetic quantum critical point
• Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals

Cited by in corpus (4)

• Granular Electronic Systems
• Thermal transport in a granular metal array
• Electronic correlations and disorder in transport through one-dimensional nanoparticle arrays
• Optical conductivity of a granular metal at not very low temperatures