Conductivity in the insulating phase of regular and disordered granular metal arrays

V. Tripathi, Y. L. Loh, and M. Turlakov

Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge

We study the Ambegaokar-Eckern-Schön model for an array of metallic grains coupled by tunnel junctions. For a regular array with intergrain dimensionless conductance g we calculate both paramagnetic and diamagnetic terms in the Kubo formula for conductivity. We find analytically, and confirm by numerical path integral Monte Carlo methods, that for 0 < g < 4, the conductivity obeys an Arrhenius law (σ(T) ~ exp[-E*(g)/T]) with an effective charging energy E*(g) when the temperature is sufficiently low, due to a subtle cancellation between T2 inelastic-cotunnelling contributions in the paramagnetic and diamagnetic terms. We present numerical results for the effective charging energy, and compare our results with recent theoretical analyses. We discuss the different ways in which the experimentally observed σ(T) ~ exp[-√T0/T] law could be attributed to disorder.