Quantum transport in a model of granular conductors

Interest in studying electronic transports properties of granular metals has persisted for a long time.1–7 The main difference between granular metals and normal disordered metals is that there exists a large temperature range where transports is dominated by incoherent processes usually called quantum dissipation, and the transports in this temperature range can be described by an effective action proposed first by Ambegaokar, Eckern, and Schön (AES).2 The competition between Coulomb interaction and quantum dissipation determines the electronic properties in this temperature range. However, it is also expected that coherent transports should recover in the low-temperature regime TøDe, where De is the average energy level spacing in the grains.3 A theory describing the crossover between the two regimes in granular metals have been proposed by Beloborodov et al.,1 where they formulated a perturbation theory valid in the intermediateto low-temperature regime ET@kBT, where ET,D /L2 is the average Thouless energy of grains and L3=V is the average grain volume. Beloborodov et al. considered a model Hamiltonian,