Effect of quantum diffusion on hopping transport

We present a study of quantum diffusion effect in granular metals, in the limit where ΔEc⪢Δε, with Δε the average energy level spacing and ΔEC the charging energy fluctuation. This effect results from the reduction, due to quantum diffusion, in the probability of a coherent hopping process, and is shown to affect the temperature dependence of hopping conductivity. To study the effect, we employ a numerical percolation calculation which includes up to the third nearest-neighbor hoppings. The effect is sizable in the low temperature range where the transport is dominated by long-range hoppings.