Crossover from tunneling to incoherent (bulk) transport in a correlated nanostructure

We calculate the junction resistance for a metal-barrier-metal device with the barrier tuned to lie just on the insulating side of the metal-insulator transition. We find that the crossover from tunneling behavior in thin barriers at low temperature to incoherent transport in thick barriers at higher temperature is governed by a generalized Thouless energy. The crossover temperature can be estimated from the low temperature resistance of the device and the bulk density of states of the barrier.