Quantum tunnelling and hopping between metallic domains in disordered two-dimensional mesoscopic electron systems

We investigate transport in 2D mesoscopic electron systems with disorder assuming a percolation mechanism through a network of disconnected conducting metallic domains. The size of the domains is determined by the level of disorder and the strength of the electron correlations. The domains are linked for transport by two competing mechanisms. The first mechanism is familiar thermally activated hopping. The second is quantum tunnelling between adjacent conducting regions bounded by equipotential contours of the same value. This mechanism leads to temperature-independent transmission at low temperatures. We calculate the transmission across the potential barriers separating adjacent domains, and we obtain agreement with recent experimental measurements of temperature-dependent resistivities in mesoscopic 2D systems. We also obtain consistent values for the spatial separation of the domains and the average variation in the random disorder potential. Finally, we show that the effect of quantum coherence can result in a small downturn in the resistivity at low temperatures, again in good agreement with the recent experimental results.