Feature article: Electronic transport in granular metal films†

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Abstract
A brief review is given of the theoretical framework for the description and calculation of electronic transport characteristics in granular metals, which are composite materials consisting of a random mixture of nanometer-sized metal and insulator grains. In the metal-rich regime, electrical conduction is by electron percolation through connected metallic networks. The formulation of an effective-medium theory is described for the calculation of this percolative aspect of the electrical transport. Even in the metallic regime, however, metallic conductivity behaviour is violated at low temperatures due to the electron localization effects caused by random scattering. A quantum percolation model is used to take into account the quantum-wave interference effects and to simulate both the temperature and magnetic-field dependence of the low-temperature electrical conductivity in thin granular metal films. The same theoretical model is also used to explore the mesoscopic transport behaviour of small granular metal samples. Four distinct mesoscopic conduction regimes are predicted. In the insulator-rich regime, the hopping conductivity is presented through the critical-path approach, with numerical simulation results to support the thesis that the widely observed -ln-sigma infinity T-1/2 behaviour is a manifestation of interpolation between the high-temperature activated behaviour and the low-temperature -ln-sigma infinity T-1/4 behaviour. The review concludes with a discussion of the role of the Coulomb gap in granular metals and its distinction with the Efros-Shklovskii correlation gap