Percolation with excluded small clusters and Coulomb blockade in a granular system |
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Authors: | A S Ioselevich and D S Lyubshin |
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Institution: | 1.Landau Institute for Theoretical Physics,Russian Academy of Sciences,Moscow,Russia;2.Moscow Institute of Physics and Technology,Moscow,Russia |
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Abstract: | We consider dc-conductivity σ of a mixture of small conducting and insulating grains slightly below the percolation threshold,
where finite clusters of conducting grains are characterized by a wide spectrum of sizes. The charge transport is controlled
by tunneling of carriers between neighboring conducting clusters via short “links“ consisting of one insulating grain. Upon
lowering temperature small clusters (up to some T-dependent size) become Coulomb blockaded, and are avoided, if possible, by relevant hopping paths. We introduce a relevant
percolational problem of next-nearest-neighbors (NNN) conductivity with excluded small clusters and demonstrate (both numerically
and analytically) that σ decreases as power law of the size of excluded clusters. As a physical consequence, the conductivity
is a power-law function of temperature in a wide intermediate temperature range. We express the corresponding index through
known critical indices of the perco lation theory and confirm this relation numerically. |
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