颗粒体系中排除小团簇的逾渗和库仑阻塞
Percolation with excluded small clusters and Coulomb blockade in a granular system
摘要：
我们认为直流电导率$σ$的小导电和绝缘颗粒的混合物略低于逾渗阈值，其中有限的集群的导电颗粒的特点是由一个广泛的频谱的大小。电荷输运由相邻导电簇之间的载流子隧穿通过由一个绝缘颗粒组成的短"链路“来控制。在降低温度时，小的簇（直到一些$T$依赖的大小）变成库仑阻塞，并且如果可能的话，通过相关的跳跃路径来避免。我们介绍了一个相关的解析问题的次近邻（NNN）的电导率与排除小集群和证明（数值和解析），$σ$减少的幂律的大小排除集群。作为一个物理结果，电导率是一个幂律函数的温度在一个广泛的中间温度范围。我们表示相应的指数通过已知的临界指数的逾渗理论，并确认这种关系的数值。
英文摘要：
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 percolation theory and confirm this relation numerically.
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