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Conduction in Granular Metals by Virtual Tunneling on the Fractal Percolation Cluster
Author(s) -
Zvyagin I.P.,
Keiper R.
Publication year - 2002
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(200203)230:1<151::aid-pssb151>3.0.co;2-b
Subject(s) - fractal , conductivity , condensed matter physics , percolation (cognitive psychology) , quantum tunnelling , cluster (spacecraft) , exponent , materials science , electrical conductor , percolation critical exponents , fractal dimension , percolation threshold , statistical physics , physics , critical exponent , electrical resistivity and conductivity , mathematics , mathematical analysis , quantum mechanics , phase transition , composite material , linguistics , philosophy , neuroscience , computer science , biology , programming language
We discuss the calculation of the dc conductivity of granular metals on the insulating side of the metal–insulator transition. The granular structure is represented by a fractal percolation cluster and the problem of virtual tunneling‐assisted conductivity is shown to be related to estimating the number of minimal paths for the problem of chemical distance metric on the fractal. The resulting conductivity temperature dependence has the form ln σ ≈ const — ( T 0 / T ) x , where x = ζ /( D B + ζ ), D B is the fractal dimensionality of the backbone cluster and ζ is the superlocalization exponent. This gives the value of x close to 0.4 both in two and three dimensions that agrees fairly well with the experimental value x ≈ 1/2 for many granular conductors.