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Hopping in Quasi‐One‐Dimensional Disordered Solids: Beyond the Nearest‐Neighbor Approximation
Author(s) -
Zvyagin I.P.,
Baranovskii S.D.,
Kohary K.,
Cordes H.,
Thomas P.
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<227::aid-pssb227>3.0.co;2-w
Subject(s) - variable range hopping , k nearest neighbors algorithm , condensed matter physics , gaussian , monte carlo method , statistical physics , physics , range (aeronautics) , electrical resistivity and conductivity , limiting , materials science , quantum mechanics , mathematics , statistics , mechanical engineering , artificial intelligence , computer science , engineering , composite material
The theory of hopping transport in quasi‐one‐dimensional disordered organic solids with Gaussian distribution of localized state energies is generalized to account for distant‐neighbor transitions. The former theories predicted a temperature dependence of the resistivity of the form ln ρ ∝ C ( σ / kT ) 2 , where C is a constant ( C ≈ 1) and σ is the disorder parameter. It is shown that the onset of second‐nearest neighbor hopping leads to a decrease of C with decreasing temperature to the limiting value C = 3/4. At lower temperatures, where the hopping range extends beyond second‐nearest neighbors, C is expected to decrease further. The analytical results are in fair agreement with the results of Monte Carlo simulation for one‐dimensional variable‐range hopping.