Variable range hopping in finite one-dimensional and anisotropic two-dimensional systems

The variable range hopping conduction is simulated in a strongly anisotropic two-dimensional (2D) percolation model, which consists of parallel conducting chains coupled to each other weakly via rare "impurities". The exponential temperature dependence of resistance has been calculated for samples of different size, interchain distance, and impurity concentration in two directions, longitudinal and perpendicular to the chain direction. In the limiting case of single finite chains the results are in good agreement with existing analytical expressions for both the length and temperature dependences, but with a low temperature limit, depending on the chain length and localization length. In the 2D case it was shown that there exists a crossover in relative behaviour between the longitudinal and transverse resistance of a finite system, which however disappears from the limit of infinite systems, where the hopping conduction should be always isotropic and obeys the 2D Mott law. (C) 2003 Elsevier Science B.V. All rights reserved.