Voltage statistics of variable-range hopping transport

Toshiaki Hayashi; Yasuhiro Tokura; Akira Fujiwara

Open Conference Systems, StatPhys 27 Main Conference

Toshiaki Hayashi, Yasuhiro Tokura, Akira Fujiwara

##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-08 11:45 AM – 03:30 PM
Last modified: 2019-06-15

Abstract

Since Mott showed the temperature dependence of conductance of amorphous materials [1], the mechanism of variable-range hopping transport (VRH) has been discussed extensively with a variety of theoretical models. The standard description of VRH is the formation of percolation networks which are sets of the bonds whose conductance is larger than a threshold value [2]. In this work, we pay more attention to the voltage distribution at local sites. To this end, we have numerically solved the linearized rate equations for the Miller-Abraham type hopping transport [3] in 2-dimensional random lattices and obtained local chemical potential μ which is defined as the difference between site voltage and electric potential created by an external field. In the calculations, the site density is kept to be 1 and the site energies are uniformly distributed between -W/2 and W/2. At high temperatures (kT > 0.1 W, T: temperature and k: Boltzmann constant), the variance of μ is small and independent of T. With decreasing T, the variance of μ is getting larger and larger, following a power law Tp (p ≈ -2). The rate equations for hopping can be described by an equivalent circuit consisted by resistors and capacitors. In this perspective, μ are determined to minimize the power generated in the circuit under an electric field . In other words, the gradient of μ should be as small as possible under the Kirchhoff’s current law. Since the distribution of hopping rates is getting wider and wider with decreasing T, μ changes slowly in space but largely in magnitude to satisfy the conditions. [1] N. F. Mott, J. Non-Cryst. Solids 1, 1 (1968). [2] B. Shklovskii and A. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, 1984). [3] V. Ambegaokar, S. Cochran, and J. Kurkijärvi, Phys. Rev. B 8, 3682 (1973).