Eur. Phys. J. B 70, 513-521 (2009)
https://doi.org/10.1140/epjb/e2009-00244-x

Conductance distribution in two-dimensional localized systems with and without magnetic fields

¹ Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
² Departamento de Física Aplicada, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
³ Departamento de Física-CIOyN, Universidad de Murcia, 30071 Murcia, Spain

Corresponding author: ^a javier.prior@upct.es

Received: 27 May 2009
Published online: 15 July 2009

Abstract

We have obtained the universal conductance distribution of two-dimensional disordered systems in the strongly localized limit. This distribution is directly related to the Tracy-Widom distribution, which has recently appeared in many different problems. We first map a forward scattering paths model into a problem of directed random polymers previously solved. We show numerically that the same distribution also applies to other forward scattering paths models and to the Anderson model. We show that most of the electric current follows a preferential percolation-type path. The particular form of the distribution depends on the type of leads used to measure the conductance. The application of a moderate magnetic field changes the average conductance and the size of fluctuations, but not the distribution when properly scaled. Although the presence of magnetic field changes the universality class, we show that the conductance distribution in the strongly localized limit is the same for both classes.