Maximum entropy models and quantum transmssion in disordered systems

Summary

Abstract

We consider the conductance g of disordered systems where the electronic quantum coherence extends over a large scale. In the first part, we show characteristic conductance fluctuations driven by a variation of the applied magnetic field B or of the Fermi energy E_F, which have been observed at very low temperature in a mesoscopic wire where the carrier density is controlled by a gate. Following the gate voltage, the wire is a conductor (g ≫ 1) or an insulator (g ≪ 1). The fluctuations of g have a normal distribution with a universal variance for conductors and a very large log-normal distribution for insulators. In a macroscopic insulator, the magnetoconductance is mostly governed by the field dependence of the localization length §. In the second part, we review a random matrix theory adapted to the transfer matrix. This macroscopic approach to quantum transmission allows us to describe in a unified and simple way the conductance fluctuations observed in conductors and insulators, and to predict new universal symmetry breaking effects on the variance of g and on §. This approach, based on symmetry considerations and on a maximum entropy criterion, gives the eigenvalue distribution of t.t (t is the transmission matrix) in terms of a simple Coulomb gas analogy. In quasi-one dimension, the analogy is valid for conductors and insulators. Outside quasi-one dimension, we derive analytically the eigenvalue correlation functions of our maximum entropy model that we compare to their direct numerical evaluations from microscopic hamiltonians.