Dielectric formalism for a quasi-one-dimensional electron gas. III. Arrays of quantum wires

Quantum transport equations for the one-particle distribution function, pertinent to one-dimensional or two-dimensional periodic arrays of quasi-one-dimensional electron gases (quantum wires), are derived from first principles. The electrons are assumed to interact weakly with an external system and/or with each other. The lateral electron confinement is modeled with a square or parabolic well and the vertical one with a triangular or square well. Screening is treated dynamically and the collision integrals are expressed in terms of the dielectric functions and potential correlators. The results are valid for periods large enough that tunneling between the wires can be neglected. The derived energy and momentum relaxation frequencies, with the help of a drifted Fermi-Dirac distribution function, are given in a form suitable for applications. The momentum relaxation frequency and the mobility are evaluated for an array of quantum wires in interaction with volume and sheet impurities at different distances from the array and it is shown that the Coulomb coupling between the quantum wires can have pronounced effects on both quantities. Both types of the considered lateral confinement lead to similar results with small quantitative differences when only the lowest lateral subband is occupied.