The Kubo formula for the conductance of finite systems in the ballistic regime: a simple algorithm

Abstract

The author presents a method for obtaining the conductance within the linear response approximation of a disordered system of finite cross section described by a tight-binding Hamiltonian. This method is an extension of previous work in which he proposed a numerical algorithm for evaluating the Kubo formula in the spirit of the recursion method. He obtains simple recursive equations for the conductance that can be easily computed. As an application the problem of ballistic transport through a constriction is studied using a confining model potential that allows one to investigate the dependence of the conductance quantisation as a function of Fermi energy, gate voltage and channel length. It is found that the conductance steps as a function of gate voltage are sensitive to the channel length. The possible extension of this work for use in studying the AC transport in these systems is briefly discussed.