Calculation of the phonon-free resistances of three-dimensional disordered quantum wires

This work is a theoretical study of the elastic resistances of fully three-dimensional quantum wires. A length L of disordered wire is connected to two semi-infinite perfect leads. The conductance G with respect to a small electrochemical potential difference between particle reservoirs at either extremity of the system is then calculated. The calculations employ an orthonormal Is tight-binding model. The Green function, and hence the conductance, for the system is calculated exactly in the disorder. The configurational averages of G, R = 1/G, InG and InR are studied as a function of L. The slope of (R) versus L in the diffusive regime is used to estimate the bulk residual resistivity of the respective disordered material. (InR) in the localisation regime is used to estimate the localisation length in the disordered wire. The configurational fluctuations of G and InG as a function of L are also studied. The standard deviation of G exhibits a peak at a wire length close to the electronic mean free path, giving an indication of the transition from the ballistic to the diffusive regime. The height of the peak is related to the ratio of the mean free path to the transverse dimension of the wire, giving an indication of the nature (ballistic versus diffusive) of the transverse electron motion in the wire. The relative fluctuation of InG is divergent at a wire length close to the localisation length, giving an indication of the transition from the diffusive to the localisation regime. Estimates of the Ohmic resistivity from the diffusive regime are used to study the interplay between interfacial roughness and bulk impurities in a metallic bilayer. This type of calculation can be used to model the giant magnetoresistance effect in magnetic multilayers.