Coherent Transport in Quantum Electron Waveguides

In the mesoscopic regime (when electrons move coherently across the sample), measurement leads have a large, sometimes dominant, effect on a resistance measurement. In order to address the increasingly large number of experiments in this regime, we have developed a general method of calculating the resistance of a coherent multiprobe structure in an arbitrary magnetic field. The first issue we address is that of the correct expression for the resistance of a multiprobe structure. We have carried out a rigorous linear response calculation which when cast into the language of a scattering problem yields the resistance formula introduced by Buttiker based on Landauer-type arguments. Thus, we find that the resistance can always be expressed in terms of quantities at the Fermi Energy evaluated at the boundaries of the coherent region. We then use this linear response expression and the recursive Green function method to calculate the resistance for three physical situations of experimental interest.