FERMI-LIQUID THEORY FOR A CONDUCTANCE THROUGH AN INTERACTING REGION ATTACHED TO NONINTERACTING LEADS

We study the conductance for the current through a finite interacting, possibly disordered region attached to two noninteracting leads withi n the Kubo formalism applying the perturbation theory for the local Fe rmi liquid developed by Yamada & Yosida and by Shiba to this finite re gion. Assuming the validity of the perturbation expansion in the Coulo mb interaction and the time reversal symmetry for the normal scatterin g potential in the finite region, we find that the contributions of th e vertex correction to the de conductance disappear at T = 0 if the cu rrents are measured in the leads. Consequently, the conductance is exp ressed as g = (2e(2)/h) \t(0)\(2). Here t(0) is the transmission coeff icient for single-particle-like excitation at the Fermi energy and is introduced by using the Green's function. The results are generalized to a quasi-one-dimensional system with a number of scattering channels .