Transmission Probability for Interacting Electrons Connected to Reservoirs
Transport through small interacting systems connected to noninteracting leads is studied based on the Kubo formalism using a Eliashberg theory of the analytic properties of the vertex part. The transmission probability, by which the conductance is expressed as $g = (2e^2/h) \int dε (- \partial f / \partial ε) {\cal T}(ε)$, is introduced for interacting electrons. Here $f(ε)$ is the Fermi function, and the transmission probability ${\cal T}(ε)$ is defined in terms of a current vertex or a three-point correlation function. We apply this formulation to a series of Anderson impurities of size N (=1,2,3,4), and calculate ${\cal T}(ε)$ using the order $U^2$ self-energy and current vertex which satisfy a generalized Ward identity. The results show that ${\cal T}(ε)$ has much information about the excitation spectrum: ${\cal T}(ε)$ has two broad peaks of the upper and lower Hubbard bands in addition to N resonant peaks which have direct correspondence with the noninteracting spectrum. The peak structures disappear at high temperatures.