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 = (2e²/h) ∫ dε (- ∂ f / ∂ ε) T(ε), is introduced for interacting electrons. Here f(ε) is the Fermi function, and the transmission probability 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 T(ε) using the order U² self-energy and current vertex which satisfy a generalized Ward identity. The results show that T(ε) has much information about the excitation spectrum: 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.