Transmission Probability for Interacting Electrons Connected to Reservoirs

Abstract

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 $g=(2e^2/h)\int d\epsilon (-\partial f/\partial \epsilon )\mathcal{T}(\epsilon )$, is introduced for interacting electrons. Here $f(\epsilon )$ is the Fermi function, and the transmission probability $\mathcal{T}(\epsilon )$ 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 $\mathcal{T}(\epsilon )$ using the order $U^2$ self-energy and current vertex which satisfy a generalized Ward identity. The results show that $\mathcal{T}(\epsilon )$ has much information about the excitation spectrum: $\mathcal{T}(\epsilon )$ 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.

18 pages, 16 figures

References in corpus (1)

• Quasi-particle description for the transport through a small interacting system

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