Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2001-06-03
J. Phys. Soc. Jpn. 70, 2666 (2001)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
18 pages, 16 figures
Scientific paper
10.1143/JPSJ.70.2666
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 $g = (2e^2/h) \int d\epsilon (- \partial f / \partial \epsilon) {\cal T}(\epsilon)$, is introduced for interacting electrons. Here $f(\epsilon)$ is the Fermi function, and the transmission probability ${\cal T}(\epsilon)$ 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 ${\cal T}(\epsilon)$ using the order $U^2$ self-energy and current vertex which satisfy a generalized Ward identity. The results show that ${\cal T}(\epsilon)$ has much information about the excitation spectrum: ${\cal T}(\epsilon)$ 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.
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