Theoretical study of electric conductance through nanostructures in terms of the phase-shift

A simple expression of the electric conductance through a nanostructure connected to two electrodes is obtained by using the phase-shift analysis. The Green function theory applicable to the nonequilibrium system is employed to formulate the electric conductance. The 0 bias limit, i.e., the linear response approximation is taken. The relation between Green functions and phase-shifts is obtained by extending the method applied to the single impurity problem in the metal. It is shown that a channel does not contribute to the conductance if its phase-shift is an integer multiple of π. Also shown is the importance of the effect due to multiple orbitals in nanostructures. Some concrete examples leading to simpler forms are given.