Theoretical study of electric conductance of atomic contact with the Friedel sum rule

We analyze the electric conductance through nanostructure bridges in terms of phase-shifts, which satisfy the Friedel sum rule. The phase-shifts are given by solving the eigenvalue equation obtained by extending the method applied to a single impurity problem in a metal. We introduce the charge neutrality condition through the Friedel sum rule. It is analytically shown that the electric conductance is quantized and can increase as the two electrodes separate under the condition in which the phase-shifts satisfy the Friedel sum rule.