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

►We calculate the electric conductances of atomic contacts consisting of Au, Al and Pt based on nonequilibrium Green's function theory and phase shift analysis. ►We analytically introduce the charge neutrality condition through the Friedel sum rule. ►We have analytically shown that the electric conductances are quantized and can increase when the distance between two electrodes increases. ►We conclude that the increment of the electric conductance is interpreted by the Friedel sum rule.