Green's function technique for a two-electrode mesoscopic system under bias

We present a Green’s function technique for studying the nonlinear conductance of a nanocontact system with two electrodes at different chemical potentials. The retarded Green’s function for a single-impurity Anderson model with two reservoirs is obtained in terms of a $5\times 5$ matrix in which the effect of bias is contained. A complete set of basis vectors for the single-impurity Anderson model has been provided before formulating the Green’s function. Finally, we present a self-consistent method to fix the undetermined quantities existing in the matrix elements for the retarded Green’s function.