Resonant tunneling through an Anderson impurity. I. Current in the symmetric model

We compute the nonlinear current-voltage characteristic for resonant tunneling through an Anderson impurity. For the symmetric Anderson model with the impurity equally coupled to the two leads the differential conductance has structure similar to the zero-bias spectral function. The nonlinear current-voltage characteristic is thus a useful probe of the Kondo resonance. In fact, because a finite voltage tends to destroy the Kondo resonance, the differential conductance is actually sharper than the zero-bias spectral function. A finite voltage is, however, not equivalent to raising the temperature, since the distribution function at the impurity for a finite bias is not a Fermi function. Throughout the paper we emphasize that not all approximations for the spectral function or self-energy lead to a current conserving approximation. In particular, the order ${\mathit{U}}^2$ self-energy of Yosida and Yamada, and Horvatic and Zlatic does not, in general, lead to a current-conserving approximation. Only in the case considered here of the symmetric Anderson model with the impurity equally coupled to the two leads does it conserve current. In the process of computing the current we develop a formula for tunneling between two perfect leads through a central site containing an arbitrary many-body interaction. This formula agrees with earlier expressions for the current in the limit where the scattering rate onto the central site is independent of energy; however, in the most general case it is not a simple generalization of the noninteracting result.