Toulouse limit for the nonequilibrium Kondo impurity: Currents, noise spectra, and magnetic properties

We present an exact solution to the nonequilibrium Kondo problem, based on a special point in the parameter space of the model where both the Hamiltonian and the operator describing the nonequilibrium distribution can be diagonalized simultaneously. Through this solution we are able to compute the differential conductance, spin current, charge-current noise, and magnetization, for arbitrary voltage bias. The differential conductance shows the standard zero-bias anomaly and its splitting under an applied magnetic field. A detailed analysis of the scaling properties at low temperature and voltage is presented. The spin current is independent of the sign of the voltage. Its direction depends solely on the sign of the magnetic field and the asymmetry in the transverse coupling to the left and right leads. The charge-current noise can exceed ${2eI}_c$ for a large magnetic field, where $I_c$ is the charge current. This is not seen in noninteracting quantum problems, but occurs here because of the tunneling of pairs of electrons. The finite-frequency noise spectrum has singularities at $ħ\Omega =\pm 2\mathrm{eV},$ which cannot be explained in terms of noninteracting electrons. These singularities are traced to a different type of pair process involving the simultaneous creation or annihilation of two scattering states. The impurity susceptibility has three characteristic peaks as a function of magnetic field, two of which are due to interlead processes and one is due to intralead processes. Although the solvable point is only one point in the parameter space of the nonequilibrium Kondo problem, we expect it to correctly describe the strong-coupling regime of the model for arbitrary antiferromagnetic coupling constants and to be qualitatively correct as one leaves the strong-coupling regime.