Perturbative treatment of the multichannel interacting resonant-level model in steady-state nonequilibrium

We consider the steady-state nonequilibrium physics of the multichannel interacting resonant-level model in the weak coupling regime. By using the scattering state method we show in agreement with the rate equations that the negative differential conductance at large enough voltages is due to the renormalization of the hopping amplitude and neither the orthogonality catastrophe nor the voltage dependence of the density of states at the resonant-level. The moderate role of the voltage dependence of the density of states on the dot is also discussed.

Figure 1

(Color online) Possible realization of the multichannel interacting resonant-level model. A single level quantum dot is attached to several lead electrodes. Hopping between the dot level and the neighboring sites of the leads $N=1,2$ are present in addition to the short range Coulomb interaction acting between the dot electron and the electrons on the neighboring sites of all $N$ electrodes. The voltage is applied between leads 1 and 2.

Figure 2

The bare Coulomb vertex (a) and hybridization vertex (b). The solid lines represent the conduction electron propagators in different channels and the dashed line the electron on the dot. Diagram (c) is the self energy, (d) the vertex correction to the hopping in first order and (e) in second order. The flow of time agrees with the direction of the dotted line.

Figure 3

(Color online) The normalized impurity density of states for $N=10$ channels at ${\varrho }_{0}U=0.1$ and different values of the bias voltage. ${\Gamma }_0=2\pi {\varrho }_0{t}_0^2$.

Figure 4

(Color online) $I\text{−}V$ characteristics with the clear evidence of the nonmonotonic behavior for the $N=10$ channel interacting resonant-level model for different values of the Coulomb repulsion.