Universal electric current of interacting resonant-level models with asymmetric interactions: An extension of the Landauer formula

We study the electron transport in open quantum-dot systems described by the interacting resonant-level models with Coulomb interactions. We consider the situation in which the quantum dot is connected to the left and right leads asymmetrically. We exactly construct many-electron scattering eigenstates for the two-lead system, where two-body bound states appear as a consequence of one-body resonances and the Coulomb interactions. By using an extension of the Landauer formula, we calculate the average electric current for the system under bias voltages in the first order of the interaction parameters. Through a renormalization-group technique, we arrive at the universal electric current, where we observe the suppression of the electric current for large bias voltages, i.e., negative differential conductance. We find that the suppressed electric current is restored by the asymmetry of the system parameters.

Figure 1

The two-lead interacting resonant-level model. Electrons flow only upward due to the linearized dispersion relations of the leads.

Figure 2

The two-electron scattering eigenfunctions for the incident two electrons coming in through the lead 1. The dotted circles surrounding the two electrons indicate the two-body bound states, which appear only when at least one of the electrons is reflected.

Figure 3

$I\text{−}V$ characteristics of the rescaled universal electric current for $\overline{U}=0.5$ with $\delta =0,0.1,0.2,0.3,0.4$.