Quantum transport through nanostructures in the singular-coupling limit

Geometric symmetries cause orbital degeneracies in a molecule’s spectrum. In a single-molecule junction, these degeneracies are lifted by various symmetry-breaking effects. We study quantum transport through such nanostructures with an almost degenerate spectrum. We show that the master equation for the reduced density matrix must be derived within the singular-coupling limit as opposed to the conventional weak-coupling limit. This results in strong signatures of the density matrix’s off-diagonal elements in the transport characteristics.

Figure 1

(Color online) Numerical evaluation of the stationary current Eq. (9) through an interacting two-level Anderson model, $t_{\text{L}\uparrow }=t_{\text{R}\downarrow }=1$, $t_{\text{L}\downarrow }=t_{\text{R}\uparrow }=1.5$, $U=2.35$, and $k_{\text{B}}T=0.02$. The tunnel amplitudes $t_{\alpha \sigma }$ and the splitting $\Omega$ are measured in units of $\frac{2\pi }{\hslash }{\nu }_0$. (a) illustrates the difference between the description by the degenerate master equation [Eqs. (7, 8)] (solid) and the $\Omega =0$ rate equation, which is obtained from the master equation by setting ${\rho }_{\uparrow \downarrow }=0$ (dashed). Both models are evaluated at $e{V}_{\text{g}}=0$ in order to highlight the quantitative as well as qualitative discrepancy. In (c) and (d), we show a full scan of the $\left(e{V}_{\text{g}},e{V}_{\text{sd}}\right)$ plane for both equations illustrating the fundamental difference of the dynamics due to the two equations in the parameter space. While the rate-equation result is the familiar sequence of steps in the stationary current, the master-equation result shows a strong current suppression for voltages below the double-charging threshold. Using the master equation in the singular-coupling limit as it is derived in the text, we interpolate the two different curves of (a) by letting $\Omega \to \infty$ in (b).