Coherent transport through an interacting double quantum dot: Beyond sequential tunneling

Various causes for negative differential conductance in transport through an interacting double quantum dot are investigated. Particular focus is given to the interplay between the renormalization of the energy levels due to the coupling to the leads and the decoherence of the states. The calculations are performed within a basis of many-particle eigenstates and we consider the dynamics given by the von Neumann equation taking into account also processes beyond sequential tunneling. A systematic comparison between the levels of approximation and also with different formalisms is performed. It is found that the current is qualitatively well described by sequential processes as long as the temperature is larger than the level broadening induced by the contacts.

Figure 1

(Color online) Current versus bias voltage and detuning $\Delta =E_{\alpha }-E_{\beta }$ for (a) $\Omega =\Gamma ∕10$, (b) $\Omega =\Gamma ∕4$, and (c) $\Omega =2\Gamma$ using the first-order approach (1vN) including the real parts. The other parameters are $E_{\alpha }+E_{\beta }=0$, ${\Gamma }_L={\Gamma }_R=\Gamma ∕2$, $k_{B}T=\Gamma$, $U=10\Gamma$, and $W=35\Gamma$.

Figure 2

(Color online) Current versus bias voltage for different detunings $\Delta$. All other values like in Fig. 1. The dashed lines are the 1vN results including the real parts, the dashed-dotted lines are the 1vN results without the real parts (noR), and the full lines are the 2vN results. The values from Eqs. (2, 3) for $\Delta =0$ and $\Delta =\pm \Gamma ∕4$ or $\Delta =\pm 2\Gamma$ (which do not depend on the sign of $\Delta$) are shown on the $y$ axis. We only show positive bias here, as the negative bias result corresponds to the results with the opposite sign of $\Delta$ for the symmetric coupling to contacts considered here.

Figure 3

(Color online) Results for low temperature $k_{B}T=\Gamma ∕5$ and $\Omega =\Gamma ∕10$. All other parameters as Figs. 1, 2. Upper panel: results of the 1vN approach. Lower panel: comparison of 1vN, 2vN, and the 1vN without real parts (noR) approaches. The 1vN strongly exaggerates the features at the current steps for this low temperature in comparison to the 2vN approach. The 1vN without real parts is qualitatively incorrect.

Figure 4

(Color online) Results for $\Delta =0$, $\Omega =\Gamma ∕10$, and different values of $U$. All other parameters as in Figs. 1, 2.

Figure 5

(Color online) The current taking into account both spin directions and an intradot Coulomb repulsion of $U_{\mathrm{intra}}=30\Gamma$ calculated by the 1vN approach. All other parameters as Fig. 1a.