Correlation-Induced Resonances in Transport through Coupled Quantum Dots

We investigate the effect of local electron correlations on transport through parallel quantum dots. The linear conductance as a function of gate voltage is strongly affected by the interplay of the interaction $U$ and quantum interference. We find a pair of novel correlation-induced resonances separated by an energy scale that depends exponentially on $U$. The effect is robust against a small detuning of the dot energy levels and occurs for arbitrary generic tunnel couplings. It should be observable in experiments on the basis of presently existing double-dot setups.

Figure 1

System of coupled quantum dots with common leads.

Figure 2

Generic results for $G(V_g)/(e^2/h)$ (solid lines), $⟨n_1⟩$ (dashed lines), and $⟨n_2⟩$ (dashed-dotted lines) at different $U$ obtained from the FRG with ${\Gamma }_1^L=0.27\Gamma$, ${\Gamma }_1^R=0.33\Gamma$, ${\Gamma }_2^L=0.16\Gamma$, ${\Gamma }_2^R=0.24\Gamma$, $\varphi =\pi$, and $\delta =0$. The two novel correlation-induced resonances are visible in the lower panels (large $U$), near $V_g=0$.

Figure 3

Comparison of FRG (lines) and NRG (symbols) results for the same parameters as in Fig. 2. Left: $G(V_g)$ for different $U$ ($U=3.5\Gamma$: solid line and circles; $U=7\Gamma$: dashed line and squares; $U=14\Gamma$: dashed-dotted line and diamonds). Right: The resonance position $V_{\mathrm{CIR}}$.

Figure 4

Renormalized dot level positions $V_1/\Gamma$ (dashed line) and $V_2/\Gamma$ (dashed-dotted line). The thick solid line is the product $V_1{V}_2/{\Gamma }^2$. The thin solid line lies at $-4{\Gamma }_1^L{\Gamma }_2^L/{\Gamma }^2$, and its intersections with the thick solid line determine the peak positions of $G$. The two crossings indicated by the arrows are at $V_g=\pm V_{\mathrm{CIR}}$. The parameters are $U=10\Gamma$, ${\Gamma }_1^L={\Gamma }_1^R=0.3\Gamma$, ${\Gamma }_2^L={\Gamma }_2^R=0.2\Gamma$, $\varphi =\pi$, and $\delta =0$ ($U_c/\Gamma \approx 5.05$ from FRG).

Figure 5

Dependence of $G(V_g)$ on the level splitting $\delta$. The parameters are $U=3\Gamma$, ${\Gamma }_1^L=0.7\Gamma$, ${\Gamma }_1^R=0.2\Gamma$, ${\Gamma }_2^L=0.02\Gamma$, ${\Gamma }_2^R=0.08\Gamma$, and $\varphi =0$ ($U_c/\Gamma \approx 0.842$ from FRG).