Shot noise in transport through two coherent strongly coupled quantum dots

Motivated by activities of several experimental groups we investigate electron transport through two coherent, strongly coupled quantum dots (“double quantum dots”), taking into account both intra- and inter-dot Coulomb interactions. The shot noise in this system is very sensitive to the internal electronic level structure of the coupled dot system and its specific coupling to the electrodes. Accordingly a comparison between experiments and our predictions should allow for a characterization of the relevant parameters. We discuss in detail the effect of asymmetries, either asymmetries in the couplings to the electrodes or a detuning of the quantum dot levels out of resonance with each other. In the Coulomb blockade region super-Poissonian noise appears even for symmetric systems. For bias voltages above the sequential tunneling threshold super-Poissonian noise and regions of negative differential conductance develop if the symmetry is broken sufficiently strongly.

Figure 1

Left panel: Current $I$ and shot noise $S$ vs bias voltage for a double dot system with $k_{\mathrm{B}}T=0.05$, $t=2$, $U=10$, $U_{nn}=5$, and $ϵ=-5.5$ resulting in a doubly occupied ground state $(q=2e)$, all units in meV. The noise $S$ is sub-Poissonian for all bias voltages. This is always the case if the first vertical excitation energy is larger than twice the sequential tunneling threshold, ${ϵ}_{\mathit{co}}>2{ϵ}_{\mathit{seq}}$, see the sketch in the right panel. Current and noise curves are normalized to $I_0=(e∕\hslash )2\Gamma$ and $S_0=(e^2∕\hslash )2\Gamma$, respectively. Right panel: sketch of the low energy spectrum. The nature of the states $G$, $T$, and $B$ is discussed in the text.

Figure 2

Left panel: Current $I$ and shot noise $S$ vs voltage for a double dot system with $k_{\mathrm{B}}T=0.05$, $t=2$, $U=12$, $U_{nn}=4$, and $ϵ=-5.3$ (all energies in meV). Super-Poissonian noise (Fano factor $F>1$) develops in the Coulomb blockade regime. Right panel: low energy spectrum, where now ${ϵ}_{\mathit{seq}}<{ϵ}_{\mathit{co}}<2{ϵ}_{\mathit{seq}}$.

Figure 3

Enlarged low bias region of Fig. 2. $2eI$, $S_{\mathit{red}}$, and $S_{\mathit{irr}}$ are plotted semilogarithmically. The first part of the noise $S_{\mathit{irr}}$ grows with bias as the current, providing a Poissonian noise contribution. The second part of the noise $S_{\mathit{red}}$ becomes appreciable for $V>2({ϵ}_{\mathit{co}}-{ϵ}_{\mathit{seq}})∕e$ and causes the total noise enhancement.

Figure 4

Left panel: Current $I$ and shot noise $S$ vs voltage for a double dot system with $k_{\mathrm{B}}T=0.05$, $t=2$, $U=12$, $U_{nn}=4$, and $ϵ=-6.3$ (all energies in meV). Super-Poissonian noise develops in the entire Coulomb blockade region. Right panel: the corresponding low energy spectrum, where ${ϵ}_{\mathit{co}}<{ϵ}_{\mathit{seq}}$.

Figure 5

Current $I$ (absolute value) and Fano factor $S$ vs voltage for asymmetric coupling in a double dot system with $k_{\mathrm{B}}T=0.05$, $t=2$, $U=10$, and $U_{nn}=5$, $ϵ=-5.5$ (all energies in meV). For strong asymmetry negative differential conductance and super-Poissonian noise appear only for negative bias voltages. Note that due to the asymmetry the total line width $\Gamma ={\Gamma }_{\mathrm{L}}+{\Gamma }_{\mathrm{R}}$ and the current are reduced relative to the symmetric case.

Figure 6

Current $I$ (absolute value) and Fano factor $S$ vs voltage for various values of level detuning ${ϵ}_{12}$ (all energies in meV) but with symmetric couplings to the leads and other energy parameters equal to the situation depicted in Fig. 1. Stronger detuning ${ϵ}_{12}$ leads to NDC and eventually super-Poissonian noise. In contrast to Fig. 5, the bias (energy) positions of current and noise features are changed due to the modified dot Hamiltonian.

Figure 7

Current $I$ (absolute value) and Fano factor $S$ vs voltage for various “hopping” parameters $t$ and a level detuning of ${ϵ}_{12}=0.2$ (all energies in meV), symmetric coupling to the leads and otherwise same parameters as in the situation depicted in Fig. 1. Reduced hopping causes a smaller total current although super-Poissonian noise and NDC develop similarly as in Fig. 6.

Figure 8

Current $I$ (absolute value) and Fano factor $S$ vs voltage for different values of hopping $t$ (units in meV) without level detuning $({ϵ}_{12}=0)$ for symmetric couplings and same parameters as in the situation depicted in Fig. 1. Note that current and Fano factor are both symmetric under the reverse of bias voltage, since there is no source of asymmetry.