Tunable dynamical channel blockade in double-dot Aharonov-Bohm interferometers

We study electronic transport through an Aharonov-Bohm interferometer with single-level quantum dots embedded in the two arms. The full counting statistics in the shot-noise regime is calculated to first order in the tunnel-coupling strength. The interplay of interference and charging energy in the dots leads to a dynamical channel blockade that is tunable by the magnetic flux penetrating the Aharonov-Bohm ring. We find super-Poissonian behavior with diverging second and higher cumulants when the Aharonov-Bohm flux approaches an integer multiple of the flux quantum.

Figure 1

The double-dot Aharonov-Bohm interferometer consists of two quantum dots ($u$ and $d$) connected to two leads in parallel. The paths through the dots enclose a magnetic flux $\Phi$, giving rise to Aharonov-Bohm interference.

Figure 2

(Color online) The normalized $n\text{th}$ cumulants ${\kappa }_n/{\kappa }_1$ diverge for $\varphi \to 2\pi m$ in a symmetric system $\left({\Gamma }_L={\Gamma }_R\right)$, due to the competition of two channels belonging to different system states. The width of the divergence is governed by the relaxation rate between these two states.

Figure 3

The current through the double-dot system is subject to Aharonov-Bohm oscillations. These are almost cosinelike so that the current remains finite for $\varphi =0$.

Figure 4

(Color online) The normalized $n\text{th}$ cumulants ${\kappa }_n/{\kappa }_1$ of the nonsymmetric system diverge [left plot: $a=\left({\Gamma }_L-{\Gamma }_R\right)/\left({\Gamma }_L+{\Gamma }_R\right)=-0.9$, right plot: $a=+0.9$]. The width of the divergence is slightly enhanced $a\to -1$ but strongly reduced for $a\to +1$.

Figure 5

(Color online) For stronger coupling to the drain $\left(a<0\right)$ the current associated with the $+$ subspace is larger than that for the $-$ subspace. Additionally, the occupations of the subspaces differ. This results in super-Poissonian statistics. For $a\to 1$ both currents and occupations are equal. This yields Poissonian statistics.

Figure 6

(Color online) Normalized cumulants in the presence of isotropic isospin relaxation (rate ${\Omega }_{\mathbf{I}}=\Gamma /10$). The divergent cumulants are suppressed: while the Fano-factor is sub-Poissonian for the relaxation rate shown, higher cumulants still show super-Poissonian behavior.

Figure 7

(Color online) Normalized cumulants in the presence of singlet-triplet relaxation (rate ${\Omega }_{ST}=\Gamma /200$). The influence of the $S\text{−}T$ relaxation is much stronger than that of the isospin relaxation.

Figure 8

(Color online) Normalized cumulants in the presence of a finite level detuning $\Delta ϵ=1/3\Gamma$. Symmetry of the flux dependence about $\varphi =\pi$ is lost, but enhancement of the cumulants are still clearly visible.

Figure 9

Internal system dynamics for flux $\varphi =\pi$ and strong coupling to the drain $a\to -1$. The double lines denote transitions much faster (with rate $2{\Gamma }_R$) than the single lines (with rates $\propto {\Gamma }_L$).

Figure 10

(Color online) The normalized $n\text{th}$ cumulants ${\kappa }_n/{\kappa }_1$ show no divergence for $\varphi =2\pi m$ if spin is neglected. Instead they assume the values expected for a noninteracting two-level system. At $\varphi =\left(2m+1\right)\pi$ the statistics becomes Poissonian due to an isospin-blockade effect.