Coulomb-interaction effects in full counting statistics of a quantum-dot Aharonov-Bohm interferometer

We study the effect of Coulomb interaction on the full counting statistics of an Aharonov-Bohm (AB) interferometer with a single-level quantum dot in one arm in the regime of weak dot-lead and lead-lead tunnel couplings. In the absence of Coulomb interaction, the interference processes are of nonresonant nature with an even AB flux dependence and obey bidirectional Poissonian statistics. For large charging energy, the statistic of these processes changes. In addition, processes of resonant nature with an odd flux dependence appear. In the limit of strongly asymmetric tunnel couplings from the dot to the left and right leads, their statistics is found to be strongly super-Poissonian.

Figure 1

The quantum-dot ABI. Two equilibrium reservoirs are connected by a direct tunneling path and one in which a QD is embedded. Together, the paths enclose a magnetic flux $\Phi$.

Figure 2

Generalized Fano factors ${\kappa }_{\text{cos},\text{sin}}^{\left(n\right)}/I_{\text{cos},\text{sin}}$ in the shot-noise regime ${\mu }_L⪢ϵ⪢{\mu }_R$. ${\kappa }_{\text{cos},\text{sin}}^{\left(n\right)}$ is the $\text{cos}\varphi$- ($\text{sin}\varphi$-) dependent part of the $n\text{th}$ cumulant ($n=2$, noise; $n=3$, skewness, etc.). (a) Cosine-dependent generalized Fano factors determined by off-resonant processes. The value 1 is assumed at ${\Gamma }_L/{\Gamma }_R=1/2$. (b) Sine-dependent generalized Fano factors determined by on-resonant processes. They approach $2^n-1$ for ${\Gamma }_L⪢{\Gamma }_R$ or ${\Gamma }_L⪡{\Gamma }_R$, while the minimum lies at ${\Gamma }_L/{\Gamma }_R=1/2$ and has the value $\left(2^n-1\right)/2^{n-1}$.

Figure 3

Logarithmic plots of the $n\text{th}$ cumulants ${\kappa }_{\text{QPC}}^{\left(n\right)}$ [in the presence of the QPC detector (black) from Eq. (23)] and ${\kappa }_{\text{sin}}^{\left(n\right)}$ [without the QPD detector (gray) from Eq. (17)] in the shot-noise regime ${\mu }_L⪢ϵ⪢{\mu }_R$ (such that $f_L=1,f_R=0$). The value 1 is plotted for reference.