Nonmonotonic behaviors of Fano factor in double quantum dot connected with Luttinger liquid electrodes

In this study, we discuss the behavior of the Fano factor in a double quantum dot (DQD) connected with Luttinger liquid (LL) electrodes. At the Toulouse point, we study the dependence of the Fano factor on the bias voltage, the energy level of the dots, the interdot coupling, and the asymmetry parameter. We show that the behavior of the Fano factor in a DQD is similar to that in a single quantum dot (SQD); however, it behaves nonmonotonically with bias voltage and three local extrema can occur. The condition for the occurrence of nonmonotonic behavior is determined, and it is shown that local extrema result from the mixing of the bare energy levels of the dots caused by the interdot coupling. The influence of the Klein factor on the conductance in a DQD and the limitation of the perturbation calculation for a DQD are discussed.