We study the case of which a non-interacting quantum dot is connected to two one-dimensional leads, one interacting and another not. We derive an exact formula of current passing through the system in terms of non-equilibrium Green’s functions of the interacting lead under an effective action. This formula is used to study the tunneling current of the system in different temperature regimes. In particular, for a given interaction parameter ϑ of the interacting lead described by spinless Luttinger Liquid, the differential conductance scales as T^ϑ−1 at high temperature and T^ϑ at low temperature. Meanwhile, at zero temperature, the differential conductance has a resonance peak near the energy level of the quantum dot, and scales as V^ϑ−2 very far away for the resonance position. In off-reso...[ Read more ]

We study the case of which a non-interacting quantum dot is connected to two one-dimensional leads, one interacting and another not. We derive an exact formula of current passing through the system in terms of non-equilibrium Green’s functions of the interacting lead under an effective action. This formula is used to study the tunneling current of the system in different temperature regimes. In particular, for a given interaction parameter ϑ of the interacting lead described by spinless Luttinger Liquid, the differential conductance scales as T^ϑ−1 at high temperature and T^ϑ at low temperature. Meanwhile, at zero temperature, the differential conductance has a resonance peak near the energy level of the quantum dot, and scales as V^ϑ−2 very far away for the resonance position. In off-resonance region, the differential conductance goes as V^ϑ, which agrees with the result of direct-tunneling. These predictions can be verified via resonant tunneling experiment, and it provides a way to measure the interaction strength of Luttinger Liquid. Finally, we also study (in the concluding chapter and appendix) the case of which the interacting lead consists of helical edge states.