Finite-frequency Shot Noise In A Serially Coupled Double Quantum Dot System Described By Generalized Hubbard Model

In the coupled double quantum dot(QD)system,an accurate understanding of the two-electron-interaction-induced electron hopping and spin exchange processes will help in the spin manipulation of a coupled quantum dot system.In general,the Hamiltonian of a coupled double quantum dot system is described by the Hubbard model and contains only an electron hopping process between two quantum dots.However,when the usual two-electron interaction is considered,the second-quantized Hamiltonian,that is,the coupled double quantum dot Hamiltonian described by the generalized Hubbard model,will also contains the three new hopping processes: the electron occupation modulated hopping processes,the electron anti-parallel-spin exchange hopping processes,and the electron-pair hopping processes.In electron-less quantum dot systems,quantum effects associated with different electron hopping processes and spin exchange processes are crucial for manipulating the spin degrees of freedom of electrons.Therefore,how to determine the existence of these three new hopping processes in coupled double quantum dots is an important topic worth studying.On the other hand,current finite frequency shot noise spectrum can provide more information about the internal dynamical features of the coupled quantum dot system relative to the average current and zero-frequency shot noise through a coupled quantum dot system.This provides a way to explore whether there are three new hopping processes predicted by generalized Hubbard models in coupled double QD system.In this paper,the particle number-resolved quantum master equations for coupled double QD systems are first derived.Then the effect of three novel hopping processes predicted by the generalized Hubbard model in coupled double QD systems at different temperatures on the average current are investigated.Finally,using an effective particle number resolved quantum master equation,in the two cases of energy level resonance and energy level detuning,the influences of the three new hopping processes,the spin polarizability of the left and right electrodes,and the tunneling coupling strength between left and right electrodes and quantum dots,on the finite-frequency shot noise in a serially coupled double QD system are studied.Based on the above conclusions,the feasibility of using the number of peaks and dips on the current finite frequency shot noise spectrum of the coupled double quantum dot system to detect the three new hopping processes predicted by the generalized Hubbard model is discussed.Numerical results show that the number of steps in the average current cannot be used to probe the three new hopping processes predicted by the generalized Hubbard model.In the presence of three new hopping processes,the maximum of the sum of the peaks and dips of the current finite frequency shot noise spectrum of two quantum dots under resonance and detuning is 8.Conversely,when no three new hopping processes exist,the maximum of the sum of the corresponding number of peaks and dips is 5 and 7,respectively.It is also obtained that the spin polarizability and electron tunneling coupling strength of the ferromagnetic electrode do not affect the number,position,but affect their depth and width.The above research results show that in the current finite frequency shot noise spectrum of the series-coupled double QD system,the number of peaks and dips can be used as the criterion for the existence of the three new hopping processes predicted by the generalized Hubbard model,provide a theoretical scheme for detecting three new hopping processes predicted by the generalized Hubbard model.