Finite-frequency Shot Noise Of Electron Through A Serially Coupled Double Quantum Dot System With Effective Spin-orbit Coupling Field

Coupled double quantum dots(DQDs)is an ideal system and research platform for studying various quantum mechanical effects and developing related quantum technologies for its inherent quantum coherence and each quantum dot energy level can be independently regulated by gate voltage.Among all kinds of spin devices based on coupled double quantum dots,how to effectively control the freedom of electronic spin in small scale space is a very important topic.Because the electric field can focus in the small scale space,the control of electron spin by the electric field adjustable spin-orbit coupling effect has become one of the hot research fields in condensed matter physics.However,for coupling double quantum dots constructed with different structures and materials,the size of the effective spin-orbit coupling field is usually different,and the accurate acquisition of its size will be helpful for in-depth analysis and comprehensive understanding of the manipulation of electron spin freedom.However,how to quantitatively ontain the effective spin-orbit coupling field of the coupled double quantum dots based on the quantum transport characteristics is still an open subject.In addition,the finite-frequency noise spectrum can provide more information about its transport characteristics and parameters characterizing its internal dynamics than the average current(differential conductance)and zero frequency scattered particle noise cannot.However,how to quantitatively extract the magnitude of the spin-orbit coupling field based on the finite-frequency shot noise has not been revealed.In this paper,we study the finite-frequency shot noise of electron transport through a serially coupled DQD system with spin-orbit coupling based on an effective particle number resolved quantum master equation and Mac Donald formula.It is demonstrated that the existence of peaks and dips of the finite-frequency shot noise results from the quantum coherence of the serially coupled DQD system,whereas the positions of peaks and dips are determined by the energy difference of the coherent singly-occupied eigenstates that forming the off-diagonal elements of the reduced density matrix.Here,the peaks and dips correspond to the degeneracy of the corresponding the energy difference of that are one and two,respectively.In particular,the spin polarization of the electrode and the QD-electrode tunnel coupling strength have no influence on the positions of peaks and dips,but have some influences on the width of peaks and dips,as well as the values of peaks and dips.Therefore,we can quantitatively determine the magnitude of the SOC and the spin-conserving hopping between the two QDs based on the positions of peaks and dips of the finite-frequency shot noise for different values of the external magnetic field.These results can provide a theoretical basis for effective manipulation of the spin degrees of freedom of coupled DQD system based on the SOC.