Effect Of The Effective Spin-orbit Coupling Field On Electron Counting Statistics In A Serially Coupled Double Quantum Dot System

Due to experimental adjustability of relevant parameters in the coupled-quantum-dots system,its quantum transport characteristics have become a research focus in the low-dimension quantum system.In particular,the spin-orbit coupling effect can provide an approach to efficiently control electron spin under the condition of no external magnetic field.Compared to magnetic field,electric fields are easier to gather and shield in small spaces.Therefore,the influence of the spin-orbit coupling effect on quantum transport characteristics of the coupled-quantum-dot system has aroused wide research attention.On the other hand,it has been experimentally verified that the high-orbit current cumulant moment can provide more electronic transport information that average current and differential conductance cannot reveal.Recently,in series coupled double quantum dot systems and two-level quantum dots,the shot noise and skewness of the current can be qualitatively obtained when the effective spin-orbit coupling field direction is parallel or perpendicular to the electrode spin polarization direction.However,the effect of the effective spin-orbit coupling field direction and magnitude on the statistical properties of electron counts in coupled quantum dot systems has not been revealed.Firstly,we present the full counting statistics formalism based on an effective particle-number-resolved quantum master equation,and outline the procedure to calculate it.Secondly,discussing the effects of ferromagnetic electrode spin polarization,quantum dot energy detuning,external magnetic field strength,spin-orbit coupling magnitude and orientation,coupling symmetry of system with left electrode and right electrode on the first-third order cumulants in the model of the serially quantum dots.Results has been obtained as follows:(1)Compared with two quantum dots at the same level,the effect of spin-orbit coupling orientation to the first-third order cumulants of current is bigger when two quantum dots have energy levels detuned.And when the magnitude of detuning of energy levels is similar to the magnitude of the coupling strength between quantum dots,the first-third order is more obvious;(2)When the magnitude of spin-orbit coupling field is smaller than the coupling magnitude between quantum dots,the first-third order cumulants of current will have a more obvious change with the change of the spin-orbit coupling strength.(3)When the angle between spin-orbit coupling field orientation and the spin quantification axis is small,the first-third order cumulants of current will change more obviously with the change of the spin-orbit coupling field orientation;(4)Only when the coupling strength between the system with the source is much larger than the coupling strength between the system with the source drain,shot noise and skewness appears the super-Poisson distribution.