with the rapid progress in miniaturization of the solid - state devices , the effect of carriers spin in semiconductor has attracted considerable attention for its potential applications in photoelectric devices and quantum computing . the traditional standard method of spin control depends on the spin injection technique , with mainly relies on optical techniques and the usage of a magnetic field or ferromagnetic material . due to its unsatisfactory efficiency in nano - scale structures , generating and controlling a spin - polarized current with all - electrical means in mesoscopic structures but if a device is formed in a semiconductor two - dimensional electron gas system with an asymmetrical - interface electric field , rashba spin  orbit interaction ( rsoi ) will occur . the rsoi is a relativistic effect at the low - speed limit and is essentially the influence of an external field on a moving spin . it can couple the spin degree of freedom to its orbital motion , thus making it possible to control the electron spin in a nonmagnetic way . many recent experimental and theoretical works indicate that the spin - polarization based on the rsoi can reach as high as 100%   or infinite [ 11 - 13 ] , and then attracted a lot of interest . recently , an aharnov - bohm ( ab ) ring device , in which one or two quantum dots ( qds ) having rsoi are located in its arms , is proposed to realize the spin - polarized transport . the qds is a zero - dimensional device where various interactions exist and is widely investigated in recent years for its tunable size , shape , quantized energy levels , and carrier number [ 14 - 16 ] . a qds ring has already been realized in experiments   and was used to investigate many important transport phenomena , such as the fano and the kondo effects . when the rsoi in the qds is taken into consideration , the electrons flowing through different arms of the ab ring will acquire a spin - dependent phase factor in the tunnel - coupling strengths and results in different quantum interference effect for the spin - up and spin - down electrons . in this article , we focus our attention on the 100% spin - polarized transport effect in a double qds ring . as shown in fig . 1 , the two qds embedded in each arms of the ring are coupled to the left and the right leads in a coupling configuration transiting from serial (  = 0 ) to symmetrical parallel (  > 0 ) geometry . we assume that the rsoi exists only in the qds and the arms of the ring and the leads are free from this interaction . furthermore , the two dots are assumed to couple to each other by a spin - polarized coupling strength   where tc is the usual tunnel coupling strength , t may arises from a constant magnetic field applied on the junction between the qds , and the phase factor r is induced by the rsoi in the qds . system of a double qds ring connected to the left and the right leads with different coupling strengths the second - quantized form of the hamiltonian that describes the double - dot interferometer can be written as ( 1 ) where   is the creation ( annihilation ) operator of an electron with momentum k , spin index   or 1 , and   and energy k in the th (  = lr ) lead ;   creates ( annihilates ) an electron in dot i with spin  and energy i;ui is the coulomb repulsion energy in dot i with   being the particle number operator , in the following we set u1 = u2 = u for simplicity ; t describes the dot  dot tunneling coupling and the matrix elements ti are assumed to be independent of k for the sake of simplicity and take the forms of   and   the phase factor ri arises from the rsoi in dot i , which is tunable in experiments . in fact , the rsoi will also induce a inter - dot spin - flip , which has little impact on the current and is neglected here . the spin - dependent tunnel - coupling strength ( line - width function ) between the dots and the leads is defined as ij = 2ktitj(k ) , (  = lr ) . according to fig . 1 , the matrix form of them read ( here we set tl1 = tr2 = t and tr1 = tl2 = t)(2)(3 ) where the spin - dependent phase factor  = r , with r = r1r2 , this indicates that the tunnel - coupling strength only depends on the difference between r1 and r2 , and then one can assume that only one qd contains the rsoi , making the structure simpler and more favorable in experiments . the phase - independent tunnel - coupling strength is  =  +  , with  = 2|t| , and  is the density of states in the leads ( the energy - dependence of  is neglected ) . the general current formula for each spin component through a mesoscopic region between two noninteracting leads can be derived as ( 4 ) where   is the fermi distribution function for lead  with chemical potential . the 2  2 matrices   and g( ) are , respectively , the lesser and the retarded ( advanced ) green s function in the fourier space . we employ the equation of motion technique to calculate both the retarded and the lesser green s functions by adopting the hartree - fock truncation approximation , and arrive at the dayson equation form for the retarded one : ( 5 ) where the retarded self - energy   the diagonal matrix elements of green s function g( ) for the isolated dqd are(6 ) and the off - diagonal matrix elements are tc . the advanced green s function g( ) is the hermitian conjugate of g( ) . the occupation number < ni > in eq . 6 needs to be calculated self - consistently ; its self - consistent equation is   within the same truncating approximation as that of the retarded green s function , the expression of   can be simply written in the keldysh form   the matrix elements of the lesser self - energy   are   in general   and thus eq . 6 of the current is reduced to the landauer - bttiker formula for the non - interacting electrons ( 7 ) and then the total transmission t( ) for each spin component can be expressed as   the linear conductance g( ) is related to the transmission t( ) by the landauer formula at zero temperature , g( ) = ( e / h)t( ) . in the following numerical calculations , we set the temperaturet = 0 throughout the article . the local density of states in the leads  is chosen to be 1 andt = 0.4 so that the corresponding linewidth   is set to be the energy unit . figure 2a  c shows the dependence of the conductance g and spin polarization   on the fermi level  for  = u = 0 and various t . the two dots now are connected in a serial configuration and the conductance of each spin component is composed of two breit - wigner resonances peaked at   respectively . since the phase factors originating from both the magnetic flux and the rsoi do not play any role , the device is free from their influences . when t = 0 , the spin - up and spin - down conductances are the same and the spin polarization p = 0 as shown by the solid lines in the three figures . with increasing t , the distance between the spin - up resonances is enhanced whereas that between the spin - down ones is shrunk because of   as shown in fig . if t is set to be t = tc , the spin - up and spin - down inter - dot tunneling coupling strengths are   and   respectively . then the spin - up conductance   has a finite value but meanwhile   as the conduction channel for the spin - down electrons breaks off , which is shown by the dot - dashed lines in fig . 2a , b. the spin orientation of the non - zero conductance can be readily reversed by tuning the direction of the magnetic field , which is applied on the tunnel junction between the dots , to set t = tc . spin - dependent conductance g and spin polarization p as functions of the fermi level  with  = u = 0 and various t . in this and all following figures , the normal inter - dot tunneling coupling tc = 1 and the dots  levels are 1 = 2 = 0 we now study how the dot - lead coupling configuration influences the spin filtering effect in fig . 3 by varying the value of . it is found that if the parameters are set to be t = tc and  = r = /2 , the spin - down conductance   remains to be zero for any  , and then only   is plotted . for non - zero  , the transmission t( ) is(8 ) where 0 = 1 = 2 . since   and the spin - down transmission   regardless of the choice of . the spin - up conductance is composed of one broad breit - wigner and one asymmetric fano resonance centered , respectively , at the bonding and antibonding states . detail investigation of this spin - dependent fano line - shape can be found in our previous papers and we do not discuss it anymore here . it should be indicated that the spin orientation of the nonzero conductance can be reversed by setting t = tc and  = /2 + 2n with n is an integer . the dependence of the spin - up conductance   on the fermi level for fixed r =  = /2 , t = tc and various . other parameters are the same as those of fig . 2 it is known that the coulomb interaction in the qds plays an important role and we now study if the spin filtering effect survives in the presence of it . figure 4a shows that the conductance of the spin down electrons is still zero and that of the spin up shows typical fano resonance . due to the existence of the intra - dot coulomb interaction , moreover , the positions of the bonding and antibonding states can be readily exchanged by tuning the magnetic flux as shown in fig . since the fano effect is a good probe for quantum phase coherence in mesoscopic structures , the tuning of its resonance position and the asymmetric tail direction is an important issue . to date , much works have been devoted to this topic concerning both the charge and the spin - dependent fano effect . but most previous works about the fano effect in qds ring ignored the coulomb interaction , especially when the spin degree of freedom is considered , and this limitation is supplemented here . spin - dependent conductance g as a function of the fermi level for fix r = /2,u = 4 , t = tc and different . in this and the following figure , the solid and the dashed lines are for the spin - up and spin - down electrons , respectively in fact , to realize the rsoi in a tiny device such as the qds is somewhat difficult , and then we study if the spin filtering effect can be found in the absence of it . in fig . 5 , we set r = 0 and plot the two spin components conductance by varying tand the magnetic flux - induced phase factor . figure 5a shows that when t = tcand  =  + 2n withnis an integer , the conductance of the spin - up electrons still has finite value whereas that of the spin - down electrons is exactly zero . moreover , to swap the spin direction of the non - zero conductance , one can simply tune tfromtcto tcwith unchanged magnetic flux as shown in fig . 5b . the peaks width and position of the non - zero conductance in fig . 5a , b are the same , indicating that one can flip the electron spin in the bonding and antibonding states without affecting its sate properties . spin - dependent conductance g as a function of the fermi level for fix r = 0,u = 4 ,  =  and different t in conclusion , we have investigated the spin filtering effect in a double qds device , in which the two dots are coupled to external leads in a configuration transiting from serial - to - parallel geometry . we show that by properly adjusting the spin - dependent inter - dot tunneling coupling strengtht , a net spin - up or spin - down conductance can be obtained with or without the help of the rsoi and the magnetic flux . the spin direction of the non - zero conductance can be manipulated by varying the signs oft. the above means of spin control can be fulfilled for a fixed rsoi - induced phase factor , and then the qds in the present system can be either a gated or a self - assembly one , making it easier to be realized in current experiments . this work was supported by the national natural science foundation of china ( grant nos .