Double Rashba Quantum Dots Ring as a Spin Filter
© to the authors 2008
Received: 11 August 2008
Accepted: 21 August 2008
Published: 3 September 2008
We theoretically propose a double quantum dots (QDs) ring to filter the electron spin that works due to the Rashba spin–orbit interaction (RSOI) existing inside the QDs, the spin-dependent inter-dot tunneling coupling and the magnetic flux penetrating through the ring. By varying the RSOI-induced phase factor, the magnetic flux and the strength of the spin-dependent inter-dot tunneling coupling, which arises from a constant magnetic field applied on the tunneling junction between the QDs, a 100% spin-polarized conductance can be obtained. We show that both the spin orientations and the magnitude of it can be controlled by adjusting the above-mentioned parameters. The spin filtering effect is robust even in the presence of strong intra-dot Coulomb interactions and arbitrary dot-lead coupling configurations.
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 [1, 2]. 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 [1, 3, 4], generating and controlling a spin-polarized current with all-electrical means in mesoscopic structures has been an actively researched topic in recent years. The electric field usually does not act on the spin. 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 [6, 7]. 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 [8, 9]. Many recent experimental and theoretical works indicate that the spin-polarization based on the RSOI can reach as high as 100% [7, 10] 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 [18, 19]. 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 [10, 13, 20, 21].
Model and Method
where the spin-dependent phase factor ϕσ = φ−σϕ R , with ϕ R = ϕ R 1−ϕ R 2, this indicates that the tunnel-coupling strength only depends on the difference between ϕ R 1 and ϕ R 2, 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 Γ = Γ L + Γ R , with Γα = 2π|t|2ρα, and ρα is the density of states in the leads (the energy-dependence of ρα is neglected).
and then the total transmission T σ(ɛ) for each spin component can be expressed as The linear conductance G σ(ɛ) is related to the transmission T σ(ɛ) by the Landauer formula at zero temperature , G σ(ɛ) = (e 2/h)T σ(ɛ).
Results and Discussion
In the following numerical calculations, we set the temperatureT = 0 throughout the article. The local density of states in the leads ρ is chosen to be 1 andt = 0.4 so that the corresponding linewidth is set to be the energy unit.
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 σ, 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 σ. 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. 10647101 and 10704011).
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