嵌有量子点分子的AB干涉器中电子及自旋性质
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摘要
半导体量子点是准零维的介观结构,其中的载流子(如:电子)受到量子束缚而具有分立的能级和较强的库仑相互作用,这使得单个量子点的电子特性类似于自然界的原子,而被称为人造原子。因而可以推知,当多个量子点相互靠近而耦合在一起时形成的量子点分子结构的电子行为与自然分子可比拟。而各种不同结构的量子点分子皆可以与外电极以不同方式相连而形成介观电路,这样可通过观察其电子输运性质研究其电子结构。与此同时,对于在电子输运过程中如何实现对电子或自旋的人为操控的研究具有重要的器件应用价值。与单个量子点相比,量子点分子结构具有更多的结构参数可以调控,其所实现的丰富的物理效应可作为未来量子信息及量子计算等纳米电子学功能器件的物理基础,量子点分子结构的电子输运特性是目前关于量子点研究的热点方向。
本文采用非平衡态格林函数方法,对几种典型的嵌有量子点分子的AB干涉器中的电子以及自旋输运性质进行了较为系统的理论研究,得到了一些有意义的结果。本论文工作的基本物理思想如下:量子相干是主导介观电子输运性质的基本物理机制,而量子点分子体系以及AB干涉器的结构为电子隧穿提供了丰富的相干路径(即所谓的Feynman路径)。电子在Feynman路径中的隧穿过程中将发生量子干涉,从而导致电子在量子点分子体系中的丰富多样的输运特性。因此,研究量子点分子体系的电子输运特性,必须揭示决定这些输运特性的量子相干图像,这是始终贯穿于本论文工作的一条主线。本论文工作开展了如下两个方面的理论研究:
第一个方面,建立了三种物理模型,即,N个量子点耦合构成的量子点链以任意两个相邻量子点分别嵌入AB干涉器的两个臂中;N个量子点耦合构成的量子点链两端点的量子点分别嵌入AB干涉器的两个臂中;N个量子点耦合构成的量子点环以相邻的两个量子点分别嵌入AB干涉器的两个臂中。我们系统地研究了这三个模型中电子输运过程中的退耦合和反共振现象。对于第一个模型,研究发现,仅仅当由偶数个量子点构成的量子点链对称地嵌入AB干涉器时,即,当器臂中的两个量子点分别耦合有相同数目的量子点时,量子点分子的一些分子态将与电极发生退耦合现象。当无磁场通过干涉器时,所有第奇数个分子态从电极上退耦合掉;而引入合适的磁通穿过AB干涉器,可使所有第偶数个分子态从电极上退耦合。有趣的是,当退耦合现象出现时,电导谱中的反共振点的位置与磁场是否存在无关。通过调节穿过AB干涉器的磁通,使穿过两个子环的磁通量不同时,可以实现一些分子态从一个电极上退耦合但仍与另一个电极耦合的现象。正是由于这一现象导致了电导谱中新的反共振点的出现,且其位置恰好与这种半退耦合态的能级位置一致。
对于第二个模型,研究发现,与前述结构相比,电子输运过程中的退耦合以及反共振现象所表现出来的特征更加丰富。在无磁场的条件下,当量子点总数为奇数时,量子点链中所有序数为偶数的分子态从电极上退耦合;与之相反,当量子点总数为偶数时,该量子点链的所有序数为奇数的分子态从电极上退耦合。伴随着该结构中所表现出的丰富的退耦合现象,电子输运中也存在明显的反共振现象。对于量子点数目是奇(偶)数的量子点链,线性电导谱中的反共振点的位置与其亚分子(不包括两端量子点的量子点链段)的奇(偶)分子态一致。当引入适当强度的磁场时,这种现象相应发生改变,量子点数目是奇(偶)数的量子点链的线性电导谱中的反共振点的位置与其亚分子的偶(奇)分子态对应能级一致。
以上的研究结果表明,电子输运过程中表现出来的退耦合以及反共振现象与体系的对称性有关。通过对第三个模型的研究发现,由量子点环嵌入AB干涉器中构成的介观电路体系的退耦合以及反共振现象更加丰富,这是因为该体系的对称性由量子点环和AB干涉器同时贡献。通过计算发现,相较于相同数目的量子点链状结构,由量子点环嵌入AB干涉器的结构中的退耦合现象更为显著,并且在该结构中存在两种导致退耦合的机制:其一是通过调节磁通相因子,使耦合量子点的分子态与电极的耦合强度为零,从而产生退耦合现象;其二是来源于量子点环本身的对称性,正是由于量子点环的对称性,使得其分子态存有简并,这些简并态的存在也诱导了退耦合现象的出现。而且,我们还能看到,在适当的磁通穿过AB干涉器时,嵌入2N+1个量子点的量子点环与量子点数目是2N的量子点链的线性电导谱完全一致。
为了阐明在上述各种典型AB干涉器中电子输运的退耦合现象所蕴含的物理机制,我们利用表象变换的理论方法,在分子轨道表象下,探讨各分子态与电极的耦合情况,分析了量子点链和量子点环两种不同结构中退耦合分子态的出现。另外,对于电子输运中的反共振现象,我们通过表象变换将所研究的结构转换成等价的T型量子点结构,分析了由于各量子态之间的相消量子干涉而引起的反共振点的出现位置。
此外,我们还在二阶截断近似(即:Hubbard近似)条件下研究了多体效应对线性电导谱的影响。研究发现,在该近似下,多体效应把电导谱线明显分成两组,但它不能够破坏退耦合以及反共振现象的出现。然而,从得到的线性电导谱中我们可以清楚地看到,退耦合效应的出现严重破坏了体系的电子-空穴对称性。最后我们研究了由退耦合机制引起的非平衡态系统中的负微分电容现象。由于施加于AB干涉器两个电极之间偏压的作用使量子点分子嵌入AB干涉器体系的结构参数发生了变化,从而破坏了退耦合态的出现,使原来的局域态电子参与电子输运,从而使体系表现出负微分电容现象。
第二个方面,我们研究了复杂AB干涉器中存在Rashba相互作用时自旋极化的电子输运和纯自旋流的出现问题。我们建立了两个物理模型:其一为三个量子点通过三个电极相互耦合的三终端结构;其二为平行耦合双量子点AB干涉器中引入两个额外电极分别与量子点侧向耦合的四终端结构。首先,研究了第一个模型中与自旋相关的电子输运性质。当在体系中引入局域Rashba轨道自旋耦合后,由于Rashba相互作用为电子提供了一个与自旋相关的相位,从而使电子的输运性质与自旋相关。我们发现一个电子从该结构的一端入射,它能够根据其自旋态选择某一特定端点离开该耦合量子点体系,结果,在此结构中自旋极化和自旋分离可同时出现,且通过调节结构参数可改变不同通道内的自旋极化方向。我们用Feynman路径语言分析和阐述了产生上述结果的量子干涉机制。在两个低阶Faynman路径之间的总相位差与Rashba相互作用、外加磁场和量子点的散射有关。此外,还注意到,量子点耦合体系的结构参数能够和外加磁场一样为不同路径的干涉贡献相位差。在此结构中,外加磁场不再是产生自旋极化的一个必要因素,通过调节量子点的参数,如量子点能级(实验上可通过门电压调节),同样可以得到自旋极化。
其次,我们又研究了第二个模型中与自旋相关的电子输运性质。在AB干涉器臂上的一个量子点中引入局域的Rashba自旋轨道相互作用,使电子的输运依赖于自旋。研究发现,当在横向的两个电极之间施加有限偏压时,Rashba相互作用可以在纵向的两个电极上诱导出纯自旋流,而且两纯自旋流的自旋极化方向始终相反。通过分析电子隧穿路径中电子的相位差,我们阐明了这些结果起因于电子隧穿路径中的量子干涉效应。此外,研究还发现,量子点能级和磁相因子的调节可以有效地调制隧穿路径中电子波的相位,因此,依赖自旋的电子隧穿概率可以借助结构参数的调节得到控制,从而引起纯自旋流的幅值和极化方向的改变。
Semiconductor quantum dot (QD) is a quasi-zero-dimensional mesoscopic structure, which presents discrete electron energy spectrum and strong electron interaction. Because of such electronic characteristics, a single QD is viewed as an artificial atom. Accordingly, a structure consisting of several coupled QDs confines electrons in a way as an artificial molecule. QDs can be incorporated into a mesoscopic circuit. Thus, the electron structure in QDs can be revealed by the observation of the electronic transport spectrum. Meanwhile, the controllable electronic transport properties through a variety of QD structures suggest many promising device applications. For example, some multiple QD structures are recently considered as the device prototype to realize the quantum computation. In contrast to a single QD, multiple QD structures possess more structural parameters to tune their electronic transport properties. Therefore, the investigations on the multiple QD structures are the current focus in the field of mesoscopic physics.
In this thesis we report our theoretical investigations about the electron and spin transport through several Aharonov-Bohm (AB) interferometers with typical embodied multiple QD structures, by means of non-equilibrium Green function technique, thereby, some interesting results are obtained. It is well-known that quantum interference plays a dominant role in the electronic transport process through a mesoscopic structure. As a typical mesoscopic structure, coupled multiple QDs and the structure of AB interferometer provide a variety of Feynman paths to take part in the quantum interference. As a result, the quantum interference among these distinct Feynman paths brings about novel electronic transport properties. We will focus on the quantum interference which is the underlying mechanism for the electronic transport properties through several different QD molecule structures. Below we outline our works briefly from two aspects:
On one hand, we established the three following models: The interferometer with arbitrary neighbor QDs of one-dimensional QD chain embodied in its two arms, the interferometer with the peripheral QDs of one-dimensional QD chain in its two arms, and the interferometer with a QD ring embodied in it. We theoretically investigated the electronic transport through three structures. For the first model, we found that when the QD chain is symmetrically placed some of its molecular states decouple from the leads. Namely, in the absence of magnetic flux all odd molecular states decouple from the leads, but all even molecular states decouple from the leads when an appropriate magnetic flux is introduced. Interestingly, the antiresonance position in the electron transport spectrum is independent of the change of the decoupled molecular states.
For the case of the peripheral QDs of one-dimensional QD chain embodied in the arms of AB interferometer, it was found that, in the absence of magnetic flux, all the even molecule states of odd-numbered QD structures decouple from the leads and in even-numbered QD systems all the odd molecule states decouple from the leads, which indicates the formation of remarkable bound states in the continuum. Meanwhile, what's interesting is that apparent antiresonance occurs in electron transport through this structure, the positions of which are accordant with all even (odd) eigenenergies of the sub-molecule of the even (odd) -numbered QDs without the peripheral dots. All these results are efficiently modified by the presence of magnetic flux through this system.
With the above results, one can understand that the decouple phenomena are tightly dependent on the symmetries of the considered structures. So it can be predicted that when a QD ring is embodied in the AB interferometer, there will be remarkable decouple results, since the symmetry from both the QD ring and the AB interferometer, respectively. Consequently, the occurrence of decouple results in electron transport through the QD ring in the interferometer is remarkable, independent of the number of quantum dots in the ring. Furthermore, by the presence of an appropriate magnetic flux through the interferometer, the linear conductance spectrum of the (2n+l) -quantum-dot ring (n∈integer) is the same as that of the 2n-quantum-dot chain, on account of the occurrence of decouple inelectron transport through these two kinds of systems.
When incorporating the many-body effect by only considering the Hubbard term andtruncating the motion equation of the Green functions to the second-order, we show that the emergence of decoupling gives rise to the apparent destruction of electron-hole symmetry. In addition, by adjusting the magnetic flux through either subring of the AB interferometer, some molecular states decouple from one lead but still couple to the other, and then some new antiresonances occur. In addition, we investigated the negative differential capacitance caused by the decoupling mechanism with a finite bias voltage between two leads. As a consequence, the decoupling phenomenon can be demolished since the structure parameters that take some specific values are destroyed by the variation of the bias voltage. Thus, the electrons located in QDs due to the decoupling effect, driven by the bias, will take part in electron tunneling and then enter the drain of the system.
On the other hand, the electron and spin properties in the complicated AB interferometers were studied. First, electron transport properties of a triple-terminal Aharonov-Bohm interferometer were theoretically studied. By applying a Rashba spin-orbit coupling to a quantum dot locally, we found that remarkable spin polarization comes about in the electron transport process with tuning the structure parameters, i.e, the magnetic flux or quantum dot levels. When the QD levels are aligned with the Fermi level, there only appear spin polarization in this structure by the presence of an appropriate magnetic flux. However, in absence of magnetic flux spin polarization and spin separation can be simultaneously realized with the adjustment of QD levels, namely, an incident electron from one terminal can select a specific terminal to depart from the QDs according to its spin state.
In the following, spin-dependent electron transport properties in a parallel double quantum dot structure with four terminals were theoretically investigated by means of the nonequilibrium Green function technique. As a result, when applying a local Rashba spin-orbit interaction on an individual QD and introducing a finite bias between the transverse terminals, we showed that in the presence of appropriate structure parameters, apparent pure spin currents come into being in the longitudinal terminals with the same amplitude and opposite polarization directions. Besides, the polarization directions of such spin currents can be efficiently inverted by the adjustment of structure parameters.
本文采用非平衡态格林函数方法,对几种典型的嵌有量子点分子的AB干涉器中的电子以及自旋输运性质进行了较为系统的理论研究,得到了一些有意义的结果。本论文工作的基本物理思想如下:量子相干是主导介观电子输运性质的基本物理机制,而量子点分子体系以及AB干涉器的结构为电子隧穿提供了丰富的相干路径(即所谓的Feynman路径)。电子在Feynman路径中的隧穿过程中将发生量子干涉,从而导致电子在量子点分子体系中的丰富多样的输运特性。因此,研究量子点分子体系的电子输运特性,必须揭示决定这些输运特性的量子相干图像,这是始终贯穿于本论文工作的一条主线。本论文工作开展了如下两个方面的理论研究:
第一个方面,建立了三种物理模型,即,N个量子点耦合构成的量子点链以任意两个相邻量子点分别嵌入AB干涉器的两个臂中;N个量子点耦合构成的量子点链两端点的量子点分别嵌入AB干涉器的两个臂中;N个量子点耦合构成的量子点环以相邻的两个量子点分别嵌入AB干涉器的两个臂中。我们系统地研究了这三个模型中电子输运过程中的退耦合和反共振现象。对于第一个模型,研究发现,仅仅当由偶数个量子点构成的量子点链对称地嵌入AB干涉器时,即,当器臂中的两个量子点分别耦合有相同数目的量子点时,量子点分子的一些分子态将与电极发生退耦合现象。当无磁场通过干涉器时,所有第奇数个分子态从电极上退耦合掉;而引入合适的磁通穿过AB干涉器,可使所有第偶数个分子态从电极上退耦合。有趣的是,当退耦合现象出现时,电导谱中的反共振点的位置与磁场是否存在无关。通过调节穿过AB干涉器的磁通,使穿过两个子环的磁通量不同时,可以实现一些分子态从一个电极上退耦合但仍与另一个电极耦合的现象。正是由于这一现象导致了电导谱中新的反共振点的出现,且其位置恰好与这种半退耦合态的能级位置一致。
对于第二个模型,研究发现,与前述结构相比,电子输运过程中的退耦合以及反共振现象所表现出来的特征更加丰富。在无磁场的条件下,当量子点总数为奇数时,量子点链中所有序数为偶数的分子态从电极上退耦合;与之相反,当量子点总数为偶数时,该量子点链的所有序数为奇数的分子态从电极上退耦合。伴随着该结构中所表现出的丰富的退耦合现象,电子输运中也存在明显的反共振现象。对于量子点数目是奇(偶)数的量子点链,线性电导谱中的反共振点的位置与其亚分子(不包括两端量子点的量子点链段)的奇(偶)分子态一致。当引入适当强度的磁场时,这种现象相应发生改变,量子点数目是奇(偶)数的量子点链的线性电导谱中的反共振点的位置与其亚分子的偶(奇)分子态对应能级一致。
以上的研究结果表明,电子输运过程中表现出来的退耦合以及反共振现象与体系的对称性有关。通过对第三个模型的研究发现,由量子点环嵌入AB干涉器中构成的介观电路体系的退耦合以及反共振现象更加丰富,这是因为该体系的对称性由量子点环和AB干涉器同时贡献。通过计算发现,相较于相同数目的量子点链状结构,由量子点环嵌入AB干涉器的结构中的退耦合现象更为显著,并且在该结构中存在两种导致退耦合的机制:其一是通过调节磁通相因子,使耦合量子点的分子态与电极的耦合强度为零,从而产生退耦合现象;其二是来源于量子点环本身的对称性,正是由于量子点环的对称性,使得其分子态存有简并,这些简并态的存在也诱导了退耦合现象的出现。而且,我们还能看到,在适当的磁通穿过AB干涉器时,嵌入2N+1个量子点的量子点环与量子点数目是2N的量子点链的线性电导谱完全一致。
为了阐明在上述各种典型AB干涉器中电子输运的退耦合现象所蕴含的物理机制,我们利用表象变换的理论方法,在分子轨道表象下,探讨各分子态与电极的耦合情况,分析了量子点链和量子点环两种不同结构中退耦合分子态的出现。另外,对于电子输运中的反共振现象,我们通过表象变换将所研究的结构转换成等价的T型量子点结构,分析了由于各量子态之间的相消量子干涉而引起的反共振点的出现位置。
此外,我们还在二阶截断近似(即:Hubbard近似)条件下研究了多体效应对线性电导谱的影响。研究发现,在该近似下,多体效应把电导谱线明显分成两组,但它不能够破坏退耦合以及反共振现象的出现。然而,从得到的线性电导谱中我们可以清楚地看到,退耦合效应的出现严重破坏了体系的电子-空穴对称性。最后我们研究了由退耦合机制引起的非平衡态系统中的负微分电容现象。由于施加于AB干涉器两个电极之间偏压的作用使量子点分子嵌入AB干涉器体系的结构参数发生了变化,从而破坏了退耦合态的出现,使原来的局域态电子参与电子输运,从而使体系表现出负微分电容现象。
第二个方面,我们研究了复杂AB干涉器中存在Rashba相互作用时自旋极化的电子输运和纯自旋流的出现问题。我们建立了两个物理模型:其一为三个量子点通过三个电极相互耦合的三终端结构;其二为平行耦合双量子点AB干涉器中引入两个额外电极分别与量子点侧向耦合的四终端结构。首先,研究了第一个模型中与自旋相关的电子输运性质。当在体系中引入局域Rashba轨道自旋耦合后,由于Rashba相互作用为电子提供了一个与自旋相关的相位,从而使电子的输运性质与自旋相关。我们发现一个电子从该结构的一端入射,它能够根据其自旋态选择某一特定端点离开该耦合量子点体系,结果,在此结构中自旋极化和自旋分离可同时出现,且通过调节结构参数可改变不同通道内的自旋极化方向。我们用Feynman路径语言分析和阐述了产生上述结果的量子干涉机制。在两个低阶Faynman路径之间的总相位差与Rashba相互作用、外加磁场和量子点的散射有关。此外,还注意到,量子点耦合体系的结构参数能够和外加磁场一样为不同路径的干涉贡献相位差。在此结构中,外加磁场不再是产生自旋极化的一个必要因素,通过调节量子点的参数,如量子点能级(实验上可通过门电压调节),同样可以得到自旋极化。
其次,我们又研究了第二个模型中与自旋相关的电子输运性质。在AB干涉器臂上的一个量子点中引入局域的Rashba自旋轨道相互作用,使电子的输运依赖于自旋。研究发现,当在横向的两个电极之间施加有限偏压时,Rashba相互作用可以在纵向的两个电极上诱导出纯自旋流,而且两纯自旋流的自旋极化方向始终相反。通过分析电子隧穿路径中电子的相位差,我们阐明了这些结果起因于电子隧穿路径中的量子干涉效应。此外,研究还发现,量子点能级和磁相因子的调节可以有效地调制隧穿路径中电子波的相位,因此,依赖自旋的电子隧穿概率可以借助结构参数的调节得到控制,从而引起纯自旋流的幅值和极化方向的改变。
Semiconductor quantum dot (QD) is a quasi-zero-dimensional mesoscopic structure, which presents discrete electron energy spectrum and strong electron interaction. Because of such electronic characteristics, a single QD is viewed as an artificial atom. Accordingly, a structure consisting of several coupled QDs confines electrons in a way as an artificial molecule. QDs can be incorporated into a mesoscopic circuit. Thus, the electron structure in QDs can be revealed by the observation of the electronic transport spectrum. Meanwhile, the controllable electronic transport properties through a variety of QD structures suggest many promising device applications. For example, some multiple QD structures are recently considered as the device prototype to realize the quantum computation. In contrast to a single QD, multiple QD structures possess more structural parameters to tune their electronic transport properties. Therefore, the investigations on the multiple QD structures are the current focus in the field of mesoscopic physics.
In this thesis we report our theoretical investigations about the electron and spin transport through several Aharonov-Bohm (AB) interferometers with typical embodied multiple QD structures, by means of non-equilibrium Green function technique, thereby, some interesting results are obtained. It is well-known that quantum interference plays a dominant role in the electronic transport process through a mesoscopic structure. As a typical mesoscopic structure, coupled multiple QDs and the structure of AB interferometer provide a variety of Feynman paths to take part in the quantum interference. As a result, the quantum interference among these distinct Feynman paths brings about novel electronic transport properties. We will focus on the quantum interference which is the underlying mechanism for the electronic transport properties through several different QD molecule structures. Below we outline our works briefly from two aspects:
On one hand, we established the three following models: The interferometer with arbitrary neighbor QDs of one-dimensional QD chain embodied in its two arms, the interferometer with the peripheral QDs of one-dimensional QD chain in its two arms, and the interferometer with a QD ring embodied in it. We theoretically investigated the electronic transport through three structures. For the first model, we found that when the QD chain is symmetrically placed some of its molecular states decouple from the leads. Namely, in the absence of magnetic flux all odd molecular states decouple from the leads, but all even molecular states decouple from the leads when an appropriate magnetic flux is introduced. Interestingly, the antiresonance position in the electron transport spectrum is independent of the change of the decoupled molecular states.
For the case of the peripheral QDs of one-dimensional QD chain embodied in the arms of AB interferometer, it was found that, in the absence of magnetic flux, all the even molecule states of odd-numbered QD structures decouple from the leads and in even-numbered QD systems all the odd molecule states decouple from the leads, which indicates the formation of remarkable bound states in the continuum. Meanwhile, what's interesting is that apparent antiresonance occurs in electron transport through this structure, the positions of which are accordant with all even (odd) eigenenergies of the sub-molecule of the even (odd) -numbered QDs without the peripheral dots. All these results are efficiently modified by the presence of magnetic flux through this system.
With the above results, one can understand that the decouple phenomena are tightly dependent on the symmetries of the considered structures. So it can be predicted that when a QD ring is embodied in the AB interferometer, there will be remarkable decouple results, since the symmetry from both the QD ring and the AB interferometer, respectively. Consequently, the occurrence of decouple results in electron transport through the QD ring in the interferometer is remarkable, independent of the number of quantum dots in the ring. Furthermore, by the presence of an appropriate magnetic flux through the interferometer, the linear conductance spectrum of the (2n+l) -quantum-dot ring (n∈integer) is the same as that of the 2n-quantum-dot chain, on account of the occurrence of decouple inelectron transport through these two kinds of systems.
When incorporating the many-body effect by only considering the Hubbard term andtruncating the motion equation of the Green functions to the second-order, we show that the emergence of decoupling gives rise to the apparent destruction of electron-hole symmetry. In addition, by adjusting the magnetic flux through either subring of the AB interferometer, some molecular states decouple from one lead but still couple to the other, and then some new antiresonances occur. In addition, we investigated the negative differential capacitance caused by the decoupling mechanism with a finite bias voltage between two leads. As a consequence, the decoupling phenomenon can be demolished since the structure parameters that take some specific values are destroyed by the variation of the bias voltage. Thus, the electrons located in QDs due to the decoupling effect, driven by the bias, will take part in electron tunneling and then enter the drain of the system.
On the other hand, the electron and spin properties in the complicated AB interferometers were studied. First, electron transport properties of a triple-terminal Aharonov-Bohm interferometer were theoretically studied. By applying a Rashba spin-orbit coupling to a quantum dot locally, we found that remarkable spin polarization comes about in the electron transport process with tuning the structure parameters, i.e, the magnetic flux or quantum dot levels. When the QD levels are aligned with the Fermi level, there only appear spin polarization in this structure by the presence of an appropriate magnetic flux. However, in absence of magnetic flux spin polarization and spin separation can be simultaneously realized with the adjustment of QD levels, namely, an incident electron from one terminal can select a specific terminal to depart from the QDs according to its spin state.
In the following, spin-dependent electron transport properties in a parallel double quantum dot structure with four terminals were theoretically investigated by means of the nonequilibrium Green function technique. As a result, when applying a local Rashba spin-orbit interaction on an individual QD and introducing a finite bias between the transverse terminals, we showed that in the presence of appropriate structure parameters, apparent pure spin currents come into being in the longitudinal terminals with the same amplitude and opposite polarization directions. Besides, the polarization directions of such spin currents can be efficiently inverted by the adjustment of structure parameters.
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