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电子在自旋-轨道耦合调制下磁受限半导体纳米结构中的传输时间及其自旋极化

温丽 卢卯旺 陈嘉丽 陈赛艳 曹雪丽 张安琪

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电子在自旋-轨道耦合调制下磁受限半导体纳米结构中的传输时间及其自旋极化

温丽, 卢卯旺, 陈嘉丽, 陈赛艳, 曹雪丽, 张安琪

Transmission time and spin polarization for electron in magnetically confined semiconducotr nanostructure modulated by spin-orbit coupling

Wen Li, Lu Mao-Wang, Chen Jia-Li, Chen Sai-Yan, Cao Xue-Li, Zhang An-Qi
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  • 通过考虑构筑在半导体GaAs/AlxGa1–xAs异质结上的磁受限半导体纳米结构中的塞曼效应和自旋-轨道耦合, 本文采用理论分析和数值计算相结合的方法研究了电子的传输时间与自旋极化. 利用矩阵对角化和改进的转移矩阵方法, 数值求解电子的薛定谔方程; 采用H.G. Winful理论求电子的居留时间, 并计算自旋极化率. 由于塞曼效应与自旋-轨道耦合, 电子的居留时间明显地与其自旋有关, 因此可在时间维度上分离自旋、实现半导体中电子的自旋极化. 因为半导体GaAs的有效g-因子很小, 电子自旋极化主要源于自旋-轨道耦合, 大约为塞曼效应引起的自旋极化的4倍. 由于电子的有效势与自旋-轨道耦合的强度有关, 电子的居留时间及其自旋极化可通过界面限制电场或应力工程进行有效调控. 这些有趣的结果不仅对半导体自旋注入具有参考价值, 而且还可为半导体自旋电子学器件应用提供时间电子自旋分裂器.
    Because digital information in semiconductor spintronics is encoded, stored, processed, and transferred by electron spins instead of its charge, the operation of a spintronic device requires that electrons in semiconductors be spin polarized. But spin states of electrons in traditional semiconductor materials are usually degenerate, therefore, conventional semiconductors cannot be directly used to design spintronic devices. Thus, how to spin polarized electrons in ordinary semiconductors (also called spin injection) including its effective manipulation, has become an important direction of research. In physics, either Zeeman effect between electron spins and external magnetic fields or spin-orbit coupling of electron spins and its spatial momentums can be employed to achieve electron-spin polarization. According to these physical mechanisms, some effective schemes have been developed successfully, such as spin filtering, temporally separating electron-spins, and spatial separations of electron spins. Utilizing the combination of theoretical analysis and numerical calculation, transmission time is investigated by considering both Zeeman effect as well as Rashba and Dresselhaus spin-orbit couplings for electron in magnetically confined semiconductor nanostructure, which is constructed on the GaAs/AlxGa1-xAs heterostructure. Schrödinger equation of an electron is numerically solved by matrix diagonalization and improved transfer-matrix method. Adopting H.G. Winful’s theory, dwell time of electron is calculated and spin polarization ratio is given. Due to Zeeman effect and spin-orbit coupling, dwell time of electron is obviously associated with the spins, which is used to separate electron-spins in time dimension and to realize spin polarization of electrons in semiconductors. Because the semiconductor GaAs has a small effective g-factor, which is about 4 times larger than that induced by Zeeman effect, electron-spin polarization originates mainly from spin-orbit coupling including Rashba and Dresselhaus types. Dwell time of electron and its spin polarization can be efficaciously modified by interfacial confining electric-field or strain engineering, because the effective potential of electron is related to spin-orbit coupling’s strength. These interesting findings not only have some references for spin injection into semiconductors, but also provide a controllable temporal electron-spin splitter for semiconductor spintronics device applications.
  • 图 1  真实MCSN结构(a)及其模型(b), 图中垂直磁化的铁磁(FM)条带沉积在GaAs/AlxGa1–xAs异质结的表面, dh和$ {M_0} $分别是FM条带的宽度、厚度和磁化强度, z0表示FM条带与2DEG之间的距离, 结构的两端分别位于xx+处, Bz(x)是FM条带在2DEG平面内产生的磁场

    Fig. 1.  The MCSN device(a)and its model(b), where a vertically magnetized ferromagnetic (FM) stripe is patterned in the surface of GaAs/AlxGa1–xAs heterostructure, d, h, $ {\vec M_0} $, x- and x+ are width, thickness, magnetization, left position and right end, respectively, z0 represents the distance between FM stripe and 2DEG, and Bz (x) is magnetic field induced by FM stripe within 2DEG.

    图 2  仅考虑塞曼效应时, 自旋向上电子和自旋向下电子在真实MCSN结构中的居留时间及其自旋极化(在插图中)随着入射能的变化, 图中电子的横向波矢取为ky = 0(垂直入射)

    Fig. 2.  When only Zeeman effect is involved, dwell time changes with incident energy for spin-up (up-triangle curve) and spin-down (down-triangle curve) electrons in the MCSN, respectively, where spin polarization ratio defined by dwell time is presented in the inset and transverse wave vector of electron is chosen as ky = 0 (i.e., the normal incidence).

    图 3  只考虑Rashba型SOC耦合 (a) 自旋向上和自旋向下电子在真实MCSN结构中的居留时间及其自旋极化(在插图中)随着入射能量的变化, 其中Rashba-SOC耦合的强度为$\eta_{\mathrm{R}} $ = 0.2; (b)当入射能量分别为E = 3.0, 5.0, 7.0时, 自旋极化随着Rashba-SOC耦合强度的变化; 图中电子的横向波矢取为ky = 0

    Fig. 3.  Only Rashba-SOC effect is considered: (a) Dwell time and spin polarization ratio (in the inset) vary with incident energy for spin-up and spin-down electrons in the MCSN, where Rashba-SOC strength is chosen as $\eta_{\mathrm{R}} $ = 0.2; (b)spin polarization ratio changes with Rashba-SOC strength for incident energy E = 3.0, 5.0, 7.0; and transverse wave vector is set to be ky = 0.

    图 4  仅计及Dresselhaus型SOC效应 (a) 自旋向上和自旋向下电子在真实MCSN结构的居留时间及其自旋极化(在插图中)随着入射能量的变化, 其中Dresselhaus-SOC耦合的强度为$\eta_{\mathrm{D}} $ = 0.2; (b)当入射能量分别为E = 3.0, 5.0, 7.0时, 自旋极化随着Dresselhaus-SOC强度的变化; 图中电子的横向波矢取为ky = 0

    Fig. 4.  Only Dresselhaus-SOC effect is considered: (a) Dwell time and spin polarization ratio (in the inset) vary with incident energy for spin-up and spin-down electrons in the MCSN, where Dresselhaus-SOC strength is chosen as $\eta_{\mathrm{D}} $ = 0.2; (b) spin polarization ratio changes with Dresselhaus-SOC strength for incident energy E = 3.0, 5.0, 7.0; and transverse wave vector is set to be ky = 0.

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  • 收稿日期:  2024-02-22
  • 修回日期:  2024-04-08
  • 上网日期:  2024-04-11

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