【作者】 张鹏；

【导师】 吴明卫；

【作者基本信息】 中国科学技术大学 ， 凝聚态物理， 2013， 博士

【摘要】 自旋电子学是研究和利用电子的自旋自由度来取代或者结合电荷自由度的一门学科,尤其以固态系统为研究主体。它的目标是为新一代的电子学器件的设计和应用提供一种方案。这种新一代的电子学器件在传统的标准微电子工艺中结合进自旋依赖的效应。这种效应来自于电子的自旋与材料本身或者外在的磁、电和光学因素的相互作用。为了实现这个目标,理解各种载体中不同电子体系的自旋动力学,包括自旋弛豫和自旋输运,是非常必要的。基于这种需要,二维电子系统,尤其是存在于半导体量子阱或者异质结中的电子系统,在过去的几十年中得到了广泛的研究。最近,单层或者双层石墨、拓扑绝缘体的表面态以及绝缘体氧化物的界面如LaAlO3/SiTiO3,也在一定程度上因为它们的二维性质而引起了人们很大的关注。这篇论文主要从理论上研究了在传统半导体以及石墨烯、拓扑绝缘体和多铁氧化物中的二维电子系统的自旋弛豫和输运。全文结构如下。在第1章的背景介绍中,我们首先简要回顾了自旋电子学的发展,论述了实现自旋电子器件的关键要素,如自旋的产生和探测。接着我们介绍了时间域里自旋的主要弛豫机制,包括D’yakonov-Perel’, Elliot-Yafet和Bir-Aronov-Pikus机制,以及由于空间上自旋轨道耦合的涨落造成的自旋翻转散射所导致的自旋弛豫机制。除此外,我们还简要明确了空间域的输运过程中的自旋弛豫机制。在第2章,我们逐一介绍了这篇论文中所研究的材料和其中的电子系统。我们首先给出Ⅲ-Ⅴ族半导体如GaAs(?)勺能带结构及有效哈密顿量。接着,我们介绍被视为严格二维体系的石墨烯,并且从紧束缚模型的角度分析了高对称点处的电子(无质量的Dirac费米子)的有效哈密顿量。然后,我们转向拓扑绝缘体,如具有代表性的二维HgTe量子阱以及体的Bi2Se3。我们展示了拓扑绝缘体的边界态和表面态,这是一种具有类金属的传导性和自旋的螺旋性的、受时间反演对称保护的电子系统。我们从k.p方法以及不变量方法两个角度引入了边界态和表面态的有效哈密顿量。最后,我们对多铁材料做了一个简要介绍。在第3章,我们特别对石墨烯中自旋动力学的研究现状做了一下介绍。在第4章,我们首先介绍动力学自旋Bloch方程。本篇论文中关于自旋动力学的研究都是基于这种动力学自旋Bloch方程方法。接着,从动力学自旋Bloch方程出发,我们从微观的角度论述了时间域以及空间域的自旋弛豫机制。之后从第5到第10章,我们分别对半导体、石墨烯、拓扑绝缘体表面态以及多铁氧化物界面中的二维电子系统的自旋动力学进行研究。我们首先在第5章研究了半导体量子阱中的自旋弛豫。具体包含下面这些内容。我们从实验和理论上研究了室温下本征的(001) GaAs量子阱中的自旋弛豫。实验数据来自时间分辨的圆偏光泵浦—探测光谱。实验结果显示,随着电子(空穴)浓度的增大,自旋弛豫时间先增大然后缓慢下降。我们用包含了D’yakonov-Perel’和Bir-Aronov-Pikus自旋弛豫机制的完全微观的计算很好地重复出了实验观察到的现象,并且揭示：当浓度低的时候,Dresselhaus自旋轨道耦合的线性项占主导,这时候随着浓度的增大自旋弛豫时间变长；当浓度足够高的时候,Dresselhaus自旋轨道耦合的三次方项变得重要,使得自旋弛豫时间随浓度的变大而下降。我们接着研究了高温下n型(001)GaAs量子阱在阱平面内存在电场情况下的涉及多能谷的自旋弛豫。我们的研究表明,由于L能谷大的自旋轨道耦合以及强的Γ-L能谷间散射,L能谷扮演了自旋极化的“漏”("drain")的角色。随着电场的增大,整个电子系统的自旋弛豫时间先增大后减小。小电场区自旋弛豫时间随电场增大而变长是由热电子效应使得电声散射增强造成的；大电场区自旋弛豫时间随电场增大而减小一方面是由于r能谷的电子占据高动量态使得自旋进动的非均匀扩展变强,另一方面是由于更多的电子占据了自旋弛豫非常快的高的L能谷。除了电子系统,我们还研究了(001)方向生长的加了应力和门电压的Si/Si0.7Ge0.3和Ge/Si0.3Ge0.7量子阱中空穴的自旋弛豫。我们首先从六带的Luttinger k·p哈密顿量出发,利用子带的Lowdin微扰理论得到了量子阱中最低空穴子带的有效哈密顿量,包括Rashba自旋轨道耦合。我们发现,在Si/SiGe (Ge/SiGe)量子阱中,最低的空穴子带是轻(重)空穴型的。在我们所考察的温度、空穴／杂质浓度和门电压范围内,对于Si/SiGe (Ge/SiGe)量子阱,计算得到的自旋弛豫时间在1～100ps (0.1～10ps)的量级。我们的研究还表明,空穴—声子的散射很弱,从而在没有杂质(低杂质浓度)的样品中突出了库仑散射的重要性。随着温度的变化,Si/SiGe量子阱中的空穴系统一直处于强散射区,但是Ge/SiGe量子阱中的空穴系统既可以处在强散射区也可以处在弱散射区。在没有杂质时,两种量子阱中,库仑散射在自旋弛豫时间对温度的依赖中导致了一个峰,它出现在从简并区到非简并区的过渡位置。除此外,对于Ge/SiGe量子阱,库仑散射还在自旋弛豫时间对温度的依赖中导致了一个谷,这个谷出现在从弱散射区到强散射区的过渡位置。在上面的研究中,根据文献中普遍采用的近似,声子都是被假设处在平衡态的。但是,实际上,当电子系统远离平衡时,声子也可以被电子驱离平衡,并进而反过来影响电子的动力学,包括自旋动力学。为了考察这个效应,我们在n型(001) GaAs量子阱中将纵向光学声子考虑成非平衡的,研究了电场下热电子的自旋弛豫。我们发现,和将声子处理成平衡态的情形比起来,自旋弛豫时间变长了,主要是因为电子的热化加强使得电声散射变强。但是,大致和电子漂移速率成正比的自旋进动频率,却或增大或减小,具体依赖于电场的强度和晶格的温度。在第6章中,我们研究半导体量子阱中的自旋输运。在有Dresselhaus和(或)Rashba自旋轨道耦合因而有D’yakonov-Perel’弛豫机制存在的情况下,比如在Ⅲ-Ⅴ族的半导体中,自旋的输运已经得到了比较广泛的研究。在这里,我们考察对称的Si/SiGe量子阱。这个系统中没有D’yakonov-Perel’弛豫机制,但是我们在量子阱平面内加了磁场。通过这个研究,我们再一次强调,即使没有来自于Dresselhaus和(或)Rashba自旋轨道耦合的动量依赖的有效磁场,单独的静磁场也可以造成在空间域自旋进动的非均匀扩展。这个非均匀扩展,连同散射,导致自旋输运过程中不可逆的自旋弛豫。实际上,在Appelbaum等人关于体Si的自旋输运的实验中[Nature447,295(2007)],这个机制是非常重要的。在第7章,我们进入到石墨烯的研究。石墨烯中的电子是无质量的Dirac费米子,具有线性能谱。关于石墨烯中起主导作用的自旋弛豫机制很受争论。我们的研究试图理解石墨烯中的主要弛豫机制。由于门电压和石墨烯结构上的弯曲导致的Rashba自旋轨道耦合所决定的自旋弛豫时间比实验上观察到的值(～100-1000ps)长大约3个量级,我们考虑进了附着原子的效应。附着原子被认为可以局域上非常可观的增强Rashba自旋轨道耦合。除此之外,附着原子也可以提供库仑散射中心。由于附着原子分布的随机性,Rashba场实际上也是空间涨落的。这种随机的Rashba场通过造成自旋翻转散射贡献自旋的弛豫,因此表现出一种类似Elliot-Yafet的自旋弛豫机制。在我们的研究中,D’yakonov-Perel’和这种类Elliot-Yafet的自旋弛豫机制都被考虑了进来。通过拟合和比较Groningen的小组[Jozsa et al., Phys. Rev. B80,241403(R)(2009)]和Riverside的小组[Pi et al, Phys. Rev. Lett.104,187201(2010); Han and Kawakami,ibid.107,047207(2011)]的实验(这些实验中有的体现D’yakonov-Perel’机制表现的常规性质,即自旋弛豫率和动量弛豫率成反比,而有的体现Elliott-Yafet机制表现的常规性质,即自旋弛豫率和动量弛豫率成正比),我们倾向于认为D’yakonov-Perel’弛豫机制在石墨烯中占主导。后来Jo等人观察到的自旋弛豫时间随扩散系数的非单调的依赖性质[Phys. Rev. B84,075453(2011)]也被我们的模型很好地重复出来。在这个研究的最后,我们还对石墨烯中自旋弛豫的实验研究的最新进展进行了介绍。新的实验给出了自旋弛豫时间对动量散射的不敏感性。结合新的实验,我们对可能的主导的自旋弛豫机制重新进行了讨论。在这一章的最后,我们还研究了低迁移率波纹状石墨烯中的自旋弛豫。这种波纹状的结构弯曲不仅导致局域的Rashba自旋轨道耦合,而且还在两个谷中引入方向相反的有效静磁场,从而导致谷间的非均匀扩展。在谷间电声散射的作用下,自旋会非常有效的弛豫。这个效应在室温附近重要,可以导致最小达100ps量级的自旋弛豫时间。第8章里,在D’yakonov-Perel’机制的框架下,我们研究了石墨烯中的自旋输运。我们假设Rashba自旋轨道耦合被涨落的衬底和附着原子大大增强。通过拟合Pi等人用Au原子进行表面掺杂得到的自旋弛豫时间对Au原子浓度的依赖[Phys. Rev. Lett.104,187201(2010)],我们发现随着Au原子浓度的变大,Rashba自旋轨道耦合的系数从0.15增到0.23meV。在这个强的自旋轨道耦合下,我们计算得到的自旋输运的长度和实验值是可比的,都在μm量级。我们发现,在强的散射极限(这里电子—杂质散射占主导),自旋的扩散仅仅由Rashba自旋轨道耦合强度决定,而对温度、电子浓度和散射不敏感。但是,当沿着自旋注入的方向施加电场时,自旋输运的长度可以被电场或者电子浓度调节。同时,我们的研究还表明自旋输运对于注入的自旋的极化方向有各向异性的依赖。这个各向异性不同于由简单的两分量漂移—扩散模型给出的各向异性。在研究完石墨烯中无质量费米子的自旋动力学后,我们在第9章研究了拓扑绝缘体Bi2Se3的表面态在高电场下(可达几个kV/cm)的热电子输运和自旋弛豫。在该表面上,除非温度特别低,电子—表面光学声子的散射占主导。由于导带和价带的自旋混合,电场除了在各个带内加速电子,还会导致带间的进动。在有电场的情况下,电子可以通过带间的电声散射和带间的进动从价带转移到导带。另外,我们还发现,由于自旋—动量的锁定,电场会导致一个平面内横向的自旋极化,其幅度与动量散射时间成正比。我们的研究还表明由于Bi2Se3中大的相对静态介电常数,库仑散射非常弱,以至于在电场驱动下电子不能建立具有统一热电子温度的漂移费米分布。当我们在稳态时把电场撤掉,热化的电子会冷却到初始的费米分布,但是需要的时间(反应了能量弛豫的速率)非常长(100-1000ps的量级)。同时,之前电场下产生的自旋极化也会弛豫,其所用的时间在动量的弛豫时间量级(0.01-0.1ps).这篇论文以在15K的温度下对生长在多铁材料TbMnO3上的氧化物LaA103/SrTi03界面处二维电子气里的自旋扩散的研究(第10章)作为结束。TbMnO3里Mn3+的螺旋磁矩与LaA103/SrTi03界面处扩散的自旋发生Heisenberg交换相互作用。我们的研究表明,由于这个相互作用,在LaA103/SrTi03界面处的二维电子气的自旋扩散长度是有限的,不管注入的自旋的极化方向如何。之前Jia和Berakdar预言,在这个二维电子气中,当注入的自旋的极化与TbMnO3中磁矩的螺旋平面垂直时,自旋将不会弛豫[Phys. Rev. B80,014432(2009)],也即有恒久的自旋流。我们的研究表明他们的这个预言是不成立的。在第11章,我们对本论文的内容做了总结。更多还原

【Abstract】 Spintronics refers to a technology exploiting the spin degree of freedom instead of or in addition to the charge degree of freedom of electrons, especially in solid-state systems. Its aim is to offer opportunities for a new generation of devices combining standard mi-croelectronics with spin-dependent effects that arise from the interaction between electron spin and the optical, electrical, or magnetic properties of the materials or external fields. To achieve this object, it is quite essential to understand the spin dynamics, including the spin relaxation and transport, of different electron systems in various hosts. For this rea-son, the two-dimensional electron system, especially in the semiconductor quantum wells or heterostructurs, has been extensively studied in the past decades. Recently, partly due to the two dimensionality, the single-layer or bilayer graphene, the surface of topological in-sulators, and also the interface of insulating oxides such as LaAlO3/SiTiO3have attracted much attention. This dissertation focuses on the theoretical study on spin relaxation and transport of the two-dimensional electron system in semiconductors, graphene, topological insulators and multiferroic oxides. It is organized as follows.In the introduciton (Chapter1), we first briefly review the background of spintronics. The key factors in realizing spintronic devices, such as the spin generataion and detection, are reviewed. We then summarize the main spin relaxation mechanisms in the time domain, including the D’yakonov-Perel’, Elliot-Yafet and Bir-Aronov-Pikus mechanisms as well as the spin-flip scattering due to the randomness of the spin-orbit coupling. We also specify the mechansim for spin relaxation during transport, i.e., in the spatial domain.In Chapter2, we introduce the materials and systems studied in this dissertation. The band structure and effective Hamiltonian are given for the usual zincblende group III-V semiconductors such as GaAs. The single-layer grahene, which is deemed to be strictly two dimensional, is also introduced, with the effective Hamiltonian for the massless Dirac Fermions at high symmetry points given from a viewpoint of tight binding model. We then turn to the topological insulators, e.g., the representative two dimensional HgTe quantum wells and bulk Bi2Se3. The metallic and helical edge or surface states in the topological insulators are presented, with the effective Hamiltonian introduced from the k· p and invariant methods. After that, we briefly introduce the multiferroic materials. In Chapter3, we review the status of research on spin dynamics in graphene.In Chapter4, we present at first the kinetic spin Bloch equations, based on which all the studies on spin dynamics included in this dissertation are performed. Then starting from these equations, we explain the spin relaxation mechanisms in both time and spatial domains in detail, based on a microscopic viewpoint. From Chapter5to10, we present our studies on spin dynamics in two dimensional electron systems formed in the semiconduc-tors, the single-layer graphene, the surface of topological insulators and the multiferroic oxide interface, respectively.We first study the spin relaxation in semiconductor quantum wells in Chapter5.The carrier density dependence of electron spin relaxation in an intrinsic (001) GaAs quantum well at room temperature is investigated both experimentally and theoretically. The experimental data are from the time-resolved circularly polarized pump-probe spec-troscopy, and indicate that the spin relaxation time first increases and then slightly de-creases with the increase of electron (hole) density. Our fully microscopic calculation with both the D’yakonov-Perel’and the Bir-Aronov-Pikus mechanisms included reproduces the observed phenomenon very well. It is revealed that the spin relaxation time first increases with density in the relatively low density regime as the linear Dresselhaus spin-orbit cou-pling terms are dominant, and then tends to decrease when the density is large as the cubic Dresselhaus spin-orbit coupling terms become important.We then study the multi-valley spin relaxation in n-type (001) GaAs quantum wells with an in-plane electric field at high temperature. We demonstrate that L valleys play the role of a "drain" of the total spin polarization due to the large spin-orbit coupling there and the strong T-L inter-valley scattering. With the increase of the electric field, the spin relaxation time first increases due to the hot-electron effect and then decreases due to both the enhanced inhomogeneous broadening in T valley and the increase in occupation of electrons in higher L valleys where the spin relaxation takes place fast.Apart from electrons, we also investigate the hole spin relaxation in (001) strained asymmetric Si/Sio.7Geo.3(Ge/Si0.3Ge0.7) quantum wells under gate voltage. The effective Hamiltonian, including the Rashba spin-orbit coupling, of the lowest hole subband is ob-tained by the subband Lowdin perturbation method starting from the six-band Luttinger k· p model. It is found that the lowest hole subband in Si/SiGe (Ge/SiGe) quantum wells is light (heavy)-hole like. The spin relaxation time is calculated to be of the or-der of1～100ps (0.1～10ps) in Si/SiGe (Ge/SiGe) quantum wells, for the temperatures, carrier/impurity densities and gate voltages of our consideration. Our study reveals that the hole-phonon scattering is very weak, making the hole-hole Coulomb scattering become very important in the impurity-free samplesx. With the change of temperature, the hole system in Si/SiGe quantum wells is generally in the strong scattering limit, while that in Ge/SiGe quantum wells can be in either the strong or weak scattering limit. In the absence of impurities, the Coulomb scattering leads to a peak in the temperature dependences of spin relaxation time in both the Si/SiGe and Ge/SiGe quantum wells, located around the crossover from the degenerate to nondegenerate regimes. Besides, the Coulomb scattering also leads to a valley in the temperature dependence of spin relaxation time in Ge/SiGe quantum wells, around the crossover from the weak to strong scattering limit.In the above studies, phonons are assumed to be equilibrium phonons, following the widely adopted approximation in the literature. However, in fact, when the carriers are far away from the equilibrium, phonons can be driven away from the equilibrium by carriers as well and in turn affect the electron dynamics. To look into this effect, we perform a study on hot-electron spin relaxation in n-type (001) GaAs quantum wells under the electric field, with the longitudinal optical phonons considered to be nonequilibrium. It is found that when the phonons are treated as the nonequilibrium rather than the equilibrium ones, the spin relaxation time is increased since the electron heating is enhanced and hence the electron-phonon scattering is strengthened. However, the frequency of spin precession, which is roughly proportional to the electron drift velocity, can be either increased or decreased, depending on the electric field strength and/or the lattice temperature.We then go on to study spin transport in semiconductor quantum wells in Chap-ter6. The spin transport in quantum wells, in the presence of the Dresselhaus and/or Rashba spin-orbit coupling and hence the D’yakonov-Perel’spin relaxation mechanism, has already been investigated in group III-V semiconductors. Here we carry out the study in symmetric Si/SiGe quantum wells where the D’yakonov-Perel’spin relaxation mecha-nism is absent but with a static magnetic field in the Voigt configuration. Through this study, we emphasize that even without the momentum dependent effective magnetic field from the spin-orbit coupling, the static magnetic field alone can still cause inhomogeneous broadening in spin precessions in the spatial domain. This inhomogeneous broadening together with the scattering leads to an irreversible spin relaxation along with the spin transport. This mechanism exactly applies to the experiment on spin transport in bulk Si with a magnetic field by Appelbaum et al.[Nature447,295(2007)].In Chapter7, we turn to the single-layer graphene where the electrons are mass-less Dirac Fermions with linear dispersion. The dominant spin relaxation mechanism in graphene is under debate and our study aims to understand the main spin relaxation mechanism there. As the Rashba spin-orbit coupling induced by the gate voltage and/or curvature leads to a spin relaxation time about three orders larger than the experimen-tal measurement (-100-1000ps), we take into account the effect of adatoms, which can enhance the Rashba spin-orbit coupling locally and substantially. Besides, the adatoms also serve as Coulomb potential scatterers. Due to the random distribution of adatoms, the Rashba field is actually fluctuating. The randomness of the Rashba field causes spin relaxation by spin-flip scattering, manifesting itself as an Elliott-Yafet-like mechanism. In our study, both the D’yakonov-Perel’and the Elliott-Yafet-like mechanisms are consid-ered. By fitting and comparing the experiments from the Groningen group [Jozsa et al, Phys. Rev. B80,241403(R)(2009)] and Riverside group [Pi et al., Phys. Rev. Lett.104,187201(2010); Han and Kawakami, ibid.107,047207(2011)] which show either D’yakonov-Perel’-(with the spin relaxation rate being inversely proportional to the mo-mentum scattering rate) or Elliott-Yafet-like (with the spin relaxation rate being propor-tional to the momentum scattering rate) properties, we suggest that the D’yakonov-Perel’ mechanism dominates the spin relaxation in graphene. The later experimental finding of a nonmonotonic dependence of spin relaxation time on diffusion coefficient by Jo et al.[Phys. Rev. B84,075453(2011)] is also well reproduced by our model. At the end of this study, we also introduce the newest experimental progress on spin relaxation in graphene and rediscuss the possibly dominant spin relaxation. After that, we study spin relaxation in low-mobility rippled graphene. In this structure, the ripples does not only lead to Rashba spin-orbit coupling, but also induces a Zeeman-like spin-orbit coupling with opposite effective magnetic fields in two valleys. The joint effect of this Zeeman-like spin-orbit coupling and the intervalley electron-optical phonon scattering opens a spin re-laxation channel, which manifests itself in low-mobility samples with the electron mean free path being smaller than the ripple size. This spin relaxation channel contributes to spin relaxation effectively around room temperature, leading to a spin relaxation time around100ps.In Chapter8the spin transport in graphene is studied in the framework of the D’yakonov-Perel’ mechanism with the Rashba spin-orbit coupling enhanced by the fluc-tuating substrate as well as the adatoms. By fitting the Au doping dependence of spin relaxation from Pi et al.[Phys. Rev. Lett.104,187201(2010)], the Rashba spin-orbit coupling coefficient is found to increase approximately linearly from0.15to0.23meV with the increase of Au density. With this strong spin-orbit coupling, the spin diffusion or transport length is comparable with the experimental values (～μm). We find that in the strong scattering limit (dominated by the electron-impurity scattering), the spin diffusion is uniquely determined by the Rashba spin-orbit coupling strength and insensitive to the temperature, electron density as well as scattering. However, with the presence of an elec-tric field along the spin injection direction, the spin transport length can be modulated by either the electric field or the electron density. It is also shown that the spin diffusion and transport show an anisotropy with respect to the polarization direction of injected spins. This anisotropy differs from the one given by the simple two-component drift-diffusion model.After studying the spin dynamics of massless Dirac Fermions in single-layer graphene, we proceed with the hot-carrier transport and spin relaxation on the surface of topological insulators in Chapter9. We investigate the charge and spin transport under high elec-tric field (up to several kV/cm) on the surface of topological insulator Bi2Se3, where the electron-surface optical phonon scattering dominates except at very low temperature. Due to the spin mixing of conduction and valence bands, the electric field not only accelerates electrons in each band, but also leads to inter-band precession. In the presence of the electric field, electrons can transfer from the valence band to the conduction one via the inter-band precession and inter-band electron-phonon scattering. Besides, we find that due to the spin-momentum locking, a transverse spin polarization, with the magnitude proportional to the momentum scattering time, is induced by the electric field. Our inves-tigation also reveals that due to the large relative static dielectric constant, the Coulomb scattering is too weak to establish a drifted Fermi distribution with a unified hot-electron temperature in the steady state under the electric field. After turning off the electric field in the steady state, the hot carriers cool down in a time scale of energy relaxation which is very long (of the order of100-1000ps) while the spin polarization relaxes in a time scale of momentum scattering which is quite short (of the order of0.01-0.1ps).The dissertation is closed with the study on spin diffusion at the interface of multi-ferroic oxides, i.e., in the two-dimensional electron gas at the interface of LaAlO3/SrTiO3grown on multiferroic TbMnO3, at15K (Chapter10). The spiral magnetic moments of Mn3+in TbMnO3couple with the diffusing spins at the LaAlO3/SrTiO3interface via the Heisenberg exchange interaction. Our study demonstrates that due to this Heisenberg exchange interaction, the spin diffusion length is always finite, despite the polarization direction of the injected spins. This result corrects the claim by Jia and Berakdar [Phys. Rev. B80,014432(2009)] that there is a persistent spin current at the interface when the injected spin’s are polarized perpendicular to the spiral plane of the magnetic moments of Mn3+in TbMnO3.At last we summarize in Chapter11.更多还原