【作者】 于涛；

【导师】 吴明卫；

【作者基本信息】 中国科学技术大学 ， 凝聚态物理， 2018， 博士

【摘要】 自旋电子学的主要目的是有效地操控固体材料中的自旋(或赝自旋)自由度。对材料中自旋和电荷的动力学及它们的相互影响的理解对自旋电子学的发展非常重要。针对这一问题,本论文根据所关心的物理系统分为三个部分。在第一部分,我们研究半导体及超冷原子中的自旋动力学,其中包括自旋弛豫和自旋扩散。在第二部分,我们研究单层和双层过渡金属硫属化物中由激子引起的谷极化的动力学,其中包括谷去极化动力学和激子的谷霍尔效应。最后在第三部分,我们集中研究s-波和(s+p)-波超导体中Bogoliubov准粒子和凝聚体的自旋及电荷动力学。第一部分,从第1章到第4章,我们集中研究超冷原子以及半导体中的自旋动力学。在第1章,我们综述了半导体自旋电子学的背景及其在超冷原子自旋动力学中的应用。我们首先综述了半导体中自旋的产生,自旋的检测,自旋的弛豫以及自旋的扩散。其中,我们介绍了自旋霍尔效应,主要的自旋弛豫机制(其中包括D’yakonov-Perel’,Elliott-Yafet和Bir-Aronov-Pikus机制)和文献中对自旋扩散的理解(其中包括漂移-扩散模型和非均匀扩展图景)。然后我们简要地介绍了超冷原子物理的背景,以及最近实现的自旋轨道耦合的超冷原子及其实验进展。在第2章中,我们发现在超冷的自旋轨道耦合40K费米气中,当塞曼能远比自旋轨道耦合能大时,D’yakonov-Perel’自旋弛豫是反常的。我们考虑了自旋极化垂直和平行于有效塞曼场的横向和纵向两种构型。我们发现当自旋极化小时,横向自旋弛豫可分成四个而不是通常的两个区域:正常弱散射区,反常类DP区,反常类EY区和正常强散射区。当自旋极化大时,我们揭示Hartree-Fock自能,作为有效磁场,能够极为有效地抑制弱散射区中的自旋弛豫。在InAs(110)量子阱中,当处在Voigt构型下的磁场远比自旋轨道耦合场大时,我们进一步揭示了Hartree-Fock自能对反常D’yakonov-Perel’自旋弛豫的影响。对于横向构型,我们发现自旋弛豫对Hartree-Fock有效磁场非常敏感。我们揭示即使非常小的自旋极化(P = 0.1%)也能够显著地影响自旋弛豫的行为。并且,当体系具有中等自旋极化时,我们发现Hartree-Fock场能够促进而不是抑制横向自旋弛豫。这些特点与通常情形都很不相同。在上述构型中我们理解了自旋弛豫的反常之处后,我们期待相同构型中自旋扩散也呈现反常的特点。在第3章中,我们研究了超冷的自旋轨道耦合40K费米气中稳态的自旋扩散。我们发现稳态自旋扩散的行为由三个特征长度决定:平均自由程,塞曼振荡长度和自旋轨道耦合振荡长度。我们解析上揭示并且数值上验证通过调节散射强度,系统可分为五个区域,其中稳态自旋极化在空间演化的行为非常丰富,其对散射强度、塞曼场和自旋轨道耦合强度的依赖关系非常不同。不同区域中自旋扩散的丰富行为很难用文献中简单的漂移-扩散模型和直接的非均匀扩展图景来进行理解。然而,几乎所有这些丰富的行为能够用我们提出的修正的漂移-扩散模型和/或修正的非均匀扩展图景来理解。特别地,我们揭示了自旋扩散的几个反常特点,其与从简单的漂移-扩散模型和直接的非均匀扩展图景所得到的十分不同。除了研究D’yakonov-Perel’自旋弛豫机制之外,我们也研究了本征锗中的Elliott-Yafet自旋弛豫机制。在第4章中,我们研究了本征锗中热电子效应对由电学方法注入的电子自旋弛豫的影响,并将其与当时在自旋注入构型下的输运实验[Phys.Rev.Lett.111,257204(2013)]进行了比较。我们的计算结果与实验结果符合得很好。我们揭示在低温下,当存在即使很弱的电场时,Elliott-Yafet自旋弛豫能够被显著加快。这是因为锗中电声相互作用非常弱,从而电场能够在体系中诱导出明显的质心漂移。这能够解释实验观测和前面理论计算[Phys.Rev.B 86,085202(2012)]之间的分歧:低温时,前面理论计算比实验结果要大约两个量级。第二部分,从第5章到第8章,我们集中研究单层和双层过渡金属硫属化物MX2(M=Mo,W;X=S,Se)中由于电子-空穴交换相互作用引起的谷去极化动力学及激子的谷霍尔效应。在第5章中,我们综述了在最近实现的单层和双层MX2中谷动力学的实验和理论进展。在单层MX2中,我们分别介绍了与自由载流子、激子和荷电激子有关的谷动力学。特别地,我们综述了最近实现谷极化的产生及探测其弛豫的丰富的实验。在双层MX2中,我们强调了实验中呈现出的激子动力学的新特点。我们也介绍了过渡金属硫属化物异质结及其电荷转移动力学。我们在第6章推导了单层MoS2中的电子-空穴交换相互作用,接着研究了由该交换相互作用引起的谷去极化动力学。我们发现长程和短程交换相互作用两者都能够引起谷间和谷内发光激子的转变。但是由于价带大的能量劈裂,谷内发光激子转变通道几乎禁戒。从而,由于Maialle-Silva-Sham机制[Phys.Rev.B 47,15776(1993)],由交换相互作用提供的谷间通道能够有效地引起谷去极化。当仅考虑交换相互作用的长程部分时,我们的计算结果与最近的谷极化实验,包括时间分辨的谷极化测量、泵浦-探测实验和稳态的光学荧光极化测量相吻合。进一步,受最近Zhu等人的光学荧光实验[PNAS 111,11606(2014)]的启发,在第7章中,我们研究了双层WS2中光激发谱和光学荧光去极化动力学。我们提出了对光学荧光谱的一种不同理解。考虑到双层WS2中同时存在层内激子和电荷转移激子,我们发现由于空穴的层间跃迁,两者的相互叠加可以构成准分子(excimer)态。相应地,实验中观察到的四种光学激发分别计算为A-电荷转移激子,A’-excimer,B’-excimer和B-层内激子。这些态与实验所推测的Γ-谷非直接激子,trion,A-激子和B-激子不同。我们接着推导了双层WS2中电子-空穴交换相互作用,并且研究了其引起的光学荧光去极化动力学。反常地,我们发现演化过程中总是存在一个为初始极化一半的剩余光学荧光极化,其持续无穷长的时间并且对初始的能量展宽和动量散射强度非常皮实。这一大的稳态光学荧光极化意味着光学荧光弛豫时间非常长,从而可能是Zhu等人在双层WS2中所观察到的接近100%、反常大的光学荧光极化的原因。我们进一步看到在单层和双层MX2中,上述电子-空穴交换相互作用是非常强的,其能够有效地改变激子的能谱。这样,在第8章中,我们揭示了激子能谱的修正对单层和双层MoS2中谷去极化动力学的影响。考虑了交换相互作用对激子能谱的修正,我们也能够研究由交换相互作用引起的激子的谷霍尔效应。对于谷去极化动力学,在单层MoS2中,我们发现在强散射区,通常强散射区中的运动致窄图景不再正确,因为一个新的谷去极化通道被打开。对于激子的谷霍尔效应,在单层和双层MoS2中,考虑到施加的单轴应变所引起的平衡态的漂移,我们发现交换相互作用能够引起谷/光学荧光霍尔流。特别地,我们揭示了谷霍尔电导对无序势强度的依赖。在强散射区,随着无序势强度的增加,谷霍尔电导减少;而在弱散射区,谷霍尔电导饱和为一个常数。由于不受泡利阻塞效应,这一常数值可以比费米系统中的远大。第三部分,从第9章到第14章,我们分别在弱和强自旋轨道耦合极限下,研究了超导态半导体量子阱中准粒子和凝聚体的自旋及电荷动力学。在第9章中,我们介绍了超导金属中的准经典动力学方程,其中包括Gor’kov方程,Eilenberger方程,Usadel方程和Ginzburg-Landau方程。所有这些方程都可以用非平衡格林函数方法建立起来。然后,我们介绍了三态超导电性及其在不同材料系统中的可能实现,其中包括3He超流体及非常规超导体Sr2RuO4,具有界面自旋轨道耦合的常规超导体,非中心反演对称超导体,和常规超导体与铁磁体界面。在第10章中,我们首先介绍常规超导体中电荷失衡和自旋失衡的概念,以及实验和理论所揭示的电荷失衡及自旋失衡的动力学,包括其产生与弛豫。然后我们综述了理论和实验对常规超导体中线性及非线性光学响应的研究,其中重点介绍超导体对THz光场的响应,其光子能量在超导能隙附近。在非线性光学响应中,我们介绍了超导体中Nambu-Goldstone模,Higgs模以及Leggett模的概念及其在光学激发过程中的动力学。在第11章中,在弱自旋轨道耦合极限下,在近邻于s-波超导体的GaAs(100)量子阱中,我们研究了超流速度可调控的准粒子态下的准粒子自旋弛豫。我们阐明GaAs(100)量子阱中准粒子态可用超流速度进行调控。在超流速度驱动的准粒子态中,我们发现准粒子的费米面由两个弧所组成(称为费米弧),其分别由类电子和类空穴分支所贡献。当费米弧出现后,当超导序参量趋于零时,我们发现D’yakonov-Perel’自旋弛豫是反常的。这是因为此时支间散射是禁戒的。当与准电子和准空穴湮灭相关的凝聚过程很慢时,这意味着类电子和类空穴费米弧是独立的。接着,费米弧的非闭合结构使得由自旋轨道耦合提供的有效磁场的角度平均不为零。这一非零值可作为一个有效的塞曼场。即使在强散射区,这一有效塞曼场也能够引起自旋振荡。另外,在强散射区,我们发现费米弧的非闭合结构也导致自旋弛豫对动量散射的不敏感,这与通常的运动致窄情形非常不同。我们接着在第12章中运用准粒子近似下规范不变的光学Bloch方程研究弱自旋轨道耦合的s-波超导态量子阱中准粒子和凝聚体对THz光场的响应。特别地,在Bloch方程中,不仅准粒子动力学的微观描述可以实现,凝聚体动力学的影响也能够包括在内,其中超流速度和有效化学势自然地出现。我们揭示超流速度自身能够对准粒子泵浦产生贡献(泵浦效应),而其变化率可贡献驱动场从而对准粒子产生驱动(驱动效应)。我们发现只要驱动出的超导动量比费米动量来得小,以两倍光场频率振荡的Higgs模主要是由驱动效应而不是泵浦效应所激发的。这与文献中用到的Liouville方程或者Bloch方程所得到的结论非常不同,其中驱动效应对反常关联的影响被忽略而仅仅泵浦效应被考虑了。更进一步,在规范不变的光学Bloch方程中,我们基于电荷的两分量模型自恰地考虑了电荷中性条件。由此,准粒子的电荷失衡能够引起凝聚体有效化学势的涨落。我们预言在光学过程中,泵浦效应和驱动效应两者都能够诱导准粒子的电荷失衡,从而导致化学势的涨落。进一步,我们发现即使在由杂质引起的弹性散射下,这一化学势的涨落也会直接提供电荷失衡的弛豫通道。这与以前文献中的理解非常不同。以前研究认为在各向同性的s-波超导体中,弹性散射不能够引起任何电荷失衡的弛豫。在强自旋轨道耦合极限下,作为下面研究动力学的基础,在第13章中,我们首先阐明在近邻于s-波超导体的强自旋轨道耦合的(100)量子阱中,具有三态序参量的超导态能够实现。我们揭示考虑到在量子阱中由近邻效应所提供的单态序参量,不仅三态库伯配对能由自旋轨道耦合诱导出来,三态序参量也能由排斥的电子-电子库仑相互作用诱导出来。具体地说,我们推导了有效的Bogoliubov-deGennes方程,其中由有效的电子-电子相互作用诱导的自能能够贡献单态和三态序参量。对于三态序参量,其为p-波(px± ipy-型)对称性,并且其d-矢量平行于由自旋轨道耦合贡献的有效磁场。我们在InSb(100)量子阱中的数值计算表明,在适当的电子浓度下,单态和三态序参量的模值甚至可以互相比拟,从而它们可以在实验上进行区分。最后,我们介绍这里所预言的(s+p)-波超导态量子阱可以作为实现helical拓扑超导体的平台。基于上述对(s+p)-波超导态InSb量子阱的平衡态的理解,在第14章中,我们进一步运用规范不变的光学Bloch方程研究其中准粒子和凝聚体对THz光场的响应。三态和单态超导电性的动力学都被研究。具体地说,对于三态超导电性,我们预言当光场中的矢势平行于量子阱时,光场能够诱导出库伯对的自旋极化,其按照光场的频率振荡。我们发现库伯对总自旋极化的方向平行于矢势。对于单态超导电性,我们阐明由于InSb(100)量子阱中具有大的自旋轨道耦合,体系存在内外两个费米面。在这一特定的构型中,超导动量可以调节得比内费米面的费米动量大而比外费米面的小。我们发现在这个区域,Higgs模和电荷失衡的动力学相比通常s-波的情形要呈现不同的特点。最后,我们在第15章中对本论文的内容做了总结。更多还原

【Abstract】 Spintronics mainly aims to actively manipulate the spin(or pseudospin)degree of freedom in solid-state materials,in which the understanding on the spin and charge dy-namics and their interplay are quite essential.Focusing on this theme,this dissertation is divided into three parts according to the concerning physical system.In part I,we study the spin dynamics in semiconductor and ultracold atoms,including the spin relaxation and spin diffusion.In part II,we investigate the dynamics of the valley polarization due to exciton in monolayer and bilayer transition metal dichalcogenides,including the valley depolarization dynamics and valley Hall effect of exciton.In part III,we focus on the spin and charge dynamics of the Bogoliubov quasiparticles and condensate in the s-wave and(s + p)-wave superconductors.In part I,from Chapter 1 to 4,we focus on the spin dynamics in ultracold atoms and semiconductor.In Chapter 1,the background of the semiconductor spintronics and its application in the spin dynamics of ultracold atoms are reviewed.We first review the spin generation,spin detection,spin relaxation and spin diffusion in semiconductors,in which the spin Hall effect,the main spin relaxation mechanisms including the Dyakonov-Perel’,Elliott-Yafet and Bir-Aronov-Pikus mechanisms,and the understanding on the spin diffusion in the literature including the drift-diffusion model and inhomogeneous picture are introduced.Then we briefly introduce the background of ultracold atoms and the recently-realized spin-orbit-coupled ultracold atoms and its experimental progress.In Chapter 2,we find in ultracold spin-orbit-coupled 40K gas,when the Zeeman energy is much larger than the spin-orbit-coupling energy,the D’yakonov-Perel’ spin relaxation is anomalous.Transverse and longitudinal configurations with spin polarization perpen-dicular and parallel to the effective Zeeman field are considered,respectively.We find that with small spin polarization,the transverse spin relaxation is divided into four rather than two regimes:the normal weak scattering regime,the anomalous D’yakonov-Perel’-like regime,the anomalous Elliott-Yafet-like regime and the normal strong scattering regime.With large spin polarization,we reveal that the Hartree-Fock self-energy,acting as an effective magnetic field,can extremely-efficiently suppress the transverse spin relaxation in the weak scattering limit.In In As(110)quantum wells with the magnetic field in the Voigt configuration much stronger than the spin-orbit-coupled field,the influence of the Hartree-Fock self-energy on the anomalous D’yakonov-Perel’ spin relaxation is further revealed.For the transverse configuration,it is found that the spin relaxation is very sensi-tive to the Hartree-Fock effective magnetic field.Even an extremely small spin polarization(P =0.1%)can significantly influence the behavior of the spin relaxation.Moreover,we find that the transverse spin relaxation can be enhanced rather than suppressed by the Hartree-Fock field with moderate spin polarization.These features are very different from the conventional situation.With the understanding on the anomalous D’yakonov-Perel’ spin relaxation,anoma-lous features for the spin diffusion are expected in the similar configuration.In Chapter 3,we investigate the steady-state spin diffusion in ultracold spin-orbit-coupled 40K gas.It is found that the behaviors of the steady-state spin diffusion are determined by three char-acteristic lengths:the mean free path,the Zeeman oscillation length and the spin-orbit coupling oscillation length.It is analytically revealed and numerically confirmed that by tuning the scattering strength,the system can be divided into five regimes,in which the behaviors of the spacial evolution of the steady-state spin polarization are very rich,show-ing different dependencies on the scattering strength,Zeeman field and spin-orbit coupling strength.The rich behaviors of the spin diffusions in different regimes are hard to be un-derstood in the framework of the simple drift-diffusion model or the direct inhomogeneous broadening picture in the literature.However,almost all these rich behaviors can be well understood by means of our modified drift-diffusion model and/or modified inhomogeneous broadening picture.Specifically,several anomalous features of the spin diffusion are re-vealed,which are in contrast to those obtained from both the simple drift-diffusion model and the direct inhomogeneous broadening picture.Apart from the study on the D’yakonov-Perel’ spin relaxation mechanism,the Elliott-Yafet mechanism in intrinsic Germanium is also investigated.In Chapter 4,we investigate the hot-electron effect in the spin relaxation of electrically injected electrons in intrin-sic Germanium,in which comparison with the recent transport experiment in the spin-injection configuration[Phys.Rev.Lett.111,257204(2013)]is performed.Reasonable agreement is obtained.We reveal that the spin relaxation is significantly enhanced at low temperature in the presence of weak electric field,originating from the obvious center-of-mass drift effect due to the weak electron-phonon interaction.This can explain the discrepancy between the experimental observation and the previous theoretical calcula-tion[Phys.Rev.B 86,085202(2012)],which deviates from the experimental results by about two orders of magnitude at low temperature.In part Ⅱ,from Chapter 5 to 8,we focus on the valley dynamics due to the electron-hole exchange interaction in mono-and bilayer transition metal dichalcogenides MX2(M=Mo,W;X=S,Se),including valley depolarization dynamics and valley Hall effect of exciton.In Chapter 5,we review the recent experimental and theoretical progresses in the valley dynamics in the newly emerging mono-and bilayer MX2.In monolayer MX2,the valley dynamics of the free carrier,exciton and trion are introduced,respectively,in which the recent rich experiments on the creation of the valley polarization and its depo-larization are reviewed.In bilayer MX2,the new features on the exciton dynamics in the experiments are emphasized.The transition metal dichalcogenide heterostructure and its charge-transfer dynamics are also introduced.In Chapter 6,the electron-hole exchange interaction in monolayer MoS2 is derived,due to which the valley depolarization is investigated.We find that both the long-and short-range exchange interactions can cause the inter-and intra-valley bright exciton tran-sitions.With the intra-valley bright exciton transition channel nearly forbidden due to the large energy splitting of the valence bands,the inter-valley channel due to the exchange interaction can cause the valley depolarization efficiently by the Maialle-Silva-Sham mech-anism[Phys.Rev.B 47,15776(1993)].With only the long-range exchange interaction,the calculations show good agreement with the recent valley polarization experiments,including the time-resolved valley polarization measurement,the pump-probe experiment and the steady-state photoluminescence polarization measurement.Furthermore,inspired by recent photoluminescence experiment by Zhu et al.[PNAS 111,11606(2014)],in Chapter 7,we investigate the optical excitation spectra and the photoluminescence depolarization dynamics in bilayer WS2.A different understanding of the optical excitation spectra is proposed.By considering there exist both the intra-layer and charge-transfer excitons in the bilayer WS2,with inter-layer hopping of the hole,there exists excimer state from the superposition of them.Accordingly,the four optical excitations observed in the experiment are calculated to be the A charge-transfer exciton,A’excimer,B’ excimer and B intra-layer exciton states,respectively.These states are different from the ones speculated in the experiment:indirect exciton for the Γ valley,trion,A exciton and B exciton excitations.We further derive the electron-hole exchange interaction in the bilayer WS2,due to which the photoluminescence depolarization dy-namics is studied.Anomalously,we find that there is always a residual photoluminescence polarization that is exactly half of the initial one,lasting for infinitely long time,which is robust against the initial energy broadening and strength of the momentum scattering.This large steady-state photoluminescence polarization indicates that the photolumines-cence relaxation time is extremely long,and hence can be the cause of the anomalously large photoluminescence polarization,nearly 100%observed in the experiment by Zhu et al.in the bilayer WS2.It can be further seen that in monolayer and bilayer MX2,above electron-hole ex-change interaction is very strong,which can modify the exciton energy spectra efficiently.Thus,in Chapter 8,we reveal the influence of this modification on the valley depolariza-tion dynamics in mono-and bilayer MoS2.With this modification,we can consider the valley Hall effect of exciton due to the exchange interaction.For the valley depolarization dynamics,in the monolayer MoS2,it is found that in the strong scattering regime,the motional narrowing picture in the conventional strong scattering regime is no longer valid,and a novel valley depolarization channel is opened.For the valley Hall effect of exciton,in both the mono-and bilayer MoS2,with the drift of the equilibrium state by applied uni-axial strain,the exchange interaction leads to the valley/photoluminescence Hall current.Specifically,the disorder strength dependence of the valley Hall conductivity is revealed.In the strong scattering regime,the valley Hall conductivity decreases with the increase of the disorder strength;whereas in the weak scattering regime,it saturates to a constant,which can be much larger than the one in Fermi system due to the absence of the Pauli blocking.In part III,from Chapter 9 to 14,we study the spin and charge dynamics of the quasi-particle and condensate in the superconducting semiconductor quantum wells in the weak and strong spin-orbit coupling limit,respectively.In Chapter 9,we introduce the quasiclas-sical kinetic equations including Gor’kov equation,Eilenberger equation,Usadel equation and Ginzburg-Landau equation in the superconducting metal.All these equations can be constructed from the non-equilibrium Green function method.Then we introduce the triplet superconductivity and its possible realization in different material system,including 3He superfluid and nonconventional superconductor Sr2RuO4,the conventional supercon-ductor with interface spin-orbit coupling,the non-centrosymmetric superconductor,and the interface between conventional superconductor and ferromagnet.In Chapter 10,we first introduce the concept of the charge and spin imbalances in the conventional supercon-ductor and their dynamics revealed in the experimental and theoretical studies,including their generation and relaxation.We then review the theoretical and experimental studies on the linear and non-linear optical response in the conventional superconductor,with the emphasis on the response to the THz field,in which the phonon energy is around the superconducting gap.In the nonlinear optical response,the concepts of Nambu-Goldstone mode,Higgs mode and Leggett mode in the superconductor are introduced and their possible dynamics in the optical excitation processes are reviewed.In Chapter 11,in the weak spin-orbit coupling limit,we first investigate the quasipar-ticle spin relaxation with superconducting-velocity-tunable state in GaAs(100)quantum wells in proximity to s-wave superconductor.We show the quasiparticle state in GaAs(100)quantum wells can be tuned by the superconducting velocity.In the driven quasi-particle state,we address that the quasiparticle Fermi surface is composed by two arcs,referred to as Fermi arcs,which are contributed by the electron-and hole-like branches.When the Fermi arc emerges,the D’yakonov-Perel’ spin relaxation is anomalous when the order parameter tends to zero,because the branch-mixing scattering is forbidden.When the condensation process associated with the annihilation of the quasi-electron and quasi-hole is slow,this indicates that the electron-and hole-like Fermi arcs are independent.The open structure of the Fermi arc leads to the nonzero angular-average of the effective magnetic field due to the spin-orbit coupling,which acts as an effective Zeeman field.This Zeeman field leads to the spin oscillations even in the strong scattering regime.Moreover,in the strong scattering regime,we find that the open structure of the Fermi arc also leads to the insensitiveness of the spin relaxation to the momentum scattering,in contrast to the conventional motional narrowing situation.In Chapter 12,we then investigate the quasiparticle and condensate dynamics in re-sponse to the THz optical pulses in the weak spin-orbit-coupled s-wave superconducting semiconductor quantum wells by using the gauge-invariant optical Bloch equations in the quasiparticle approximation.Specifically,in the Bloch equations,not only can the micro-scopic description for the quasiparticle dynamics be realized,but also the dynamics of the condensate is included,with the superfluid velocity and the effective chemical potential naturally incorporated.We reveal that the superfluid velocity itself can contribute to the pump of quasiparticles(pump effect),with its rate of change acting as the drive field to drive the quasiparticles(drive effect).We find that the oscillations of the Higgs mode with twice the frequency of the optical field are contributed dominantly by the drive ef-fect rather than the pump effect as long as the driven superconducting momentum is less than the Fermi momentum.This is in contrast to the conclusion from the Liouville or Bloch equations in the literature,in which the drive effect on the anomalous correlation is overlooked with only the pump effect considered.Furthermore,in the gauge-invariant optical Bloch equations,the charge neutrality condition is consistently considered based on the two-component model for the charge,in which the charge imbalance of quasiparticles can cause the fluctuation of the effective chemical potential for the condensate.It is pre-dicted that during the optical process,the quasiparticle charge imbalance can be induced by both the pump and drive effects,leading to the fluctuation of the chemical potential.This fluctuation of the chemical potential is further demonstrated to directly lead to a relaxation channel for the charge imbalance even with the elastic scattering due to impu-rities.This is very different from the previous understanding that in the isotropic s-wave superconductivity,the elastic scattering cannot cause any charge-imbalance relaxation.In the strong spin-orbit coupling limit,to start,in Chapter 13,we first show that the gapped triplet superconductivity,i.e.,a triplet superconductor with triplet order pa-rameter,can be realized in strong spin-orbit-coupled(100)quantum wells in proximity to s-wave superconductor.It is revealed that with the singlet order parameter induced from the superconducting proximity effect,in quantum wells,not only can the triplet pairings arise due to the spin-orbit coupling,but also the triplet order parameter can be induced due to the repulsive electron-electron Coulomb interaction.Specifically,we derive the effective Bogoliubov-de Gennes equation,in which the self-energies due to the effective electron-electron interaction contribute to the singlet and triplet order parameters.For the triplet order parameter,it is the p-wave(px±ipy)one with the d-vector parallel to the effective magnetic field due to the spin-orbit coupling.The numerical calculation in InSb(100)quantum wells shows that with proper electron density,the singlet and triplet order parameters can be even comparable,which can be experimentally distinguished.Finally,we introduce that the predicted(s+p)-wave superconducting quantum wells can be the platform for the helical topological superconductor.Based on the understanding on the equilibrium state in above(s+p)-wave supercon-ducting InSb quantum wells,in Chapter 14,we further investigate the quasiparticle and condensate dynamics in response to the THz optical pulses by using the gauge-invariant optical Bloch equations.Both the dynamics of triplet and singlet superconductivity are studied.Specifically,for the triplet superconductivity,we predict that with the vector po-tential parallel to the quantum wells,the optical field can cause the total spin polarization of Cooper pairs,oscillating with the frequency of the optical field.The direction of the total Cooper-pair spin polarization is shown to be parallel to the vector potential.For the singlet superconductivity,we show that due to the large spin-orbit coupling in InSb(100)quantum wells,there exist two Fermi surfaces including the inner and outer ones.In this specific configuration,the superconducting momentum can be tuned to be larger than the inner Fermi momentum but smaller than the outer one.We find that in this regime,the dynamics of the Higgs mode and charge imbalance shows different features in comparison with the conventional s-wave case.Finally,we summarize in Chapter 15.更多还原