【作者】 付博；

【导师】 李群祥； 石勤伟；

【作者基本信息】 中国科学技术大学 ， 凝聚态物理学， 2017， 博士

【摘要】 利用拓扑的概念来表征和分类固体能带的各种量子相已经成为国际上非常关注的研究课题之一。与传统的绝缘体不同的是,拓扑绝缘体的典型特征是在样品边界上存在受拓扑保护的无能隙边缘激发,这种边缘激发能够产生量子自旋霍尔效应并提供量子化的导电通道。与此同时,人们发现体系的拓扑性质还可以用拓扑不变量(如陈数,Z2指数等)来表征。进一步的研究发现,拓扑概念也可以用于表征无能隙的半金属材料。这些材料的共性是,其低能准粒子的动力学可以用无能隙的狄拉克方程或是变形的狄拉克方程来描述,并且在狄拉克点周围具有非平庸的拓扑性质。研究这些拓扑材料中的各种有趣的量子现象不仅仅具有基础物理研究意义,还将为相关的实验和应用提供理论依据。在第一章中,基于现有研究基础,我们系统地介绍如何利用拓扑概念来表征固体能带的各种拓扑量子相:以Haldane模型为例讨论了陈数和量子霍尔电导之间的关系;以质量畴壁模型和BHZ哈密顿量模型为例计算了拓扑绝缘体里很重要的拓扑保护的边缘态;在具有时间反演不变性的自旋轨道耦合作用下,介绍了拓扑不变量(Z2)和量子自旋霍尔效应之间的紧密联系以及相应的数值计算方案。在第二章中,我们总结出一些处理无序问题的标准微扰理论框架,介绍了图形微扰论的计算方法。以石墨烯体系为例,在自洽波恩近似下,计算了准粒子的自能函数,并进一步的讨论了顶角及最大交叉图对于电导率的贡献。以二维,三维狄拉克粒子为例,用微扰论重整化群方案,推导出相应的重整化群流方程。并在此基础上,利用相应的重整化群流方程,分析了无序对拓扑体系的色散关系、态密度、以及电导率等物理量的影响。这些已有的研究表明,无序对于狄拉克类型的准粒子及其输运性质有很大的影响。在第三章的第一部分,我们提出了利用空间周期势的调制,来实现材料从普通绝缘态到量子自旋霍尔态的转变。以HgTe/CdTe量子阱为例,当体系初始处于拓扑平庸相时,随着空间周期势调制强度的增大,我们的计算表明,由于能级排斥效应会导致导带底和价带顶发生相向移动,并导致能带反转,从而实现拓扑量子相变。通过计算体系的自旋陈数和相应的边界态进一步地证实了这个拓扑量子相变的发生和能带反转相一致。有趣的是,随着调制强度的增加,体系还可以呈现出具有多个拓扑保护的边缘量子导电通道的拓扑相,体系相应的能隙大小足以保证体系在室温下工作。从物理上,我们发现不同陈数的量子相之间的转变与体系共振隧穿能级产生交叉一一对应。在第二部分中,我们侧重研究硅烯吸附问题中的杂质态的性质。已有研究表明在硅烯中可以通过施加垂直于材料的电场,从而实现其拓扑量子相变。我们的理论计算结果表明,在拓扑非平庸相中,吸附原子在能隙中会产生束缚态,而在拓扑平庸相里,吸附原子则只能产生共振态。显然,这个观察到的性质可以帮助实验上表征体系的拓扑性质。在探讨有限浓度的吸附原子对边界态输运性质的影响时,我们发现一旦杂质的束缚态能级和入射波能量一致,则体系的量子电导会随着吸附浓度的增加很快的衰减。其物理根源是,体系一边的边界态很容易通过束缚态和另一边的边界态发生共振隧穿,导致背散射,从而使得体系的电导衰减。在第四章的第一部分,利用动量空间Lanczos方案,我们研究了三维狄拉克半金属中半金属相到扩散金属相的量子相变过程中的准粒子性质以及相应的输运性质。我们的数值模拟结果表明,利用准粒子的性质可以很好的表征这个量子相变以及相应的临界行为。通过拟合数值得到自能函数,我们发现准粒子的自能虚部在相变前后满足一个幂指数关系,其指数依赖于无序强度。当体系进入扩散金属相后,狄拉克点处的自能虚部迅速增加,而在量子相变临界点,体系自能虚部的指数为1,相应的自能实部呈现非解析的对数行为。在量子相变临界点附近,我们进一步讨论了这个非解析修正会引起的各种物理量有趣的反常性质。在第二部分中,利用相同的理论数值方案,我们着重研究了短程无序是如何影响石墨烯的准粒子性质。由于石墨烯低能准粒子具有线性色散关系,使其在狄拉克点附近很容易进入强散射区。众所周知,已有的微扰理论以及自洽的微扰理论在强散射区是不能很好的描述准粒子的行为。尽管如此,相应的基于自洽波恩近似和重整化群计算表明,无序散射会导致准粒子性质产生一个对数修正。而我们的数值模拟结果表明,无序散射会引起自能函数产生幂指数修正,而不是对数修正。此外,我们发现这个定性不同会引起很多有趣而新的物理结果,它们尚有待实验验证。值得指出的是,我们发展的动量空间Lanczos数值方案可以推广到讨论各种线性波在强散射区的准粒子行为。在本博士学位论文中,我们研究了几类拓扑材料的电子结构、输运性质及其无序效应,这些理论研究工作不仅加深了对于拓扑材料物理性质的理解,还为这些拓扑材料将来的实验观测和应用提供了理论支持。更多还原

【Abstract】 Due to the discovery of topological insulators and its experimental realization,the study of the band topology of solid materials has become an important subject of mod-ern condensed matter physics.Unlike conventional band insulators,there may exist a single pair of gapless helical edge or surface states in the bulk gap,exhibiting quan-tized conductance in transport experiments,when the Fermi level locates within the bulk gap.And the band topology can be characterized by a topological invariant such as Chern number or Z2 index.In recent years,topological semimetals have gradually become an important research topics due to their experimental realization.The low-energy quasiparticle can be described by the Dirac equation or the Weyl equation,and its band touching point has a nontrivial topology.The theoretical investigation of these novel and interesting quantum phenomenon in these topological materials not only has the significance of basic physics research,but also provides theoretical insights for re-lated experiments and applications.In Chapter 1,we briefly introduce the concept of topological materials,the bulk-boundary correspondence in topological materials,and the method of determining the band topology and its physical reasons.Firstly,as an example,the Haldane model is adopted to calculate the Chern number.Then,the concept of the topologically protected edge state is introduced by using the mass domain model and the BHZ Hamiltonian.Fi-nally,we discuss the Z2 invariant in topological insulators with time reversed symmetry preserved,and present the numerical methods to calculate the Z2 invariant.In Chapter 2,several widely adopted theoretical methods for dealing with disor-der problem are summarized.Firstly,after briefly introducing the diagrammatic per-turbation theory,we take graphene as an example to discuss the self-consistent Born approximation approach,and calculate the conductivity correction from quantum inter-ference.Then,we turn to the renormalization group(RG)calculation,another power-ful analytical tool for dealing with disordered problems.Taking two-dimensional and three-dimensional Dirac particles as examples,we calculate the RG flow equation of the disordered system.Based on the solution of the flow equation,we will discuss how the physical quantities(i.e.conductivity,density of states and group velocity)will be renormalized by disorder effect,and compare these results with what obtained from the scaling function theory.In the first section of Chapter 3,we introduce one simple approach to realize a topological phase transition by introducing a spatial periodic potential.As an example,we examine the electronic structures of HgTe/CdTe quantum wells,and demonstrate that their band structures can be effectively manipulated by the periodic potential.At a critical potential,we find that a conventional band insulator undergoes a topological phase transition into a quantum spin Hall system,which is characterized by an abrupt change of the spin Chern number and emerging edge states.Our proposal provides an interesting way to dynamically turn on or off topologically protected edge states for application in switching devices.In the second section,we explore the adsorbate effect on the electronic properties of silicene.The calculated local density of states around the adsorbates clearly reveal that the induced localized states contain the band topology information,which can be used to distinguish whether the system is a topological insu-lator or not.We also examine the impact of randomly distributed adsorbates with a low concentration on the electronic structures and the transport properties of silicene,and find that the edge mode backscattering is significantly enhanced when the energies of the incoming modes from leads match that of the in-gap localized states.In the first section of Chapter 4,we determine accurately the quasiparticle and s-caling properties of disordered 3D Dirac semimetals surrounding the quantum critical point separating the Dirac semimetal and diffusive metal regimes,with all higher or-ders of disorder scatterings fully treated,by using the enabling computational approach(the Lanczos method in momentum space).The imaginary part of the quasiparticle self-energy obeys a common power law before,at,and after the quantum phase transi-tion,but the power law is nonuniversal,whose exponent is dependent on the disorder strength.More intriguingly,whereas a common power law is also found for the real part of the self-energy before and after the phase transition,a distinctly different be-havior is identified at the critical point,characterized by the existence of a nonanalytic logarithmic singularity.This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point.The second section of Chapter 4,we explore the quasiparticle behaviors in dis-ordered graphene especially in the strong disorder limit.The self-energy function-s obey the power law behavior for the whole disorder regime.In the weak disorder limit and away from the Dirac point,our simulations give the consistent results with self-consistent Born approximation,while in the strong disorder limit,our simulation-s avoid the singularity around the low energy scale and give more reasonable results.Moreover,we can also obtain the reliable conductivity in the strong disorder limit by using our obtained self-energy function.It is worth noting that our developed Lanczos numerical method in momentum space can be generalized to discuss the quasiparticle behaviors in the strong scattering regime in various waves with linear dispersion.In this thesis,we study the effects of various modulations on the electronic struc-tures and transport properties of topological materials.Our theoretical simulations and findings not only deepen the understanding of the physical properties of topological ma-terials,but also provide theoretical insights for future related experimental observations and applications.更多还原