【作者】 吕敏；

【导师】 完绍龙；

【作者基本信息】 中国科学技术大学 ， 理论物理， 2011， 博士

【摘要】 石墨烯,即具有六角晶格结构的二维碳原子单层,是近几年凝聚态物理中出现的一个十分热门的研究领域。在实验方面,物理学家们发现石墨烯系统具有极其高的电子迁移率,比目前广泛使用的半导体硅的电子迁移率还要高出两个数量级,因而被认为是下一代可以替代硅的新型半导体材料。在理论方面,石墨烯的载流子能谱是手征无质量的Dirac能谱,其能量线性正比于动量,这种类型的能谱在目前的物理系统中是比较罕见的,使得石墨烯系统具有许多与以往的系统截然不同的独特性质和现象,因此也引起了理论物理学家们的广泛关注。双层石墨烯,是由石墨烯派生的另一个重要的二维系统,它是两个单层石墨烯通过Bernal堆积而成的。在低能有效理论中,双层石墨烯系统的载流子能谱是手征无质量的能谱,其能量正比于动量的二次方,与单层石墨烯和传统的二维电子气体系统既不尽相同又兼有两者的部分特性。这也是双层石墨烯在某种程度上可以看成是单层石墨烯和传统的二维电子气体系统的中介态的一个体现。类似单层石墨烯,双层石墨烯也具有非常高的电子迁移率。因为它在施加电场后很容易打开一个能隙而变成半导体,所以作为新型的超高速场效应晶体管材料而备受期待。我们知道,研究一个系统对外场的线性响应是一种非常重要的获知该系统内部特性的手段:一方面系统对外场的响应可以从理论上通过线性响应理论进行计算,另一方面这些响应又是实验上可以直接测量的物理量,因此它们作为一座桥梁沟通理论和实验,并从实验的结果检验理论的正确与否。在物理实验中,最常见、最重要的线性响应就是它对外加电场的电响应和对外加磁场的磁响应,它们就是该系统的密度-密度响应和流-流响应函数。因此,研究一个系统的电和磁响应,对我们了解系统的基本性质具有十分重要的意义。本博士论文正是运用线性响应理论对双层石墨烯的电和磁响应进行理论上的计算和研究。这篇博士论文的第一章简单回顾了石墨烯和双层石墨烯的一些基本概念以及在这些系统中发生的令人惊奇的物理效应,包括反常的量子霍尔效应、Klein隧穿和镜对称Andreev反射效应等,在第二章和第三章的主体部分,分别阐述了作者在双层石墨烯的电和磁响应方面所做的具体工作:(1)在电响应方面,我们用无规相位近似(RPA)方法,计算了在有屏蔽库仑杂质散射影响的情况下,在有限温度下双层石墨烯载流子的电荷输运。在目前的实验室条件下,很多石墨烯和双层石墨烯样品都是在放置在衬底上的,这些衬底上带有的库仑电荷杂质会对石墨烯和双层石墨烯系统的载流子输运性质产生重要的影响。因此,研究石墨烯系统的库仑屏蔽问题以及在这些电荷杂质的屏蔽库仑势影响下石墨烯的电导行为,都是十分有意义的。之前的文献中,已经有人研究了单层石墨烯在零温和有限温度时的库仑屏蔽以及双层石墨烯在零温时的库仑屏蔽,但是还没有人研究双层石墨烯在有限温度时的库仑屏蔽情况。本文第一部分的工作正是弥补了这一缺憾。作者解析地研究了在各个动量空间区域内,双层石墨烯的电极化率随温度的变化行为:发现对于任意的温度,极化率的大小在零动量转移时都等于态密度,但在大动量转移时则增大一个因子log4,在动量为k_F附近则表现出非单调的温度相关行为。由于强的2k_F散射所导致的静态极化率的尖峰将随着温度的提升而被抹平。在所有的动量区域,静态极化率都表现出很弱的温度相关性,这体现了双层石墨烯独特的电子特性。我们同样也第一个解析地研究了在高载流子密度的情况下,低温和高温极限下双层石墨烯的电导率的渐近行为,并发现随着温度的提升,双层石墨烯从一个类似二维电子气体的随温度线性变化的金属行为逐渐过渡到一个类似单层石墨烯的随温度平方变化的绝缘体行为。我们认为这是双层石墨烯作为单层石墨烯和二维电子气体的中间态所特有的一种过渡行为。(2)在磁响应方面,作者用线性响应理论研究了在一个空间缓慢变化的外磁场下,一个弱掺杂的双层石墨烯系统的轨道抗磁性。早期的研究表明,Landau抗磁性(又称轨道抗磁性)相比Pauli顺磁性而言,在对石墨磁性的贡献中占据了主导地位。这种情况到了石墨烯和双层石墨烯系统也同样如此。因此,研究石墨烯系统的轨道抗磁性无疑对我们理解石墨烯系统的磁性具有重要的意义。在之前的文献中,已经有人研究了单层石墨烯在零温、有限费米能量、零动量和有限动量时的轨道磁化率,以及双层石墨烯在零温、有限费米能量、零动量时的轨道磁化率,但还没有人研究双层石墨烯在零温、有限费米能量、有限动量时的轨道磁化率。我们第二部分的工作就是完善这一点。在这一部分工作,我们解析研究了在零温、有限费米能量、有限动量时双层石墨烯轨道磁化率,并给出了在零温、有限费米能量、有限动量时双层石墨烯轨道磁化率的解析表达式。我们发现双层石墨烯的磁场屏蔽因子是与动量有关的,因而将导致比单层时更复杂的磁场屏蔽行为。我们同样也研究了在各种不均匀外磁场诱导下,在双层石墨烯体内产生的磁化强度和电流,发现它们迥异于在单层石墨烯时的情况。但是,我们发现类似单层石墨烯,放置在双层石墨烯上方的磁性物质会受到一个抗磁排斥力的作用,该排斥力近似等同于在双层石墨烯另一边的虚拟镜像对该磁性物质的斥力,只是其作用强度会减弱,减弱幅度是与系统特征尺度有关的磁场屏蔽因子。在最后一章,作者对所做的工作做了一个总结与展望。更多还原

【Abstract】 Graphene, a two-dimensional single layer of carbon atoms arranged on a honey-comb lattice, is a very hot research field of condensed matter physics in recent years.On its applied side, experimental physicists have found that the graphene system hasan extremely high mobility, which is even two orders higher than that of the semicon-ductor material silicon. Thus it is regarded as a new semiconductor material to replacesilicon. On its academic side, the charge carrier of graphene has a chiral mass-less lin-ear Dirac dispersion, which is rather peculiar in present physical systems. Due to thisdispersion, the graphene system has many unique properties and phenomena rather dif-ferent from the regular systems, and therefore attracts much attentions from theoreticalinvestigators. Bilayer graphene, which is formed by stacking two single layer graphenein Bernal stacking, is anther significant graphene-related system. In its low energy ef-fective theory, the charge carrier of bilayer graphene has a chiral mass-less parabolicdispersion. It is different from that of single layer graphene and 2 dimensional electrongas system, but in some parts it is similar to them. In some sense, bilayer graphene isconsidered as the intermediate between single layer graphene and 2 dimensional elec-tron gas system. Similar to the single layer graphene, bilayer graphene also has a veryhigh mobility. Because bilayer graphene is easy to open a gap and became a semicon-ductor by an external electric field, it is expected as a new ultra high speed material ofthe field effect transistor.As we know, investigating the responses to the external fields is a very importantmethod to understand the internal properties of the system: On one side, the responsescan be calculated theoretically by using the linear response theory, and on the other sidethey can determined directly from experiments. Therefore they can be considered asa bridge connecting the theories and experiments and used to check whether the theo-ries are correct by comparing with the experimental results. Through the experimentalinvestigation, the most common and important responses of a system are its charge re-sponse to the external electric field and magnetic response to the magnetic field, whichare actually the density-density response and current-current response of this system.For a certainty it is significant to investigate the charge and magnetic responses of asystem, and that is the issue we have done in this thesis for bilayer graphene.In the first chapter of this thesis, we simply review some basic concepts of graphene and bilayer graphene and the wondrous effects occurring in these systems, including theanumalous quantum Hall effect, Klein tunneling and the specular Andreev re?ection. Inthe second and third chapters, we represent our two works on the charge and magneticresponses of bilayer graphene.(1) In terms of the charge response, we calculate the temperature-dependent chargecarrier transport of bilayer graphene impacted by Coulomb impurity scattering withinthe random-phase approximation. In conditions of the present laboratory, many sam-ples of graphene and bilayer graphene are laid upon the substrates, where the screenedCoulomb impurities will have an unavoidable in?uence on the charge carrier trans-port of graphene and bilayer graphene. Therefore, it is significative to investigate theCoulomb screening and the screening-induced temperature-dependent behavior of con-ductivity in graphene-related systems. Before this work, the Coulomb screening of sin-gle layer graphene at zero and finite temperatures and bilayer graphene at zero temper-ature have been well investigated, however, the analytically investigation of Coulombscreening of bilayer graphene, which is the issue we will discuss in the second chapter,has not yet been provided.We analytically calculate the temperature-dependent behaviors of the polarizabil-ity of bilayer graphene in all wave vector regimes:We find the polarizability at zero mo-mentum transfer is equal to the density of states and enhanced by a factor log 4 at largemomentum transfer for arbitrary temperature while the around k_F it has nonmonotonictemperature-dependent behavior. The sharp cusp of static polarizability arising fromthe strong 2k_F backward scattering would been smoothed by the increasing tempera-tures. In all wave-vector regimes, the static polarizability shows a weak temperaturedependence, representing the distinctive electron property of bilayer graphene. We alsofirstly obtain the asymptotic behaviors of conductivity of bilayer graphene at low andhigh temperature at the high carrier density, and finds the behavior of bilayer grapheneturns from a two-dimensional electron gas like linear temperature metallic behaviorto a single-layer graphene and quadratic temperature insulating behavior as the tem-perature increases. We argue this shows a crossover behavior of bilayer graphene asintermediate between the single layer graphene and 2 dimensional electron gas.(2) In terms of the magnetic response, within the linear response theorem we inves-tigate the orbital diamagnetism of a weak-doped bilayer graphene in spatially smoothlyvarying magnetic field. As shown in the early investigations, compared with the Pauliparamagnetism, Landau diamagnetism (i.e., orbital diamagnetism) dominates the con-tribution to the whole magnetism of graphite. The same argument is fit for the case of graphene and bilayer graphene. Therefore, it is significant to investigate orbital dia-magnetism of graphene systems for understanding their magnetism. Before our work,the orbital susceptibility of single layer graphene at zero temperature with finite Fermienergy, zero and finite wave vector and bilayer graphene at zero temperature with finiteFermi energy, zero wave vector have been studies, but the analytically investigation oforbital susceptibility of bilayer graphene at zero temperature with finite Fermi energyand finite wave vector, which is the issue we will discuss in third chapter, has not yetbeen provided.In this part, we obtain the general analytic expression of the orbital susceptibilityof bilayer graphene, with finite wave vector and Fermi energy, at zero temperature.We find that the magnetic field screening factor of bilayer graphene is dependent withthe wave vector, which results in a more complicated screening behavior comparedwith that of single layer graphene. We also study the induced magnetization, electriccurrent in bilayer graphene under several types of nonuniform magnetic field, and findthey are qualitatively different from that in single layer graphene and 2 dimensionalelectron gas. However, we find that similar to the single layer graphene, the magneticobject placed above bilayer graphene is repelled by a diamagnetic force from bilayergraphene, approximately equivalent to a force produced by its mirror image on the otherside of bilayer graphene with a reduced amplitude dependent with the typical length ofthe systems.In the last chapter, we make a summary and scope of our works.更多还原