【作者】 杨辉；

【导师】 乔振华；

【作者基本信息】 中国科学技术大学 ， 物理学， 2022， 博士

【摘要】 以石墨烯为代表的二维层状材料以其新颖的材料性能、优异的电磁学、光学、热力学性质受到了凝聚态物理学界广泛的关注。由于某一维度上的尺寸减小到原子层厚度,二维层状材料在面内与面外两个方向均展现了新奇的电子输运特性。关于面内输运的研究,研究者们希望通过量子反常霍尔效应无能隙的边缘态实现低耗散的电子输运。虽然受拓扑保护的边缘态具有鲁棒性,但实际材料中存在的各种强无序仍会阻碍以它为基础的电子器件的设计,造成安德森局域化现象。在这个过程中,电子因磁性杂质影响而出现自旋翻转,使安德森相变过程变得更为复杂,尤其是在大陈数量子反常霍尔效应体系中,存在多条边缘态,使得安德森相变过程更加复杂多变,在某种程度上也阻碍了学者们对这部分内容的研究。而在面外方向,石墨烯能够提供更多可调控的自由度,比如层间耦合距离、不同层之间的扭角、层间电压差等,因而被制作成不同类型的电子器件。以往的研究往往聚焦于单/双层石墨烯结在同一平面内的电子透射,缺少对于不同层之间的电荷转移以及垂直输运的机理的研究,而相关的实验却日益增多。因此,探究层间耦合、载流子浓度等因素在石墨烯中的垂直输运所起的作用具有非常重要的意义。针对上述在二维层状材料中存在的输运问题,本研究主要采用紧束缚模型和Landauer-Büttiker公式来探究体系的输运性质。本文分为如下六个部分:第一章主要介绍了量子反常霍尔效应的形成原理和经典模型,以及两种主要实现大陈数绝缘体的体系。针对面内输运方面,我们梳理了在拓扑材料中杂质造成的安德森局域化的研究现状;与此同时,我们也对石墨烯体系中垂直输运相关的研究做了简要的总结。第二章简要介绍了本文的主要研究方法,即紧束缚模型和非平衡格林函数,以及如何计算不同参数空间的贝里曲率和陈数。第三章和第四章中,我们以双层石墨烯和磁性拓扑绝缘体两种大陈数体系为例,研究了当掺杂能影响电子自旋的磁性杂质时整个体系的安德森局域化现象。在陈数为4的双层石墨烯中,磁性杂质促使体系从量子反常霍尔绝缘相先转变为金属相,进而转变为安德森绝缘相。而在磁性拓扑绝缘体中,随着杂质强度增大,整数化的霍尔电导平台从高到低逐个被破坏,陈数为-N的量子反常霍尔绝缘体会先进入金属相,进而转变为陈数为-(N-1)的量子反常霍尔绝缘相,经历N-1次循环后才变为安德森绝缘相。上述现象可以通过价带和导带所携带的贝里曲率交换的图像来加以解释。最后,我们给出了关于拓扑电荷的唯象模型以形象地展示局域化过程。该研究解决了大陈数体系中影响电子自旋的磁性杂质的安德森局域化问题。第五章中,我们利用石墨烯来构建四端口器件以研究石墨烯中的垂直输运。在AB堆垛的armchair型边界的双层石墨烯中,在电荷中立点附近,电子本征波函数在中心区域的相互干涉造成了电导周期性震荡,并且变化周期只受到层间相互作用影响,而不受中心区域横向方向尺寸大小的影响,此时入射电流被该电子器件均分到其余端口。而当电子处于高能级时,多通道之间的散射使得不同端口电导出现互补的现象。该研究阐明了费米能级、层间耦合以及体系尺寸在石墨烯体系垂直输运中所起的作用,为设计控制电流分配、开关的电子器件提供了理论指导。我们在第六章对本研究做了简要的总结,并对上述两个课题未来的发展方向进行了展望。更多还原

【Abstract】 Two-dimensional layered materials represented by graphene have attracted considerable attention in condensed matter physics due to their novel material properties and excellent electromagnetic,optical and thermodynamic properties.Since the size in one dimension can be reduced to atomic layer thickness,two-dimensional layered materials show novel electronic transport properties in both in-plane and out-of-plane directions.For the studies of in-plane transport,researchers hope to realize electronic transport with low dissipation through the edge states of quantum anomalous Hall effect.Although the edge states protected by topology are robust,varieties of strong disorders in practical materials still hinder the design of electronic devices based on the edge states,which will cause Anderson localization.In this process,the spin flip of electrons caused by magnetic impurities makes the Anderson phase transition more complex.Especially in the large-Chen-number quantum anomalous Hall effect system,there are multiple edge states which make the Anderson phase transition even more complicated and changeable,which also hinders the scholars’researches on this topic to some extent.In the out-of-plane direction,graphene can provide more degrees of freedom which can be regulated,such as interlayer coupling distance,twisted angle between different layers,and interlayer voltage difference.Previous studies usually focus on the electron transmission of monolayer/bilayer graphene junction in the same plane,and lack the researches on the mechanisms of charge transfer and vertical transport between different layers,while the experiment results about vertical transports are on the increase.Therefore,it is of great significance to explore the functions of the factors like interlayer coupling and carrier concentration in the vertical transport of graphene.In view of the above problems in the transport of two-dimensional layered materials,our research mainly adopts the tight-binding model and Landauer-Büttiker formula to explore the transport properties of the system.This dissertation is divided into the following six parts:The first chapter mainly introduces the formation principle and classical model of quantum anomalous Hall effect,and two main systems that can realize large-Chernnumber insulators.In the aspect of in-plane transport,we sort out the current researches of Anderson localization caused by disorders in topological materials;at the same time,we also briefly summarize the researches on vertical transport in graphene system.In Chapter 2,we provide a brief introduction to the main research methods of this dissertation,namely tight-binding model and non-equilibrium Green’s function,and the ways to calculate the Berry curvature and Chen number in different parameter spaces.In Chapter 3 and Chapter 4,taking two large-Chern-number systems of bilayer graphene and magnetic topological insulator as examples,we give an insight into the Anderson localization of the whole system when magnetic impurities that can affect electronic spin are doped.In the bilayer graphene with Chern number 4,magnetic impurities promote the system to change from quantum anomalous Hall insulation phase into metallic phase,and then into Anderson insulating phase.In the magnetic topological insulator,with the increase of impurity strength,the integer Hall conductance plateau is destroyed one by one from high to low.The quantum anomalous Hall insulator with Chern number-N will first enter the metallic phase,and then change into the quantum anomalous Hall insulating phase with Chern number-(N-1),and finally turn into Anderson insulating phase after N-1 cycles.The above phenomena can be explained via the Berry curvature exchange carried by valence and conduction bands.At the end of this chapter,we provide a phenomenological model of topological charge to vividly illustrate the localization process.This research solves the Anderson localization problems of magnetic impurities which affect electronic spin in large-Chen-number systems.In Chapter 5,we use graphene to construct four-terminal devices to study the vertical transport.In the AB-stacked bilayer graphene with the armchair boundary,around the charge neutral point,the interference of the electronic eigenwave functions in the central region causes the periodic oscillation of conductivity,and the variation period is only influenced by the interlayer interaction,not by the size of the transverse direction of the central region.Here,the incident current is equally distributed to the other terminals by the electronic device.However,when Fermi energy is at the high energy level,the scattering between multiple channels makes the conductance of different terminals complementary.This research illustrates the functions of Fermi energy,interlayer coupling and system size in the vertical transport of graphene system.which provides theoretical guidance for the design of electronic devices that can be adapted to controlling the distribution and switching of current.At the end of this dissertation,we make a brief summary of this research,and look to the future development of the above two topics in Chapter 6.更多还原