拓扑绝缘体表面态有限尺寸效应研究

Three-dimensional topological insulators are a new class of materials that have a bulk band gap and gapless Dirac surface states.Recently, research on the topological insulators, such as Bi2Se3, has attracted much interest because the robust, nontrivial surface states are topologically protected against back scattering from time-reversal invariant defects and impurities. The goal of this project is to investigate the finite-size effect of surface states in the topologicanl insulators according to the low-energy effective Hamiltonian. We plan to study the effect of the thickness,width of the thin film, and the external magnetic field on the dispersion relation and the transport properties of the top, bottom and side surface states in the topological insulator. The content of the research project includes the effect of the width and the magnetic field on the band gap and the conductance for a waveguide on the surface of the topological insulator; the effect of the thickness, width of the topological insulator thin film, and the external magnetic field on the dispersion relation and the transport properties of the top, bottom and side surface states; the quantitative relation between the band gap and the radius, length of the cylindrical nanowire; developing a low-energy effective Hamitonian to describe the surface states of the cylindrical nanowire, and comparing the surface states between the cylindrical nanowire and the cuboid topological insulator nanoribbon. To study the finite-size effect of the surface state of the topological insulators may find some new quantum effects and phenomena different from that of the normal two-dimensional electron gases. It indicates the possibility of devising a novel performance tunable spintronics devices on the basis of the investigation of the finite-size effect.

三维拓扑绝缘体具有类似于绝缘体的能隙但存在无能隙的表面态，这种新奇量子物态及其性质近年来受到广泛关注。本项目拟在能带理论框架内研究拓扑绝缘体表面态的有限尺寸效应，即拓扑绝缘体薄膜厚度、宽度及外磁场对薄膜上下表面、侧表面能带结构、输运性质的影响。具体研究内容包括：拓扑绝缘体一维波导表面态能隙、电导与波导宽度、外磁场强度之间的定量关系；拓扑绝缘体薄膜厚度、宽度对薄膜上下表面、侧表面能带结构、输运性质的影响，以及该薄膜在外磁场下的能带结构及输运特性；圆柱形纳米线表面态能隙与纳米线半径和长度间的定量关系，建立纳米线表面态低能有效哈密顿量模型，区分其与长方体状薄膜表面态性质的异同点。探索拓扑绝缘体表面态的有限尺寸效应，将展现一些与常规半导体异质结二维电子气不同的新量子现象和效应，并可能为从原理上设计一些功能可调的新型自旋电子学器件提供物理基础。

拓扑绝缘体具有较大的自旋轨道耦合，可诱导显著的量子自旋霍尔效应，有望用来制备可实际应用的自旋电子学器件，从而激发了物理学家极大的研究热情。本课题研究了二维拓扑绝缘体边缘态的输运性质，发现边缘态间自旋反转耦合作用可显著调节体系电流，使其增大或减小，可利用门电压改变边缘态间的耦合相互作用，实现有效调控器件输运性质的目的。研究了拓扑绝缘体波导在外磁场作用下的能带结构和磁阻效应，发现磁场可以减小横向有限尺寸诱导的能隙，甚至使表面态能隙闭合；体系磁阻随磁场增加呈线性增长，且具有高场不饱和特性，上述室温下磁阻的稳定性可用来设计磁电器件。分析了拓扑绝缘体表面态在含时电场作用下的手征性输运问题，发现电极间不存在偏压时，垂直入射的电子能完全透射通过含时电场区，保持了Klein隧穿的输运特性。而当电极间存在偏压时，垂直入射电子的透射率显著减小，含时场对大角度入射电子的调控作用明显。拓展研究了石墨烯p-n结，p-n-p结在外磁场作用下的Klein隧穿效应，发现磁场会破坏完美的Klein隧穿，并使角分辨透射率曲线向特定方向偏移。我们解析求得透射率的对称角，并分析了Fabry-Pérot干涉现象，给出了有效调节体系电导的电势和磁场参数，可为器件的制备提供理论指导。