基于拓扑边缘态输运性质的器件设计与研究

拓扑绝缘体是近年来在凝聚态物理领域发现的一类新型物质相，以其独特的性质而受到研究者广泛关注。拓扑绝缘体的体能隙中会出现基于体边对应关系而产生的拓扑边缘态，这种边缘态通常表现出无质量的线性色散关系，提供的传输通道具有自旋和动量锁定、高迁移率、低耗散以及不受局部缺陷和杂质影响等特点。因此基于拓扑绝缘体的拓扑晶体管为新型电子元器件和自旋电子器件的设计提供了新方向，然而目前拓扑晶体管设计方案通常需要复杂的外场调控系统发生拓扑相变。在这种情况下，探究无需系统发生拓扑相变的拓扑晶体管对提升电子元器件性能具有重要的科学意义。

另一种备受关注的拓扑材料是拓扑超导体，它不仅具有超导能隙而且在能隙内存在手征边缘态，其手征边缘态可描述为满足非阿贝尔统计的马约拉纳费米子。马约拉纳费米子的非局域简并基态可用于构成拓扑量子比特，有望实现容错量子计算。一直以来对于实验上是否真正探测到马约拉纳费米子仍然存在一些争议，因此寻找可供实验上验证马约拉纳费米子存在的直接证据对促进拓扑量子计算的发展具有十分重要的意义。

本论文主要研究了拓扑边缘态的量子隧穿效应以及非局域安德烈夫反射效应。基于拓扑边缘态量子隧穿效应提出了一种无需拓扑相变的拓扑晶体管设计方案，并系统地分析了拓扑晶体管的性能以及实验可行性；同时利用拓扑边缘态的非局域安德烈夫反射，在超导异质结中实现了由电场调制的反常约瑟夫森效应和马约拉纳模量子相干输运现象；基于表面态和体态干涉效应，提出了一种由横向电场调制的单结超导量子干涉仪设计方案。具体的研究内容包括以下几点：

（1）采用一维方势垒散射模型近似求解了拓扑边缘态与能隙间的散射系数并研究了散射系数与能隙大小、入射能量以及电场的依赖关系。在此基础之上，基于二维拓扑绝缘体边缘态隧穿效应设计了一种通过电场调制的拓扑晶体管。数值模拟结果发现拓扑晶体管的量子化电导倍数在电场调制下发生从0到1的跃变，实现了一种完美的开关工作状态，且量子化电导跃变过程不需要发生拓扑相变。同时受拓扑性质的保护，量子化电导对无序和杂质表现出较强的鲁棒特性以及较高的温度适用范围；基于二维磁性拓扑绝缘体的手征边缘态隧穿提出了一种对磁场敏感的拓扑晶体管设计方案。通过数值模拟发现这种拓扑晶体管对磁场方向和强度的变化非常敏感，因此未来有望在磁场敏感探测领域实现应用。

（2）研究了拓扑超导异质结中非局域安德烈夫束缚态在电场作用下的输运性质。在拓扑超导界面上，手征马约拉纳模可诱导拓扑边缘态电子发生非局域安德烈夫反射，导致电子和空穴空间分离，形成具有非局域性质的安德烈夫束缚态。通过外加横向电场改变空间分离的电子和空穴的能量，使得非局域安德烈夫束缚态发生相位移动，实现了反常约瑟夫森效应。此外，非局域安德烈夫束缚态相位移动会诱导手征马约拉纳模产生量子相干输运，由此实现了一种由外加横向电场控制的电导振荡效应。这些结果为实验验证手征马约拉纳模的存在提供了理论依据，并在相位调控的约瑟夫森器件和基于手征马约拉纳模的拓扑晶体管中具有潜在的应用前景。

（3）研究了由外尔半金属组成的单个约瑟夫森结在电场作用下的超导量子干涉现象。其中拓扑表面态由于发生非局域安德烈夫反射可以实现一种由电场调控的反常约瑟夫森效应，其基态相位与横向电场和截面面积的乘积成正比；而体态约瑟夫森效应的基态相位不受横向电场的影响。因此在横向电场的调制下，拓扑表面态约瑟夫森电流与体态电流的相位差诱导电流产生量子干涉效应，从而实现了电场调制的超导量子干涉仪。该结果为超导电子学和超导量子计算的应用提供了新的平台。

As a new class of matter phase, topological insulators have attracted extensive attention in recent years due to their unique properties. For topological insulators, topological edge states can emerge in the energy gap based on the bulk-edge correspondence relation. Such edge states generally exhibit a massless linear dispersion relationship, enabling a transport channel to be spin and momentum locking, high mobility, low dissipation, and insensitivity to local defects and impurities, etc. Hence, topological transistors based on topological insulators can provide a new direction for the design of novel electronic components and spintronic devices. However, the proposed topological transistors strategy usually requires topological phase transition which needs complex external field. Therefore, it is of great significance to explore topological transistors without topological phase transition. 

The other kind of topological matter that attracts much attention is topological superconductors which have superconducting gap and chiral edge states in the gap. The behavior of this edge states can be described as Majorana Fermions, satisfying non-Abelian statistics. Majorana Fermions have a non-local degenerate ground state, which might be used in fault-tolerant quantum computation. However, there are still some controversies over whether Majorana fermions have been confirmed experimentally. Thus, it is very important for the development of topological quantum computing to find direct evidence for the existence of Majorana Fermions. 

In this thesis, we mainly study the quantum tunneling and non-local Andreev reflection of the topological edge states. Based on the quantum tunneling effect of topological edge states, a design of topological transistors without topological phase transition is proposed. The performance and experimental feasibility of the topological transistor have been systematically analyzed. The anomalous Josephson effect and quantum coherent transportation of Majorana mode modulated by the electric field are realized in the superconducting heterojunction according to the non-local Andreev reflections of topological edge states. Based on the interference effect between topological surface states and bulk states, an electrically modulated superconducting quantum interference device consisting of a single Josephson junction is proposed. The specific research contents are summarized as follows:

(1) The scattering coefficient between topological edge states and gaps is approximately solved using one-dimensional square barrier scattering model, and its dependence on the size of energy gap, incident energy and electric field have been studied. On this basis, we design an electric-field-modulated topological transistor based on the helical edge states tunneling in a two-dimensional topological insulator. The calculated results show that the topological transistor can realize a quantized conductance from 0 to 1, exbiting a perfect on/off performance. Such quantized conductance jump does not require topological phase transition. In addition, the quantized conductance of the topological transistor is robust to disorder and impurity and persists at a high applicable temperature due to the topological property. We also design a magnetic sensitive topological transistor based on the chiral edge states of two-dimendional magnetic topological insulator. The numerical simulated results show that the topological transistor is extremely sensitive to both the direction and intensity of the magnetic field, and thus it may find potential application in magnetic field sensors.

(2) The transport property of the non-local Andreev bound states in topological superconductor heterojunction modulated by electric field is studied here. The chiral Majorana modes appeared at the topological superconducting interface can induce non-local Andreev reflections of edge states, which leads to the separation of electrons and holes and thus forms the non-local Andreev bound states. The phase of such non-local Andreev bound states can be shifted derived from the electrically tunable energy change of the spatially separated electrons and holes. As a result, an electrically modulated anomalous Josephson effect should be observable. Moreover, the electrically tunable phase shift in non-local Andreev bound states results in a conductance oscillation because of the quantum coherent transportation of the chiral Majorana modes. These findings provide different proposals to experimentally verify the existence of chiral Majorana modes, and promise potential applications in phase-controllable Josephson devices and topological transistors based on chiral Majorana modes.

(3) The superconducting quantum interference of a single Josephson junction composed of Weyl semi-metal is studied. Owing to non-local Andreev reflection, the topological edge states can realize an anomalous Josephson effect, which can be modulated by electric field. The ground state phase is proportional to the product of the transverse electric field and cross-section area of the junction. However, the Josephson effect contributed by bulk states cannot be affected by the transverse electric field and the related ground state phase remains unchanged. Thus, a phase difference between the topological surface states and bulk states occurs under the modulation of the transverse electric field, producing the quantum interference effect of the current consequently. These results promise a platform for applications in the fields of superconducting electronics and superconducting quantum computation.

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