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随着对拓扑态体系理解的深入, 大家普遍认为非平庸的拓扑态直接关联于某些独特的拓扑界面. 基于这一思路, 通过构建不同的拓扑界面, 能够实现对不同自由度输运的调控. 目前, 拓扑界面态已经在多类拓扑体系中被实现, 并且在相关领域引起了广泛关注. 拓扑界面态主要表现出两个基本特点: (i)它是受拓扑保护的; (ii)由于两侧体系的不同又会展现出独特的输运性质. 特别地, 不同特性的拓扑界面态在空间自由度体系中会表现出新奇的拓扑输运特性. 这些输运特性是构建新型拓扑器件的重要理论基础. 结合我们近年的理论工作以及相关进展, 本综述介绍了基于拓扑界面态的可编程集成电路以及层电子学器件的最新进展与未来展望.With the development of the topological theory, it is believed that topological states originate from topologically protected interfaces in condensed matter systems. Significantly, by adjusting the topological interfaces, one can manipulate the transport properties of a sample, thereby possessing distinct features. This paper briefly reviews recent progresses about topological interfaces and their potential applications in quantum devices. In the first part, we expound the fundamental ideas about topological interfaces in disordered Chern insulators. Based on their transport properties, the designs of programmable circuits and logical gates are also clarified. These designs significantly improve the utilization of sample compared with topological surface devices. The second part focuses on the topological interfaces in three-dimensional systems, which exhibits the layertronics of the interfaces. We present axion insulator MnBi2Te4 as a typical example, and the realization of the basic layertronics devices is proposed. Finally, this work summarizes the advantages of topological interface devices and proposes some potential breakthroughs to be achieved in this field.
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图 1 (a) 陈绝缘体及其边缘态分布. 灰色部分表示真空, 蓝色部分表示陈绝缘体样品, 红色箭头表示陈绝缘体的边缘态. (b) 边缘态的形成可以简化为由拓扑平庸与非平庸界面形成的束缚态. 其中真空可以简化为具有带隙无穷大的普通绝缘体
Fig. 1. (a) Schematic of Chern insulator and the edge state. The grey region represents the vacuum, the blue region represents the Chern insulator, and the red arrow shows the edge state. (b) The edge state can be viewed as a bound state located at the interface of topological trivial state and non-trivial state. The vacuum can be viewed as normal insulator with infinite energy gap.
图 2 (a)体能带图[29]; (b)干净(实线)与无序(虚线)样品的陈数$ C_{xy} $随费米能级的演化, 其中霍尔电导率$ \sigma_{xy}=C_{xy}e^2/h $[29]; (c)具有电压势阶梯的样品示意图, 其中电压势可以通过外接门电压调控[29]; (d), (e)特定无序下样品的二端口电导G以及对应的电导涨落δG随费米能的分布[29]
Fig. 2. (a) Bulk energy band diagram[29]; (b) Chern number in clean sample (solid line) and disordered sample (dashed line)[29]; (c) schematic of the sample with electrical potential ladder. The voltage potential is under the control of external gate voltage[29]; (d), (e) the conductances and the distribution of corresponding fluctuations versus Fermi energy for different sample sizes and disorder strengthes[29].
图 3 (a)具有两个拓扑界面的二端口电导随费米能的变化. 插图为实空间电势引起的两个拓扑界面的示意图[29]. (b) 陈数界面示意图, 这里考虑三个陈数界面. 每部分的陈数标记为$ C_i $, 其中$ i = 1, 2, 3\cdots $. 定义$ {\text{δ}}C=C_{i}-C_{i+1} $, 染色区域标记非平庸量子化输运区域, 不同颜色标记它们来源于对应的i和$ i+1 $拓扑界面[29]. (c), (d)分别对应图(a)中红色和蓝色箭头能量位置的局域电流[29]
Fig. 3. (a) The two-terminal conductance versus Fermi energy. The inset shows two topological interfaces caused by the voltage potential in real space[29]. (b) Schematic plots of Chern number distribution. We consider three interfaces, with the corresponding Chern number $ C_i $ marked in the figure. Here, $ i = 1, 2, 3\cdots $. We define $ {\text{δ}} C=C_{i}-C_{i+1} $. Colored regions represent the non-trivial transport energy regions[29]. (c), (d) Correspond the local current density marked by red or blue arrow in panel (a)[29].
图 4 (a)线性势$ V=U_y/N_y $下的电导随费米能的变化, 其中样品尺寸$ N_x=N_y=N $[29]; (b), (c) 局域电流分布, 分别对应于图(a)中对应颜色箭头标示的能量位置[29]
Fig. 4. (a) Conductance versus Fermi energy under linear voltage potential $V=U_y/N_y $, and the size of sample $ N_x=N_y=N $[29]; (b), (c) distribution of local current, which are labeled by arrows with the same color in panel (a)[29].
图 5 样品中电输运通道不同时, 不同标准电压下电导与无序强度的关系[42] (a)—(c) 单通道; (d)—(f) 多通道; (g)—(i) 单通道对多通道
Fig. 5. Relationship between conductance and disorder strength at different standard voltages with different transmission channels in the sample[42]: (a)–(c) Single-channel; (d)–(f) multi-channel; (g)–(i) single-terminal to multi-terminal.
图 7 (a)拓扑绝缘体示意图及其表面态能谱; (b)考虑表面磁化后的结构示意图及其能带. 不同颜色对应不同的表面. 白色箭头表示上表面形成了拓扑非平庸界面态
Fig. 7. (a) Schematic of topological insulator and the band of its surface state; (b) schematic plot of the sample and their surface states. White arrow represents the interface states.
图 9 (a)层阀示意图[69]; (b), (c) 输运电流随上下层过滤器化学势的变化[69]; (d)不同无序强度下输运电流随上层过滤器化学势的变化[69]; (e)不同距离(图(a)中D)输运电流随上层过滤器化学势的变化[69]
Fig. 9. (a) Schematic of a layer valve[69]; (b), (c) transmission current J versus the chemical potential of top layer filter and bottom layer filter[69]; (d) transmission current versus the chemical potential of top layer filter for different disorder[69]; (e) transmission current versus the chemical potential of top layer filter for different distance (D in panel (a))[69]
图 10 (a), (b)层转换器示意图, 箭头表示输运方向, 不同颜色表示不同模式[69]; (c), (d)分别描绘了图(a)和(b)的局域电流分布[69]; (e)两种层转换器中端口1与端口2间电导随化学式的变化[69]; (f)上层-下层转换器的局域电阻随化学式的变化[69]
Fig. 10. (a), (b) Schematic of layer reversers, the arrows show the direction of transmission, while different colors represents opposite mode[69]; (c), (d) distributions of local current in panels (a) and (b)[69]; (e) conductance between terminals 1 and 2 versus chemical potential in two kinds of reversers[69]; (f) local resistances of the top-bottom reverse versus chemical potential[69].
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