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随着对于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, 人们通过构建不同的拓扑界面, 能够实现对于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. 结合我们近年理论工作以及相关进展, 本综述将介绍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 are generally originating from topological protected interfaces in condensed matter systems. Significantly, by adjusting the topological interfaces, one is able to manipulate the transport properties of a sample, which could possess 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 idea about topological interfaces in disordered Chern insulators. Based on their transport properties, the designs of programable 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 some potential breakthroughs to be achieved in this area are also raised.
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图 1 (a) 陈绝缘体及其边缘态分布. 其中灰色部分表示真空, 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) The 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. (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 $. (c)具有电压势阶梯的样品示意图. 其中电压势可以通过外接门电压调控. (d)和(e)分别是特定无序下样品的二端口电导G以及对应的电导涨落$ \delta G $随费米能的分布. 引自文献[29]
Fig. 2. (a)Bulk energy band diagram. (b)Chern number in clean sample (solid line) and disordered sample (dashed line). (c)Schematic of the sample with electrical potential ladder. The voltage potential is under the control of external gate voltage. (d) and (e) The conductances and the distribution of corresponding fluctuations versus Fermi energy for different sample sizes and disorder strengthes. From Ref. [29]
图 3 (a)具有两个拓扑界面的二端口电导随费米能的变化. 插图: 实空间电势引起的两个拓扑界面的示意图. (b) 陈数界面示意图, 我们考虑三个陈数界面. 每部分的陈数标记为$ C_i $. 其中, $ i = 1, 2, 3\cdots $. 我们定义$ \delta 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. (c)和(d)分别对应图(a)中红色和蓝色箭头能量位置的局域电流. 引自文献[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. (b) Schematic plots of Chern number distribution. We consider 3 interfaces, with the corresponding Chern number $ C_i $ marked in the figure. Here, $ i = 1, 2, 3\cdots $. We define $ \delta C=C_{i}-C_{i+1} $. Colored regions represent the non-trivial transport energy regions. (c) and (d) correspond the local current density marked by red or blue arrow in (a). From Ref. [29]
图 4 (a)线性势$ V=Uy/N_y $下的电导随费米能的变化. 其中, 样品尺寸$ Nx=Ny=N $ (b)和(c)为局域电流分布, 分别对应于图(a)中对应颜色箭头标示的能量位置. 引自文献[29]
Fig. 4. (a)Conductance versus Fermi energy under linear voltage potential. Here, the size of sample $ Nx=Ny=N $. (b) and (c) show the distribution of local current, which are labeled by arrows with the same color in (a). From Ref. [29]
图 5 样品中电输运通道、电流分布与电导. (a)—(c)存在单通道时电流分布及不同标准电压下电导与无序强度的关系; (d)—(f)存在多通道时电流分布及不同标准电压下电导与无序强度的关系; (g)—(i)存在单端口对多个端口的通道时电流分布及不同标准电压下电导与无序强度的关系. 引自文献[42]
Fig. 5. The sample and their conductances and local current density distributions. (a)$ - $(c)single-channel cases. (d)$ - $(f) multi-channel cases. (g)$ - $(i) single-terminal to multi-terminal cases. From Ref. [42]
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; (b)(c) 输运电流随上下层过滤器化学势的变化; (d)不同无序强度下输运电流随上层过滤器化学势的变化; (d) 不同距离[图(a)中D]输运电流随上层过滤器化学势的变化. 引自文献[70]
Fig. 9. (a)Schematic of a layer valve. (b)(c)Transmission current J versus the chemical potential of top layer filter and bottom layer filter. (d)Transmission current versus the chemical potential of top layer filter for different disorder. (e)Transmission current versus the chemical potential of top layer filter for different distance(D in figure(a)). From Ref. [70]
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; (c)(d)分别描绘了(a)(b)的局域电流分布; (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; (f)上层-下层转换器的局域电阻随化学式的变化. 引自文献[70]
Fig. 10. (a)(b) Schematic of layer reversers. Arrows show the direction of transmission, while different colors represents opposite mode. (c)(d) depict the distributions of local current in (a) and (b), respectively. (e)Conductance between terminals 1 and 2 versus chemical potential in two kinds of reversers. (f)Local resistances of the top-bottom reverse versus chemical potential. From Ref. [70]
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[1] Klitzing K, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494
Google Scholar
[2] Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61
Google Scholar
[3] Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2008 Phys. Rev. Lett. 101 146802
Google Scholar
[4] Qi X L, Wu Y S, Zhang S C 2006 Phys. Rev. B 74 085308
Google Scholar
[5] Qi X L, Hughs T L, Zhang S C 2008 Phys. Rev. B 78 159901
Google Scholar
[6] Nomura K, Nagaosa N 2011 Phys. Rev. Lett. 106 166802
Google Scholar
[7] Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K S, Nagaosa N, Kawasaki M, Tokura Y 2015 Nat. Commun. 6 8530
Google Scholar
[8] Gao Y, Zhang Y Y, Sun J T, Zhang L, Zhang S, Du S 2020 Nano Res 13 1571
Google Scholar
[9] Dutta O, Przysirzna A, Zakrzewski J 2015 Sci Rep 5 11060
Google Scholar
[10] Kane C L, Mele E J 2005 Phys. Rev. B 95 226801
[11] Kane C L, Mele E J 2005 Phys. Rev. B 95 146802
[12] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
Google Scholar
[13] Read N, Green D 2000 Phys. Rev. B 61 10267
Google Scholar
[14] Kitaev A Y 2001 Phys. Usp 44 131
Google Scholar
[15] König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766
Google Scholar
[16] Hsieh D, Qian D, Wray L, Xia Y Q, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970
Google Scholar
[17] Xu Y, Miotkowski I, Liu C, Tian J, Nam H, Alidoust N, Hu J, Shih C K, Hasan M Z, Chen Y P 2014 Nat. Phys. 10 596
[18] Yoshimi R, Tsukazaki A, Kozuka Y, Falson J, Takahashi K S, Checkelsky J G, Nagaosa N, Kawasaki M, Tokura Y 2015 Nat. Commun. 6 6627
Google Scholar
[19] Zou W, Wang W, Kou X, Lang M, Fan Y, Choi E S, Fedorov A V, Wang K, He L, Xu Y, Wang K L 2017 Appl. Phys. Lett 110 212401
Google Scholar
[20] Koirala N, Brahlek M, Salehi M, Wu L, Dai J, Waugh J, Nummy T, Han M G, Moon J, Zhu Y, Dessau D, Wu W, Armitage N P, Oh S 2015 Nano Lett. 15 8245
Google Scholar
[21] Moon J, Koirala N, Salehi M, Zhang W, Wu W, Oh S 2018 Nano Lett. 18 820
Google Scholar
[22] Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167
Google Scholar
[23] Fang Y, Feng X, Ou Y, Wang J, Liu C, Zhang L, Zhao D, Jiang G, Zhang S C, He K, Ma X, Xue Q K 2015 Phys. Rev. Lett 115 126801
Google Scholar
[24] Chang C Z, Zhao W, Kim D Y, Zhang H, Assaf B A, Heiman D, Zhang S C, Liu C, Chan M H W, Moodera J S 2015 Nat Mater 14 473
Google Scholar
[25] Checkelsky J G, Yoshimi R, Tsukazaki A, Takahashi K S, Kozuka Y, Falson J, Kawasaki M, Tokura Y 2014 Nat. Phys. 10 731
Google Scholar
[26] Kou X, Guo S T, Fan Y, Pan L, Lang M, Jiang Y, Shao Q, Nie T, Murata K, Tang J, Wang Y, He L, Lee T K, Lee W L, Wang K L 2014 Phys. Rev. Lett 113 137201
Google Scholar
[27] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
Google Scholar
[28] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
Google Scholar
[29] Zhang Z Q, Chen C Z, Wu Y J, Jiang H, Liu J W, Sun Q F, Xie X C 2021 Phys. Rev. B 103 075434
Google Scholar
[30] Thouless D J, Kohmoto M, Nightingale M P, Nijs M D 1982 Phys. Rev. Lett 49 405
Google Scholar
[31] Simons B 1983 Phys. Rev. Lett 51 2167
Google Scholar
[32] Niu Q, Thouless D J, Wu Y S 1985 Phys. Rev. B 31 3372
Google Scholar
[33] Haldane F D M, 1988 Phys. Rev. Lett 61 2015
Google Scholar
[34] Onoda M, Avishai Y, Nagaosa N 2007 Phys. Rev. Lett 98 2007
[35] Onada M, Nagaosa N 2003 Phys. Rev. Lett 90 206601
Google Scholar
[36] Wang W, Wang X, Ma G 2022 Nature 608 50
Google Scholar
[37] Dou?ot B, Kovrizhin D, Moessner R 2024 Proc. Natl. Acad. Sci. U.S.A. 121 39
[38] Rosen I T, Anderson M P, Rodenbach L K, Tai L, Zhang P, Wang K L, Kastner M A, Goldhaber-Gordon D Phys. Rev. Lett 129 246602
[39] Ferguson G M, Xiao R, Richardella A R, Low D, Samarth N, Nowack K C 2023 Nat. Mater. 22 1100
Google Scholar
[40] Beenakker C W J 1997 Rev. Mod. Phys. 69 731
Google Scholar
[41] Evers F, Mirlin A D 2008 Rev. Mod. Phys. 80 1355
Google Scholar
[42] Wu B L, Wang Z B, Zhang Z Q, Jiang H 2021 Phys. Rev. B 104 195416
Google Scholar
[43] Zhao Y F, Zhang R X, Cai J Q, Zhou D Y, Zhou L J, Yan Z J, Chan M H W, Xu X D, Chang C Z 2023 Nat. Commun. 14 770
Google Scholar
[44] Remeo F, Bartolomeo A D 2023 Nat. Commun. 14 3709
Google Scholar
[45] Ovchinnikov D, Cai J Q, Lin Z, Fei Z Y, Liu Z Y, Cui Y T, Cobden D H, Chu J H, Chang C Z, Xiao D, Yan J Q, Xu X D 2022 Nat. Commun. 13 5967
Google Scholar
[46] Li J, Li Y, Du S, Wang Z, Gu B L, Zhang S C, He K, Duan W, Xu Y 2019 Sci. Adv. 5 eaaw5685
Google Scholar
[47] Rienks E D L, Wimmer S, Sanchez-Barriga J, Caha O, Mandal P S, Ruzicka J, Ney A, Steiner H, Volobuev V V, Groiss H, Albu M, Kothleitner G, Mickalicka J, Khan S A, Minar J, Ebert H, Bauer G, Freyse F, Varykhalov A, Rader O, Springholz G 2019 Nature 576 423
Google Scholar
[48] Gong Y, Guo J W, Li J H, et al 2019 Chin. Phys. Lett. 36 076801
Google Scholar
[49] Otrokov M M, Klimovskikh I I, Bentmann H, et al 2019 Nature 576 416
Google Scholar
[50] Zhang D, Shi M, Zhu T, Xing D, Zhang H, Wang J 2019 Phys. Rev. Lett. 122 206401
Google Scholar
[51] Otrokov M M, Rusinov I P, Blanco-Ray M, Hoffmann M, Vyazovskaya A Y, Eremeev S V, Ernst A, Echenique P M, Arnau A, Chulkov E V 2019 Phys. Rev. Lett. 122 107202
Google Scholar
[52] Gao A, Liu Y F, Hu C, Qiu J X, Tzschaschel C, Ghosh B, Ho S C, Berube D, Chen R, Sun H, Zhang Z, Zhang X Y, Wang Y X, Wang N, Huang Z, Felser C, Agarwal A, Ding T, Tien H J, Akey A, Gardener J, Singh B, Watanabe K, Taniguchi T, Burch K S, Bell D C, Zhou B B, Gao W, Lu H Z, Bansil A, Lin H, Chang T R, Fu L, Ma Q, Ni N, Xu S Y 2021 Nature 595 521
Google Scholar
[53] Liu C, Wang Y, Li H, Wu Y, Li Y, Li J, He K, Xu Y, Zhang J, Wang Y 2020 Nat. Mater. 19 522
Google Scholar
[54] Guo J F, Wang H, Wang X Y, Gu S Z, Mi S, Zhu S Y, Hu J W, Pang F, Ji W, Gao H J, Xia T L, Cheng Z H 2022 J. Phys. Chem. C 126 32
[55] Zhang D, Shi M, Zhu T, Xing D, Zhang H, Wang J 2019 Phys. Rev. Lett. 122 206401
Google Scholar
[56] Li H L, Jiang H, Chen C Z, Xie X C 2021 Phys. Rev. Lett. 126 156601
Google Scholar
[57] Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438
Google Scholar
[58] Liu C X, Qi X L, Zhang H, Dai X, Fang Z, Zhang S C 2010 Phys. Rev. B 82 045122
Google Scholar
[59] Rycerz A, Tworzydlo J, Beenakker C W J 2007 Nat. Phys. 3 172
Google Scholar
[60] Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett 99 236809
Google Scholar
[61] Akhmerov A R, Bardarson J H, Rycerz A, Beenakker C W J 2008 Phys. Rev. B 77 205416
Google Scholar
[62] Jung J, Zhang F, Qiao Z, MacDonald A H 2011 Phys. Rev. B 84 075418
Google Scholar
[63] Qiao Z, Jung J, Niu Q, MacDonald A H 2011 Nano Lett. 11 3453
Google Scholar
[64] Zhang F, Jung J, Fiete G A, Niu Q, MacDonald A H 2011 Phys. Rev. Lett 106 156801
Google Scholar
[65] Gunlycke D, White C T 2011 Phys. Rev. Lett 106 136806
Google Scholar
[66] Cai T, Yang S A, Li X, Zhang F, Shi J, Yao W, Niu Q 2013 Phys. Rev. B 88 115140
Google Scholar
[67] Pan H, Li X, Zhang F, Yang S A 2015 Phys. Rev. B 92 041404
Google Scholar
[68] Cheng S G, Zhou J, Jiang H, Sun Q F 2016 New J. Phys. 18 103024
Google Scholar
[69] Lee J, Mak K F, Shan J 2016 Nat. Nanotechnol. 11 421
Google Scholar
[70] Li S, Gong M, Cheng S G, Jiang H, Xie X C 2023 Natl. Sci. Rev. 10 nwad262
Google Scholar
[71] Chu R L, Shi J, Shen S Q 2011 Phys. Rev. B 84 085312
Google Scholar
[72] Vernava N, Vanderbilt D 2018 Phys. Rev. B 98 245117
Google Scholar
[73] Zhou H M, Li H L, Xu D H, Chen C Z, Sun Q F, Xie X C Phys. Rev. Lett 129 096601
[74] Sass P M, Ge W, Yan J, Obeysekera D, Yang J J, Wu W 2020 Nano Lett. 20 2609
Google Scholar
[75] Gao A, Liu Y F, Hu C, Qiu J X, Tzschaschel C, Ghosh B, Ho S C, Bérubé D, Chen R, Sun H, Zhang Z, Zhang X Y, Wang Y X, Wang N, Huang Z, Felser C, Agarwal A, Ding T, Tien H J, Akey A, Gardener J, Singh B, Watanabe K, Taniguchi T, Burch K S, Bell D C, Zhou B B, Gao W, Lu H Z, Bansil A, Lin H, Chang T R, Fu L, Ma Q, Ni N, Xu S Y 2021 Nature 595 521
Google Scholar
[76] Averkiev N S, Golub L E 1999 Phys. Rev. B 60 15582
Google Scholar
[77] Li H L, Jiang H, Sun Q F, Xie X C 2024 Sci. Bull. 69 1221
Google Scholar
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