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近年来, 磁性拓扑材料特别是磁性Weyl半金属越来越多地被发现, 为研究拓扑输运行为提供了重要载体. 磁性拓扑半金属材料具有动量空间的强贝利曲率, 显著增强了电子的常规横向输运行为, 也使得曾经被忽略或无法观测的输运效应逐渐浮现出来, 导致当前广泛采用的经典输运方程不能准确地描述磁性拓扑电子的输运行为. 本文从半经典输运方程出发, 介绍磁性拓扑材料中新近出现的非常规电输运行为, 内容涉及化学掺杂、磁场调制拓扑电子态、贝利曲率相关的线性正磁电阻及磁场线性依赖的输运行为. 这些行为为磁性与拓扑相互作用下的电输运行为提供新的理解和思考. 最后, 对非常规电输运的发展进行总结和展望.In recent years, more and more magnetic topological materials, especially magnetic Weyl semimetals, have been discovered, providing a platform for studying the electronic transport behavior. The strong Berry curvature of magnetic topological materials can significantly enhance the conventional transverse transport behaviors, and can also make the transport phenomena that have been overlooked or unobserved appear gradually. In this review, the semi-classical equation is used to understand the anomalous transport behaviors in magnetic topological materials. The intrinsic anomalous Hall conductivity is obtained by integrating the Berry curvature of the occupied states, which is determined by the electronic band structure. The topological electronic state can be modulated by magnetic field and doping, and the anomalous Hall conductivity was changed with the evolution of the Berry curvature. A linear positive magnetoresistance behavior associated with the Berry curvature and magnetic field is introduced, which establishes the relation between the Berry curvature and the longitudinal transport. Due to the presence of tilted Weyl cone, the conductivity terms related to the first power of magnetic field are observed in magnetic Weyl systems. These behaviors under the interaction of topology and magnetic provide a new understanding and insight for the electric transport behaviors. At last, this review also provides a viewpoint on the field of magnetic topological physics.
[1] Chang C Z, Zhang J S, Feng X, Shen J, Zhang Z C, Guo M H, Li K, Ou Y B, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S H, Chen X, Jia J F, Dai X, Fang Z, Zhang S C, He K, Wang Y Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167Google Scholar
[2] Deng Y J, Yu Y J, Meng Z S, Guo Z X, Xu Z H, Wang J, Chen X H, Zhang Y B 2020 Science 367 895Google Scholar
[3] Liu E K, Sun Y, Kumar N, Muechler L, Sun A L, Jiao L, Yang S Y, Liu D F, Liang A J, Xu Q N, Kroder J, Suss V, Borrmann H, Shekhar C, Wang Z S, Xi C Y, Wang W H, Schnelle W, Wirth S, Chen Y L, Goennenwein S T B, Felser C 2018 Nat Phys 14 1125Google Scholar
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[10] Okamura Y, Minami S, Kato Y, Fujishiro Y, Kaneko Y, Ikeda J, Muramoto J, Kaneko R, Ueda K, Kocsis V, Kanazawa N, Taguchi Y, Koretsune T, Fujiwara K, Tsukazaki A, Arita R, Tokura Y, Takahashi Y 2020 Nat. Commun. 11 4619Google Scholar
[11] Wang Q Y, Zeng Y, Yuan K, Zeng Q Q, Gu P F, Xu X L, Wang H R, Han Z, Nomura K, Wang W H, Liu E K, Hou Y L, Ye Y 2022 Nat. Electron. 6 119Google Scholar
[12] Yang S Y, Noky J, Gayles J, Dejene F K, Sun Y, Dorr M, Skourski Y, Felser C, Ali M N, Liu E K, Parkin S S P 2020 Nano Lett. 20 7860Google Scholar
[13] Howard S, Jiao L, Wang Z, Morali N, Batabyal R, Kumar-Nag P, Avraham N, Beidenkopf H, Vir P, Liu E K, Shekhar C, Felser C, Hughes T, Madhavan V 2021 Nat. Commun. 12 4269Google Scholar
[14] Tanaka M, Fujishiro Y, Mogi M, Kaneko Y, Yokosawa T, Kanazawa N, Minami S, Koretsune T, Arita R, Tarucha S, Yamamoto M, Tokura Y 2020 Nano Lett. 20 7476Google Scholar
[15] Zeng Q Q, Gu G X, Shi G, Shen J L, Ding B, Zhang S, Xi X K, Felser C, Li Y Q, Liu E K 2021 Sci. China Phys. Mech. Astron. 64 287512Google Scholar
[16] Sanchez D S, Chang G, Belopolski I, Lu H, Yin J X, Alidoust N, Xu X, Cochran T A, Zhang X, Bian Y, Zhang S S, Liu Y Y, Ma J, Bian G, Lin H, Xu S Y, Jia S, Hasan M Z 2020 Nat. Commun. 11 3356Google Scholar
[17] Shen J L, Gao J C, Yi C J, Li M, Zhang S, Yang J Y, Wang B B, Zhou M, Huang R J, Wei H X, Yang H T, Shi Y G, Xu X H, Gao H J, Shen B G, Li G, Wang Z J, Liu E K 2023 The Innovation 4 100399Google Scholar
[18] Yao Y G, Kleinman L, MacDonald A H, Sinova J, Jungwirth T, Wang D S, Wang E G, Niu Q 2004 Phys. Rev. Lett. 92 037204Google Scholar
[19] Shen J L, Yao Q S, Zeng Q Q, Sun H Y, Xi X K, Wu G H, Wang W H, Shen B G, Liu Q H, Liu E K 2020 Phys. Rev. Lett. 125 086602Google Scholar
[20] Zhang S, Wang Y, Zeng Q Q, Shen J L, Zheng X, Yang J, Wang Z, Xi C, Wang B, Zhou M, Huang R, Wei H, Yao Y, Wang S, Parkin S S P, Felser C, Liu E K, Shen B 2022 Proc. Natl. Acad. Sci. USA 119 e2208505119Google Scholar
[21] Xiao D, Shi J R, Niu Q 2005 Phys. Rev. Lett. 95 137204Google Scholar
[22] Ma D, Jiang H, Liu H, Xie X C 2019 Phys. Rev. B 99 115121Google Scholar
[23] Das K, Agarwal A 2019 Phys. Rev. B 99 085405Google Scholar
[24] Jiang B Y, Wang L J Y, Bi R, Fan J W, Zhao J J, Yu D P, Li Z L, Wu X S 2021 Phys. Rev. Lett. 126 236601Google Scholar
[25] Zeng Q Q, Yi C, Shen J L, Wang B B, Wei H, Shi Y G, Liu E K 2022 Appl. Phys. Lett. 121 162405Google Scholar
[26] Berry M V 1997 Proc. Math. Phys. Eng. Sci. 392 45Google Scholar
[27] Chang M C, Niu Q 1995 Phys. Rev. Lett. 75 1348Google Scholar
[28] Chang M C, Niu Q 1996 Phys. Rev. B 53 7010Google Scholar
[29] Sundaram G, Niu Q 1999 Phys. Rev. B 59 14915Google Scholar
[30] Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959Google Scholar
[31] Shen J L, Zeng Q Q, Zhang S, Sun H Y, Yao Q S, Xi X K, Wang W H, Wu G H, Shen B G, Liu Q H, Liu E K 2020 Adv. Funct. Mater. 30 2000830Google Scholar
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表 1 各类输运效应与材料体系对照表
Table 1. Comparison of various transport effects and material systems.
输运效应 物理机制 材料体系 反常霍尔效应 掺杂引起局域无序导致拓扑能带被调制 Ni-doped Co3Sn2S2 反常霍尔效应 外磁场调制外尔点的产生和湮灭 Co2MnAl 反常霍尔效应 外磁场诱发非线性磁结构调制拓扑能带 EuB6 纵向磁电阻 贝利曲率和外磁场共同作用 CoS2 平面霍尔效应和各向异性磁电阻 倾斜外尔锥导致的关于磁场奇对称行为 Co3Sn2S2, EuB6 -
[1] Chang C Z, Zhang J S, Feng X, Shen J, Zhang Z C, Guo M H, Li K, Ou Y B, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S H, Chen X, Jia J F, Dai X, Fang Z, Zhang S C, He K, Wang Y Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167Google Scholar
[2] Deng Y J, Yu Y J, Meng Z S, Guo Z X, Xu Z H, Wang J, Chen X H, Zhang Y B 2020 Science 367 895Google Scholar
[3] Liu E K, Sun Y, Kumar N, Muechler L, Sun A L, Jiao L, Yang S Y, Liu D F, Liang A J, Xu Q N, Kroder J, Suss V, Borrmann H, Shekhar C, Wang Z S, Xi C Y, Wang W H, Schnelle W, Wirth S, Chen Y L, Goennenwein S T B, Felser C 2018 Nat Phys 14 1125Google Scholar
[4] Ilya Belopolski K M, Sanchez D S, Chang G Q, Ernst B, Yin J X, Zhang S T, Cochran T, Shumiya N, Zheng H, Singh B, Bian G, Multer D, Litskevich M, Zhou X T, Huang S M, Wang B K, Chang T R, Xu S Y, Bansil A, Felser C, Lin H, Hasan M Z 2019 Science 365 1278Google Scholar
[5] Li P, Koo J, Ning W, Li J, Miao L, Min L, Zhu Y, Wang Y, Alem N, Liu C X, Mao Z, Yan B 2020 Nat. Commun. 11 3476Google Scholar
[6] Guin S N, Vir P, Zhang Y, Kumar N, Watzman S J, Fu C, Liu E, Manna K, Schnelle W, Gooth J, Shekhar C, Sun Y, Felser C 2019 Adv. Mater. 31 e1806622Google Scholar
[7] Guin S N, Manna K, Noky J, Watzman S J, Fu C, Kumar N, Schnelle W, Shekhar C, Sun Y, Gooth J, Felser C 2019 NPG Asia Mater. 11 16Google Scholar
[8] Xing Y Q, Shen J L, Chen H, Huang L, Gao Y X, Zheng Q, Zhang Y Y, Li G, Hu B, Qian G J, Cao L, Zhang X L, Fan P, Ma R S, Wang Q, Yin Q W, Lei H C, Ji W, Du S X, Yang H T, Wang W H, Shen C M, Lin X, Liu E K, Shen B G, Wang Z Q, Gao H J 2020 Nat. Commun. 11 5613Google Scholar
[9] Liu D F, Liang A J, Liu E K, Xu Q N, Li Y W, Chen C, Pei D, Shi W J, Mo S K, Dudin P, Kim T, Cacho C, Li G, Sun Y, Yang L X, Liu Z K, Parkin S S P, Felser C, Chen Y L 2019 Science 365 1282Google Scholar
[10] Okamura Y, Minami S, Kato Y, Fujishiro Y, Kaneko Y, Ikeda J, Muramoto J, Kaneko R, Ueda K, Kocsis V, Kanazawa N, Taguchi Y, Koretsune T, Fujiwara K, Tsukazaki A, Arita R, Tokura Y, Takahashi Y 2020 Nat. Commun. 11 4619Google Scholar
[11] Wang Q Y, Zeng Y, Yuan K, Zeng Q Q, Gu P F, Xu X L, Wang H R, Han Z, Nomura K, Wang W H, Liu E K, Hou Y L, Ye Y 2022 Nat. Electron. 6 119Google Scholar
[12] Yang S Y, Noky J, Gayles J, Dejene F K, Sun Y, Dorr M, Skourski Y, Felser C, Ali M N, Liu E K, Parkin S S P 2020 Nano Lett. 20 7860Google Scholar
[13] Howard S, Jiao L, Wang Z, Morali N, Batabyal R, Kumar-Nag P, Avraham N, Beidenkopf H, Vir P, Liu E K, Shekhar C, Felser C, Hughes T, Madhavan V 2021 Nat. Commun. 12 4269Google Scholar
[14] Tanaka M, Fujishiro Y, Mogi M, Kaneko Y, Yokosawa T, Kanazawa N, Minami S, Koretsune T, Arita R, Tarucha S, Yamamoto M, Tokura Y 2020 Nano Lett. 20 7476Google Scholar
[15] Zeng Q Q, Gu G X, Shi G, Shen J L, Ding B, Zhang S, Xi X K, Felser C, Li Y Q, Liu E K 2021 Sci. China Phys. Mech. Astron. 64 287512Google Scholar
[16] Sanchez D S, Chang G, Belopolski I, Lu H, Yin J X, Alidoust N, Xu X, Cochran T A, Zhang X, Bian Y, Zhang S S, Liu Y Y, Ma J, Bian G, Lin H, Xu S Y, Jia S, Hasan M Z 2020 Nat. Commun. 11 3356Google Scholar
[17] Shen J L, Gao J C, Yi C J, Li M, Zhang S, Yang J Y, Wang B B, Zhou M, Huang R J, Wei H X, Yang H T, Shi Y G, Xu X H, Gao H J, Shen B G, Li G, Wang Z J, Liu E K 2023 The Innovation 4 100399Google Scholar
[18] Yao Y G, Kleinman L, MacDonald A H, Sinova J, Jungwirth T, Wang D S, Wang E G, Niu Q 2004 Phys. Rev. Lett. 92 037204Google Scholar
[19] Shen J L, Yao Q S, Zeng Q Q, Sun H Y, Xi X K, Wu G H, Wang W H, Shen B G, Liu Q H, Liu E K 2020 Phys. Rev. Lett. 125 086602Google Scholar
[20] Zhang S, Wang Y, Zeng Q Q, Shen J L, Zheng X, Yang J, Wang Z, Xi C, Wang B, Zhou M, Huang R, Wei H, Yao Y, Wang S, Parkin S S P, Felser C, Liu E K, Shen B 2022 Proc. Natl. Acad. Sci. USA 119 e2208505119Google Scholar
[21] Xiao D, Shi J R, Niu Q 2005 Phys. Rev. Lett. 95 137204Google Scholar
[22] Ma D, Jiang H, Liu H, Xie X C 2019 Phys. Rev. B 99 115121Google Scholar
[23] Das K, Agarwal A 2019 Phys. Rev. B 99 085405Google Scholar
[24] Jiang B Y, Wang L J Y, Bi R, Fan J W, Zhao J J, Yu D P, Li Z L, Wu X S 2021 Phys. Rev. Lett. 126 236601Google Scholar
[25] Zeng Q Q, Yi C, Shen J L, Wang B B, Wei H, Shi Y G, Liu E K 2022 Appl. Phys. Lett. 121 162405Google Scholar
[26] Berry M V 1997 Proc. Math. Phys. Eng. Sci. 392 45Google Scholar
[27] Chang M C, Niu Q 1995 Phys. Rev. Lett. 75 1348Google Scholar
[28] Chang M C, Niu Q 1996 Phys. Rev. B 53 7010Google Scholar
[29] Sundaram G, Niu Q 1999 Phys. Rev. B 59 14915Google Scholar
[30] Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959Google Scholar
[31] Shen J L, Zeng Q Q, Zhang S, Sun H Y, Yao Q S, Xi X K, Wang W H, Wu G H, Shen B G, Liu Q H, Liu E K 2020 Adv. Funct. Mater. 30 2000830Google Scholar
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