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Berry curvature induced unconventional electronic transport behaviors in magnetic topological semimetals

Yang Jin-Ying Wang Bin-Bin Liu En-Ke

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Berry curvature induced unconventional electronic transport behaviors in magnetic topological semimetals

Yang Jin-Ying, Wang Bin-Bin, Liu En-Ke
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  • 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.
      Corresponding author: Liu En-Ke, ekliu@iphy.ac.cn
    • Funds: Project supported by the State Key Development Program for Basic Research of China (Grant Nos. 2022YFA1403800, 2022YFA1403400), the National Natural Science Foundation of China (Grant No. 11974394), the Strategic Priority Research Program (B) of Chinese Academy of Sciences (Grant No. XDB33000000), and the Synergetic Extreme Condition User Facility (SECUF), Chinese Academy of Sciences.
    [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

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    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

  • 图 1  贝利曲率相关的非常规电输运行为

    Figure 1.  The unconventional electric transport behaviors related to the Berry curvature.

    图 2  Co3–xNixSn2S2的能带结构与内禀反常霍尔电导[19]

    Figure 2.  The band structure and intrinsic anomalous Hall conductivity in Co3–xNixSn2S2[19].

    图 3  Co2MnAl中随着外磁场转动贝利曲率分布的演化[5]

    Figure 3.  The evolution of Berry curvature distribution in Co2MnAl with the rotation of magnetic field[5].

    图 4  EuB6实空间磁矩方向、k空间能带结构及输运行为演化示意图[17]

    Figure 4.  Schematic diagram of the evolution of the real space magnetic moment direction, the k-space band structure and the transport behavior in EuB6[17].

    图 5  CoS2线性正磁电阻行为及含温度纵向横向输运实验数据拟合结果[20]

    Figure 5.  The linear positive magnetoresistance behavior in CoS2 and experimental data fitting results of longitudinal and transverse with temperature[20].

    图 6  EuB6中PHE和AMR中关于磁场奇对称输运行为[25]

    Figure 6.  The antisymmetric transport behavior of PHE and AMR in EuB6[25].

    图 7  Co3Sn2S2中关于磁场奇对称的纵向和横向电阻[24]

    Figure 7.  The antisymmetric longitudinal and transverse electric resistivity in Co3Sn2S2[24].

    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
    DownLoad: CSV
  • [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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  • Received Date:  16 June 2023
  • Accepted Date:  20 July 2023
  • Available Online:  04 September 2023
  • Published Online:  05 September 2023

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