Berry curvature induced unconventional electronic transport behaviors in magnetic topological semimetals

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

doi:10.7498/aps.72.20230995

Abstract

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.

Keywords:

Authors and contacts

1.
State Key Laboratory for Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

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.

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References

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[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 e2208505119 Google Scholar
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Cited By

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.

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图 2 Co_3–xNi_xSn₂S₂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 Co_3–xNi_xSn₂S₂^[19].

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

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].

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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].

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

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].

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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

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[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 340 167 Google 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 367 895 Google 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 1125 Google 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 1278 Google 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 3476 Google 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 e1806622 Google 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 16 Google 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 5613 Google 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 1282 Google 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 4619 Google 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. 6 119 Google 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 7860 Google 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 4269 Google 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 7476 Google 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 287512 Google 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 3356 Google 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 100399 Google 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 037204 Google 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 086602 Google 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 e2208505119 Google Scholar
[21]	Xiao D, Shi J R, Niu Q 2005 Phys. Rev. Lett. 95 137204 Google Scholar
[22]	Ma D, Jiang H, Liu H, Xie X C 2019 Phys. Rev. B 99 115121 Google Scholar
[23]	Das K, Agarwal A 2019 Phys. Rev. B 99 085405 Google 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 236601 Google 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 162405 Google Scholar
[26]	Berry M V 1997 Proc. Math. Phys. Eng. Sci. 392 45 Google Scholar
[27]	Chang M C, Niu Q 1995 Phys. Rev. Lett. 75 1348 Google Scholar
[28]	Chang M C, Niu Q 1996 Phys. Rev. B 53 7010 Google Scholar
[29]	Sundaram G, Niu Q 1999 Phys. Rev. B 59 14915 Google Scholar
[30]	Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959 Google 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 2000830 Google Scholar

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Vol. 72, Issue 17 - 2023-09-05

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