RKKY interaction in helical higher-order topological insulators

doi:10.1088/1674-1056/ad3ef9

中国物理B ›› 2024, Vol. 33 ›› Issue (7): 77503-077503.doi: 10.1088/1674-1056/ad3ef9

RKKY interaction in helical higher-order topological insulators

Sha Jin(金莎)¹, Jian Li(李健)^1,2,3, Qing-Xu Li(李清旭)^1,2,3, and Jia-Ji Zhu(朱家骥)^1,2,3,†

1 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
2 Institute for Advanced Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
3 Southwest Center for Theoretical Physics, Chongqing University, Chongqing 401331, China

收稿日期:2024-02-27 修回日期:2024-04-13 接受日期:2024-04-16 出版日期:2024-06-18 发布日期:2024-06-20
通讯作者: Jia-Ji Zhu E-mail:zhujj@cqupt.edu.cn;
基金资助:
This work was supported by the research foundation of Institute for Advanced Sciences of CQUPT (Grant No. E011A2022328).

RKKY interaction in helical higher-order topological insulators

Sha Jin(金莎)¹, Jian Li(李健)^1,2,3, Qing-Xu Li(李清旭)^1,2,3, and Jia-Ji Zhu(朱家骥)^1,2,3,†

1 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
2 Institute for Advanced Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
3 Southwest Center for Theoretical Physics, Chongqing University, Chongqing 401331, China

Received:2024-02-27 Revised:2024-04-13 Accepted:2024-04-16 Online:2024-06-18 Published:2024-06-20
Contact: Jia-Ji Zhu E-mail:zhujj@cqupt.edu.cn;
Supported by:
This work was supported by the research foundation of Institute for Advanced Sciences of CQUPT (Grant No. E011A2022328).

摘要/Abstract

摘要： We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in helical higher-order topological insulators (HOTIs), revealing distinct behaviors mediated by hinge and Dirac-type bulk carriers. Our findings show that hinge-mediated interactions consist of Heisenberg, Ising, and Dzyaloshinskii-Moriya (DM) terms, exhibiting a decay with impurity spacing $z$ and oscillations with Fermi energy $\varepsilon_{\scriptscriptstyle{\rm F}}$. These interactions demonstrate ferromagnetic behaviors for the Heisenberg and Ising terms and alternating behavior for the DM term. In contrast, bulk-mediated interactions include Heisenberg, twisted Ising, and DM terms, with a conventional cubic oscillating decay. This study highlights the nuanced interplay between hinge and bulk RKKY interactions in HOTIs, offering insights into designs of next-generation quantum devices based on HOTIs.

关键词: magnetic impurity interactions, magnetic ordering, spintronics, topological phases

Abstract: We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in helical higher-order topological insulators (HOTIs), revealing distinct behaviors mediated by hinge and Dirac-type bulk carriers. Our findings show that hinge-mediated interactions consist of Heisenberg, Ising, and Dzyaloshinskii-Moriya (DM) terms, exhibiting a decay with impurity spacing $z$ and oscillations with Fermi energy $\varepsilon_{\scriptscriptstyle{\rm F}}$. These interactions demonstrate ferromagnetic behaviors for the Heisenberg and Ising terms and alternating behavior for the DM term. In contrast, bulk-mediated interactions include Heisenberg, twisted Ising, and DM terms, with a conventional cubic oscillating decay. This study highlights the nuanced interplay between hinge and bulk RKKY interactions in HOTIs, offering insights into designs of next-generation quantum devices based on HOTIs.

Key words: magnetic impurity interactions, magnetic ordering, spintronics, topological phases

中图分类号: (Magnetic impurity interactions)

75.30.Hx

75.10.-b (General theory and models of magnetic ordering) 03.65.Vf (Phases: geometric; dynamic or topological)

Sha Jin(金莎), Jian Li(李健), Qing-Xu Li(李清旭), and Jia-Ji Zhu(朱家骥). RKKY interaction in helical higher-order topological insulators[J]. 中国物理B, 2024, 33(7): 77503-077503.

Sha Jin(金莎), Jian Li(李健), Qing-Xu Li(李清旭), and Jia-Ji Zhu(朱家骥). RKKY interaction in helical higher-order topological insulators[J]. Chin. Phys. B, 2024, 33(7): 77503-077503.

参考文献

[1] Kim M, Jacob Z and Rho J 2020 Light Sci. Appl. 9 130
[2] Xie B, Wang H X, Zhang X, Zhan P, Jiang J H, Lu M and Chen Y 2021 Nat. Rev. Phys. 3 520
[3] Benalcazar W A, Bernevig B A and Hughes T L 2017 Science 357 61
[4] Liu F and Wakabayashi K 2017 Phys. Rev. Lett. 118 076803
[5] Lin Z K, Wu S Q, Wang H X and Jiang J H 2020 Chin. Phys. Lett. 37 074302
[6] Chen H, Liu Z R, Chen R and Zhou B 2024 Chin. Phys. B 33 01720
[7] Ni X, Li M, Weiner M, Alu A and Khanikaev A B 2020 Nat. Commun. 11 2108
[8] Liu S, Ma S, Zhang Q, Zhang L, Yang C, You O, Gao W, Xiang Y, Cui T J and Zhang S 2020 Light Sci. Appl. 9 145
[9] Hackenbroich A, Hudomal A, Schuch N, Bernevig B A and Regnault N 2021 Phys. Rev. B 103 L161110
[10] Wang J H, Yang Y B, Dai N and Xu Y 2021 Phys. Rev. Lett. 126 206404
[11] Fu B, Hu Z A and Shen S Q 2021 Phys. Rev. Res. 3 033177
[12] Schindler F, Cook A M, Vergniory M G, Wang Z, Parkin S S, Bernevig B A and Neupert T 2018 Sci. Adv. 4 eaat0346
[13] Hsieh T H, Lin H, Liu J, Duan W, Bansil A and Fu L 2012 Nat. Commun. 3 982
[14] Tanaka Y, Ren Z, Sato T, Nakayama K, Souma S, Takahashi T, Segawa K and Ando Y 2012 Nat. Phys. 8 800
[15] Benalcazar W A, Bernevig B A and Hughes T L 2017 Phys. Rev. B 96 245115
[16] Sessi P, Sante D D, Szczerbakow A, Glott F, Wilfert S, Schmidt H, Bathon T, Dziawa P, Greiter M, Neupert T, Sangiovanni G, Story T, Thomale R and Bode M 2016 Science 354 1269
[17] Bernevig B A and Zhang S C 2006 Phys. Rev. Lett. 96 106802
[18] Fang C and Fu L 2019 Sci. Adv. 5 eaat2374
[19] Kohda M, Okayasu T and Nitta J 2019 Sci. Rep. 9 1909
[20] Yang Z Q, Shao Z K, Chen H Z, Mao X R and Ma R M 2020 Phys. Rev. Lett. 125 013903
[21] Aggarwal L, Zhu P, Hughes T L and Madhavan V 2021 Nat. Commun. 12 4420
[22] Schindler F, Wang Z, Vergniory M G, Cook A M, Murani A, Sengupta S, Kasumov A Y, Deblock R, Jeon S, Drozdov I, Bouchiat H, Guéon S, Yazdani A, Bernevig B A and Neupert T 2018 Nat. Phys. 14 918
[23] Hsu C H, Zhou X, Ma Q, Gedik N, Bansil A, Pereira V M, Lin H, Fu L, Xu S Y and Chang T R 2019 2D Mater. 6 031004
[24] Shumiya N, Hossain M S, Yin J X, et al. 2022 Nat. Mater. 21 1111
[25] Wang Z, Wieder B J, Li J, Yan B and Bernevig B A 2019 Phys. Rev. Lett. 123 186401
[26] Noguchi R, Kobayashi M, Jiang Z, et al. 2021 Nat. Mater. 20 473
[27] Laubscher K, Keizer P and Klinovaja J 2023 Phys. Rev. B 107 045409
[28] Yang Z Z, Li X, Peng Y Y, Zou X Y and Cheng J C 2020 Phys. Rev. Lett. 125 255502
[29] Craig N, Taylor J, Lester E, Marcus C, Hanson M and Gossard A 2004 Science 304 565
[30] Usaj G, Lustemberg P and Balseiro C A 2005 Phys. Rev. Lett. 94 036803
[31] Dugaev V K, Litvinov V I and Barnas J 2006 Phys. Rev. B 74 224438
[32] Brey L, Fertig H A and Das Sarma S 2007 Phys. Rev. Lett. 99 116802
[33] Liu Q, Liu C X, Xu C, Qi X L and Zhang S C 2009 Phys. Rev. Lett. 102 156603
[34] Zhu J J, Yao D X, Zhang S C and Chang K 2011 Phys. Rev. Lett. 106 097201
[35] Chang H R, Zhou J, Wang S X, Shan W Y and Xiao D 2015 Phys. Rev. B 92 241103
[36] Hosseini M V and Askari M 2015 Phys. Rev. B 92 224435
[37] Yarmohammadi M and Cheraghchi H 2020 Phys. Rev. B 102 075411
[38] Cheraghchi H and Yarmohammadi M 2021 Sci. Rep. 11 5273
[39] Yarmohammadi M, Bukov M and Kolodrubetz M H 2023 Phys. Rev. B 107 054439
[40] Hickel T and Nolting W 2004 Phys. Rev. B 69 085110
[41] Nolting W, Reddy G G, Ramakanth A and Meyer D 2001 Phys. Rev. B 64 155109
[42] Schindler F, Tsirkin S S, Neupert T, Bernevig B A and Wieder B J 2022 Nat. Commun. 13 5791
[43] Laubscher K, Miserev D, Kaladzhyan V, Loss D and Klinovaja J 2023 Phys. Rev. B 107 115421
[44] Schmidt T M, Miwa R H and Fazzio A 2011 Phys. Rev. B 84 245418
[45] Henk J, Ernst A, Eremeev S V, Chulkov E V, Maznichenko I V and Mertig I 2012 Phys. Rev. Lett. 108 206801
[46] Zhang J M, Zhu W, Zhang Y, Xiao D and Yao Y 2012 Phys. Rev. Lett. 109 266405
[47] Sun J, Chen L and Lin H Q 2014 Phys. Rev. B 89 115101
[48] Duan H J, Wu Y J, Yang Y Y, Zheng S H, Zhu C Y, Deng M X, Yang M and Wang R Q 2022 New J. Phys. 24 033029
[49] Mohammadi R G and Moghaddam A G 2020 Phys. Rev. B 101 075421
[50] Mross D F and Johannesson H 2009 Phys. Rev. B 80 155302
[51] Duan H J, Wang C, Zheng S H, Wang R Q, Pan D R and Yang M 2018 Sci. Rep. 8 6185

RKKY interaction in helical higher-order topological insulators

RKKY interaction in helical higher-order topological insulators

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