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具有巨型Rashba自旋劈裂和量子自旋霍尔效应的材料在自旋电子器件应用中具有重要意义. 基于第一性原理, 提出一种可以将巨型Rashba自旋劈裂和量子自旋霍尔效应实现完美共存的二维(two dimension, 2D)六角晶格材料H-Pb-Cl. 由于系统空间反转对称性的破坏和本征电场的存在, H-Pb-Cl的电子能带中出现了巨型Rashba自旋劈裂现象(αR = 3.78 eV·Å). 此外, H-Pb-Cl的Rashba自旋劈裂是可以随双轴应力(–16%—16%)调控的. 通过分析H-Pb-Cl的电子性质, 发现在H-Pb-Cl费米面附近有一个巨大的带隙(1.31 eV), 并且体系由于Pb原子的s-p轨道翻转使得拓扑不变量Z2 = 1, 这就表明H-Pb-Cl是一个具有巨大拓扑带隙的2D拓扑绝缘体. 我们的研究为探索和实现Rashba自旋劈裂和量子自旋霍尔效应的共存提供了一种优良的潜在候选材料.
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关键词:
- 二维拓扑绝缘体 /
- Rashba自旋劈裂 /
- 空间反演对称性 /
- 自旋轨道耦合
Rashba spin splitting and quantum spin Hall effect have attracted enormous interest due to their great significance in the application of spintronics. According to the first-principles calculation, we propose a two-dimensional hexagonal lattice material H-Pb-Cl, which realizes the coexistence of giant Rashba spin splitting and quantum spin Hall effect. Owing to the break of space inversion symmetry and the existence of intrinsic electric field, H-Pb-Cl has a huge Rashba spin splitting phenomenon (αR = 3.78 eV·Å), and the Rashba spin splitting of H-Pb-Cl(–16%—16%) can be adjusted by changing the biaxial stress. By analyzing the electronic properties of H-Pb-Cl, we find that H-Pb-Cl has a huge band gap near the Fermi surface (1.31 eV), and the topological invariant Z2 = 1 of the system is caused by the inversion of s-p orbit, which indicates that H-Pb-Cl is a two-dimensional topological insulator with a huge topological band gap, and the gap is large enough to observe the topological edge states at room temperature. In addition, we further consider the effect of BN and graphane substrates on the topological band gap of H-Pb-Cl by using the H-Pb-Cl (111)-(1×1) /BN (111)-(2×2) and H-Pb-Cl(1×1)/ graphane (2×2) system, and find that the lattice mismatch between H-Pb-Cl (5.395 Å) and BN (2.615 Å) and between H-Pb-Cl (5.395 Å) and graphane (2.575 Å) are about 3% and 4.5%, respectively. According to our calculation results, H-Pb-Cl still retains the properties of topological insulator under the effect of spin orbit coupling, and is not affected by BN nor graphane. Our results show that the nontrivial topological band gap of H-Pb-Cl can be well preserved under both biaxial stress effect and substrate effect. In addition, H-Pb-Cl can well retain the nontrivial topological band gap under the stress of –16%–16%, and thus there are many kinds of substrate materials used to synthesize this material, which is very helpful in successfully realizing preparation experimentally. Our research provides a promising candidate material for exploring and realizing the coexistence of Rashba spin splitting and quantum spin Hall effect. And the coexistence of giant Rashba spin splitting and quantum spin Hall effect greatly broadens the scope of potential applications of H-Pb-Cl in the field of spintronic devices.-
Keywords:
- two dimensional topological insulator /
- Rashba spin splitting /
- spatial inversion symmetry /
- spin orbit coupling
[1] Moore J E 2010 Nature 464 194
Google Scholar
[2] Soumyanarayanan A, Reyren N, Fert A, Panagopoulos C 2016 Nature 539 509
Google Scholar
[3] Feng Y, Jiang Q, Feng B J, Yang M, Xu T, Liu W J, Yang X F, Arita M, Schwier E F, Shimada K, Jeschke H O, Thomale R, Shi Y G, Wu X X, Xiao S Z, Qiao S, He S L 2019 Nat. Commun. 10 4765
Google Scholar
[4] Lu J P, Yau J B, Shukla S P, Shayegan M 1998 Phys. Rev. Lett. 81 1282
Google Scholar
[5] Kuhlen S, Schmalbuch K, Hagedorn M, Schlammes P, Patt M, Lepsa M, Guntherodt G, Beschoten B 2012 Phys. Rev. Lett. 109 146603
Google Scholar
[6] Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150
Google Scholar
[7] Wang Z Y, Cheng X C, Wang B Z, Zhang J Y, Lu Y H, Yi C R, Niu S, Deng Y, Liu X J, Chen S, Pan J W 2021 Science 372 271
Google Scholar
[8] Lu Y H, Wang B Z, Liu X J 2020 Sci. Bull. 65 2080
Google Scholar
[9] Zezyulin D A, Konotop V V 2022 Phys. Rev. A 105 063323
Google Scholar
[10] Xu Z C, Zhou Z, Cheng E H, Lang L J, Zhu S L 2022 Sci. Chin. Phys. Mech. Astron. 65 283011
Google Scholar
[11] Zhao Q 2022 Mod. Phys. Lett. B 36 2250070
[12] Liu H, Zhang T, Wang K, Gao F, Xu G, Zhang X, Li S X, Cao G, Wang T, Zhang J, Hu X, Li H O, Guo G P 2022 Phys. Rev. Appl. 17 044052
Google Scholar
[13] Smith L W, Chen H B, Chang C W, Wu C W, Lo S T, Chao S H, Farrer I, Beere H E, Griffiths J P, Jones G A C, Ritchie D A, Chen Y N, Chen T M 2022 Phys. Rev. Lett. 128 027701
Google Scholar
[14] Dai X Y, Liu B Y 2022 Phys. Rev. A 105 043313
Google Scholar
[15] Hai K, Wang Y F, Chen Q, Hai W H 2021 Sci. Rep. 11 18839
Google Scholar
[16] Manchon A, Koo H C, Nitta J, Frolov S M, Duine R A 2015 Nat. Mater. 14 871
Google Scholar
[17] 红兰, 戈君, 双山, 刘达权 2022 71 016301
Google Scholar
Hong L, Ge J, Shuang S, Liu D Q 2022 Acta. Phys. Sin. 71 016301
Google Scholar
[18] Li Y, Ma X K, Zhai X K, Gao M N, Dai H T, Schumacher S, Gao T G 2022 Nat. Commun. 13 3785
Google Scholar
[19] Ghosh D, Roy K, Maitra S, Kumar P 2022 J. Phys. Chem. Lett. 13 5
[20] Schlipf M, Giustino F 2021 Phys. Rev. Lett. 127 237601
Google Scholar
[21] Zhu L, Zhang T, Chen G, Chen H 2018 Phys. Chem. Chem. Phys. 20 30133
Google Scholar
[22] Awschalom D, Samarth N 2009 Physics 2 50
Google Scholar
[23] Henk J, Hoesch M, Osterwalder J, Ernst A, Bruno P 2004 J. Phys. Condens. Matter 16 43
[24] Gong S J, Cai J, Yao Q F, Tong W Y, Wan X, Duan C G, Chu J H 2016 J. Appl. Phys. 119 125310
Google Scholar
[25] Krupin O, Bihlmayer G, Starke K, Gorovikov S, Prieto J E, Dobrich K, Blügel S, Kaindl G R 2005 Phys. Rev. B 71 201403
Google Scholar
[26] Koroteev Y M, Bihlmayer G, Gayone J E, Chulkov E V, Blugel S, Echenique P M, Hofmann 2004 Phys. Rev. Lett. 93 046403
Google Scholar
[27] Vajna S, Simon E, Szilva A, Palotas K, Ujfalussy B, Szunyogh L 2012 Phys. Rev. B 85 075404
[28] Meier F, Dil H, Lobo-Checa J, Patthey L, Osterwalder J 2008 Phys. Rev. B 77 089902
Google Scholar
[29] Ast C R, Henk J, Ernst A, Moreschini L, Falub M C, Pacile D, Bruno P, Kern K, Grioni M 2007 Phys. Rev. Lett. 98 186807
Google Scholar
[30] Popović D, Reinert F, Hüfner S, Grigoryan V G, Springborg M, Cercellier H, Fagot-Revurat Y, Kierren B, Malterre D 2005 Phys. Rev. B 72 045419
Google Scholar
[31] Cercellier H, Didiot C, Fagot-Revurat Y, Kierren B, Moreau L, Malterre D, Reinert F 2006 Phys. Rev. B 73 195413
Google Scholar
[32] 龚士静, 段纯刚 2015 64 187103
Google Scholar
Gong S J, Duan C G, 2015 Acta. Phys. Sin. 64 187103
Google Scholar
[33] Peng Q, Lei Y, Deng X, Deng J, Wu G, Li J, He C, Zhong J 2022 Physica E 135 114944
Google Scholar
[34] Sakano M, Bahramy M S, Katayama A, Shimojima T, Murakawa H, Kaneko Y, Malaeb W, Shin S, Ono K, Kumigashira H, Arita R, Nagaosa N, Hwang H Y, Tokura Y, Ishizaka K 2013 Phys. Rev. Lett. 110 107204
Google Scholar
[35] Bahramy M S, Arita R, Nagaosa N 2011 Phys. Rev. B 84 041202
[36] Narayan A 2015 Phys. Rev. B 92 220101
Google Scholar
[37] Xiang F X, Wang X L, Veldhorst M, Dou S X, Fuhrer M S 2015 Phys. Rev. B 92 035123
Google Scholar
[38] Krempaský J, Volfova H, Muff S, Pilet N, Landolt G, Radovic M, Shi M, Kriegner D, Holy V, Braun J, Ebert H, Bisti F, Rogalev V A, Strocov V N, Springholz G, Minar J, Dil J H 2016 Phys. Rev. B 94 205111
Google Scholar
[39] Di Sante D, Barone P, Bertacco R, Picozzi S 2013 Adv. Mater. 25 509
Google Scholar
[40] Ishizaka K, Bahramy M S, Murakawa H, Sakano M, Shimojima T, Sonobe T, Koizumi K, Shin S, Miyahara H, Kimura A, Miyamoto K, Okuda T, Namatame H, Taniguchi M, Arita R, Nagaosa N, Kobayashi K, Murakami Y, Kumai R, Kaneko Y, Onose Y, Tokura Y 2011 Nat. Mater. 10 521
Google Scholar
[41] Krempaský J, Muff S, Min´ar J, Pilet N, Fanciulli M, Weber A P, Guedes E B, Caputo M, Müller E, Volobuev V V, Gmitra M, Vaz C A F, Scagnoli V, Springholz G, Dil J H 2018 Phys. Rev. X 8 021067
[42] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
Google Scholar
[43] Knez I, Du R R, Sullivan G 2012 Phys. Rev. Lett. 109 186603
Google Scholar
[44] Liu W J, Xiong X L, Liu M L, Xing X W, Chen H L, Ye H, Han J F, Wei Z Y 2022 Appl. Phys. Lett. 120 053108
Google Scholar
[45] Yang M, Liu Y D, Zhou W, Liu C, Mu D, Liu Y N, Wang J O, Hao W C, Li J, Zhong J X, Du Y, Zhuang J C 2022 ACS Nano 16 2
[46] Ezawa M 2012 New J. Phys. 14 033003
Google Scholar
[47] Zhang R W, Ji W X, Zhang C W, Li S S, Li P, Wang P J 2016 J. Mater. Chem. C 4 2088
Google Scholar
[48] Xu Y, Yan B, Zhang H J, Wang J, Xu G, Tang P, Duan W, Zhang S C 2013 Phys. Rev. Lett. 111 136804
Google Scholar
[49] Zhao H, Zhang C W, Ji W X, Zhang R W, Li S S, Yan S S, Zhang B M, Li P, Wang P J 2016 Sci. Rep. 6 20152
Google Scholar
[50] Zhou L, Kou L, Sun Y, Felser C, Hu F, Shan G, Smith S C, Yan B, Frauenheim T 2015 Nano Lett. 15 7867
Google Scholar
[51] Weng H, Dai X, Fang Z 2014 Phys. Rev. X 4 011002
[52] Li X, Ying D, Ma Y, Wei W, Lin Y, Huang B 2015 Nano Res. 8 2954
Google Scholar
[53] Luo W, Xiang H 2015 Nano Lett. 15 3230
Google Scholar
[54] Jiang J W, Guo X Q, Ma Z, Wang G, Xu Y G, Zhang X W 2022 J. Mater. Chem. C 10 11329
Google Scholar
[55] Guo Z P, Yan D Y, Sheng H H, Nie S M, Shi Y G, Wang Z J 2021 Phys. Rev. B 103 115145
Google Scholar
[56] Wang X, Wan W H, Ge Y F, Zhang K C, Liu Y 2022 Physica E 143 115325
Google Scholar
[57] Perez M N R, Villaos R A B, Feng L Y, Maghirang A B, Cheng C P, Huang Z Q, Hsu C H, Bansil A, Chuang F C 2022 Appl. Phys. Rev. 9 011410
Google Scholar
[58] Li J, He C Y, Xiao H P, Tang C, Wei X L, Kim J, Kioussis N, Stocks M, Zhong J X 2015 Sci. Rep. 5 14115
Google Scholar
[59] Yuhara J, He B, Matsunami N, Nakatake M, Le Lay G 2019 Adv. Mater. 31 e1901017
Google Scholar
[60] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
Google Scholar
[61] Perdew J P, Burke K, Ernzerhof M 1998 Phys. Rev. Lett. 77 3865
[62] Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685
Google Scholar
[63] Wu Q S, Zhang S N, Song H F, Troyer M, Soluyanov A A 2018 Comput. Phys. Commun. 224 405
Google Scholar
[64] Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106
Google Scholar
[65] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
Google Scholar
[66] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
Google Scholar
[67] Zhang H J, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438
Google Scholar
[68] König M, Wiedmann S, Brüne C, Roth A, Buhmann H, W. Molenkamp L, Qi X L, Zhang S C 2007 Science 318 766
Google Scholar
[69] Liu Q, Guo Y, Freeman A 2013 Nano Lett. 13 5264
Google Scholar
[70] Gong Q, Zhang G L 2022 Int. J. Mol. Sci. 23 7629
Google Scholar
[71] Sino P A L, Feng L Y, Villaos R A B, Cruzado N H, Huang Z Q, Hsu C H, Chuang F C 2021 Nanoscale Adv. 3 6608
Google Scholar
[72] Hussain G, Samad A, Ur Rehman M, Guono G, Autieri C 2022 J. Magn. Magn. Mater. 563 169897
Google Scholar
[73] Xue W M, Li J, Peng X Y, He C Y, Ouyang T, Zhang C X, Tang C, Li Z Q, Lu D L, Zhong J X 2020 J. Phys. D: Appl. Phys 53 025302
Google Scholar
[74] Patel S, Dey U, Adhikari N P, Taraphder A 2022 Phys. Rev. B 106 035125
Google Scholar
[75] Xue W M, Li J, Peng X Y, He C Y, Ouyang T, Zhang C X, Tang C, Li Z Q, Liu H T, Zhong J X 2019 J. Phys. Condens. Matter 31 365002
Google Scholar
[76] Lee K, Yun W S, Lee J D 2015 Phys. Rev. B 91 125420
Google Scholar
[77] LaShell S, McDougall B, Jensen E 1996 Phys. Rev. Lett. 77 3419
Google Scholar
-
图 1 (a) 2D层状材料H-Pb-Cl结构的侧视图和俯视图; (b) H-Pb-Cl结构在布里渊区沿高对称点的声子谱
Fig. 1. (a) Side and top view of the crystal structure H-Pb-Cl; (b) phonon dispersion of 2D H-Pb-Cl along the high symmetry points in Brillouin zone.
图 2 采用PBE和HSE06的2D H-Pb-Cl的能带结构 (a), (c) 不考虑SOC; (b), (d)考虑SOC. 蓝点、红点和绿点分别表示Pb原子的s, px, y和pz轨道的投影权重. 图(b)中的插图表示的是费米面附近的能带劈裂现象
Fig. 2. The band structure of 2D H-Pb-Cl using PBE and HSE06: (a), (c) Without SOC; (b), (d) with SOC. Blue, red and green dots represent the contribution of s, px, y, pz orbitals of Pb atoms, respectively. The illustration in Figure (b) shows the band splitting near the Fermi surface.
图 3 (a) 沿着ky方向的瓦尼尔中心演化, 得到Z2 = 1; (b) H-Pb-Cl沿着锯齿形边缘的边缘态; (c) H-Pb-Cl在Γ点的能级演化
Fig. 3. (a) The evolutions of Wannier centers along ky, yielding Z2 = 1; (b) edge states of H-Pb-Cl on the zigzag edges; (c) evolution of energy bands at Γ for H-Pb-Cl.
图 4 (a) 无双轴应力作用下H-Pb-Cl的功函数, ∆Φ表示的是静电势差; (b) H-Pb-Cl的静电势差在双轴应力从–16% 到16%作用下的变化图
Fig. 4. (a) Work functions of H-Pb-Cl under 0 biaxial stress, where ∆Φ represents the electrostatic potential difference under different biaxial stresses; (b) the variations of electrostatic potential difference ∆Φ of H-Pb-Cl with the biaxial stress of –16% to 16%.
图 5 (a) 在双轴应力(–16%到16%)作用下H-Pb-Cl体系内的Rashba自旋劈裂系数αR的变化图; (b) H-Pb-Cl (1×1)/BN (2×2)的能带结构, 其中红色部分代表的是基底BN在能带中的贡献情况; (c) H-Pb-Cl (1×1)/石墨烷 (2×2), 其中紫色点线代表的是石墨烷在能带中的贡献情况
Fig. 5. (a) The variations of Rashba spin splitting αR of H-Pb-Cl with the biaxial stress of –16% to 16%; (b) band structure of H-Pb-Cl (1×1)/BN (2×2), with the red stars-lines contributed by BN substrate; (c) band structure of H-Pb-Cl (1×1)/graphane (2×2), with the purple dotted line contributed by graphane substrate.
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[1] Moore J E 2010 Nature 464 194
Google Scholar
[2] Soumyanarayanan A, Reyren N, Fert A, Panagopoulos C 2016 Nature 539 509
Google Scholar
[3] Feng Y, Jiang Q, Feng B J, Yang M, Xu T, Liu W J, Yang X F, Arita M, Schwier E F, Shimada K, Jeschke H O, Thomale R, Shi Y G, Wu X X, Xiao S Z, Qiao S, He S L 2019 Nat. Commun. 10 4765
Google Scholar
[4] Lu J P, Yau J B, Shukla S P, Shayegan M 1998 Phys. Rev. Lett. 81 1282
Google Scholar
[5] Kuhlen S, Schmalbuch K, Hagedorn M, Schlammes P, Patt M, Lepsa M, Guntherodt G, Beschoten B 2012 Phys. Rev. Lett. 109 146603
Google Scholar
[6] Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150
Google Scholar
[7] Wang Z Y, Cheng X C, Wang B Z, Zhang J Y, Lu Y H, Yi C R, Niu S, Deng Y, Liu X J, Chen S, Pan J W 2021 Science 372 271
Google Scholar
[8] Lu Y H, Wang B Z, Liu X J 2020 Sci. Bull. 65 2080
Google Scholar
[9] Zezyulin D A, Konotop V V 2022 Phys. Rev. A 105 063323
Google Scholar
[10] Xu Z C, Zhou Z, Cheng E H, Lang L J, Zhu S L 2022 Sci. Chin. Phys. Mech. Astron. 65 283011
Google Scholar
[11] Zhao Q 2022 Mod. Phys. Lett. B 36 2250070
[12] Liu H, Zhang T, Wang K, Gao F, Xu G, Zhang X, Li S X, Cao G, Wang T, Zhang J, Hu X, Li H O, Guo G P 2022 Phys. Rev. Appl. 17 044052
Google Scholar
[13] Smith L W, Chen H B, Chang C W, Wu C W, Lo S T, Chao S H, Farrer I, Beere H E, Griffiths J P, Jones G A C, Ritchie D A, Chen Y N, Chen T M 2022 Phys. Rev. Lett. 128 027701
Google Scholar
[14] Dai X Y, Liu B Y 2022 Phys. Rev. A 105 043313
Google Scholar
[15] Hai K, Wang Y F, Chen Q, Hai W H 2021 Sci. Rep. 11 18839
Google Scholar
[16] Manchon A, Koo H C, Nitta J, Frolov S M, Duine R A 2015 Nat. Mater. 14 871
Google Scholar
[17] 红兰, 戈君, 双山, 刘达权 2022 71 016301
Google Scholar
Hong L, Ge J, Shuang S, Liu D Q 2022 Acta. Phys. Sin. 71 016301
Google Scholar
[18] Li Y, Ma X K, Zhai X K, Gao M N, Dai H T, Schumacher S, Gao T G 2022 Nat. Commun. 13 3785
Google Scholar
[19] Ghosh D, Roy K, Maitra S, Kumar P 2022 J. Phys. Chem. Lett. 13 5
[20] Schlipf M, Giustino F 2021 Phys. Rev. Lett. 127 237601
Google Scholar
[21] Zhu L, Zhang T, Chen G, Chen H 2018 Phys. Chem. Chem. Phys. 20 30133
Google Scholar
[22] Awschalom D, Samarth N 2009 Physics 2 50
Google Scholar
[23] Henk J, Hoesch M, Osterwalder J, Ernst A, Bruno P 2004 J. Phys. Condens. Matter 16 43
[24] Gong S J, Cai J, Yao Q F, Tong W Y, Wan X, Duan C G, Chu J H 2016 J. Appl. Phys. 119 125310
Google Scholar
[25] Krupin O, Bihlmayer G, Starke K, Gorovikov S, Prieto J E, Dobrich K, Blügel S, Kaindl G R 2005 Phys. Rev. B 71 201403
Google Scholar
[26] Koroteev Y M, Bihlmayer G, Gayone J E, Chulkov E V, Blugel S, Echenique P M, Hofmann 2004 Phys. Rev. Lett. 93 046403
Google Scholar
[27] Vajna S, Simon E, Szilva A, Palotas K, Ujfalussy B, Szunyogh L 2012 Phys. Rev. B 85 075404
[28] Meier F, Dil H, Lobo-Checa J, Patthey L, Osterwalder J 2008 Phys. Rev. B 77 089902
Google Scholar
[29] Ast C R, Henk J, Ernst A, Moreschini L, Falub M C, Pacile D, Bruno P, Kern K, Grioni M 2007 Phys. Rev. Lett. 98 186807
Google Scholar
[30] Popović D, Reinert F, Hüfner S, Grigoryan V G, Springborg M, Cercellier H, Fagot-Revurat Y, Kierren B, Malterre D 2005 Phys. Rev. B 72 045419
Google Scholar
[31] Cercellier H, Didiot C, Fagot-Revurat Y, Kierren B, Moreau L, Malterre D, Reinert F 2006 Phys. Rev. B 73 195413
Google Scholar
[32] 龚士静, 段纯刚 2015 64 187103
Google Scholar
Gong S J, Duan C G, 2015 Acta. Phys. Sin. 64 187103
Google Scholar
[33] Peng Q, Lei Y, Deng X, Deng J, Wu G, Li J, He C, Zhong J 2022 Physica E 135 114944
Google Scholar
[34] Sakano M, Bahramy M S, Katayama A, Shimojima T, Murakawa H, Kaneko Y, Malaeb W, Shin S, Ono K, Kumigashira H, Arita R, Nagaosa N, Hwang H Y, Tokura Y, Ishizaka K 2013 Phys. Rev. Lett. 110 107204
Google Scholar
[35] Bahramy M S, Arita R, Nagaosa N 2011 Phys. Rev. B 84 041202
[36] Narayan A 2015 Phys. Rev. B 92 220101
Google Scholar
[37] Xiang F X, Wang X L, Veldhorst M, Dou S X, Fuhrer M S 2015 Phys. Rev. B 92 035123
Google Scholar
[38] Krempaský J, Volfova H, Muff S, Pilet N, Landolt G, Radovic M, Shi M, Kriegner D, Holy V, Braun J, Ebert H, Bisti F, Rogalev V A, Strocov V N, Springholz G, Minar J, Dil J H 2016 Phys. Rev. B 94 205111
Google Scholar
[39] Di Sante D, Barone P, Bertacco R, Picozzi S 2013 Adv. Mater. 25 509
Google Scholar
[40] Ishizaka K, Bahramy M S, Murakawa H, Sakano M, Shimojima T, Sonobe T, Koizumi K, Shin S, Miyahara H, Kimura A, Miyamoto K, Okuda T, Namatame H, Taniguchi M, Arita R, Nagaosa N, Kobayashi K, Murakami Y, Kumai R, Kaneko Y, Onose Y, Tokura Y 2011 Nat. Mater. 10 521
Google Scholar
[41] Krempaský J, Muff S, Min´ar J, Pilet N, Fanciulli M, Weber A P, Guedes E B, Caputo M, Müller E, Volobuev V V, Gmitra M, Vaz C A F, Scagnoli V, Springholz G, Dil J H 2018 Phys. Rev. X 8 021067
[42] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
Google Scholar
[43] Knez I, Du R R, Sullivan G 2012 Phys. Rev. Lett. 109 186603
Google Scholar
[44] Liu W J, Xiong X L, Liu M L, Xing X W, Chen H L, Ye H, Han J F, Wei Z Y 2022 Appl. Phys. Lett. 120 053108
Google Scholar
[45] Yang M, Liu Y D, Zhou W, Liu C, Mu D, Liu Y N, Wang J O, Hao W C, Li J, Zhong J X, Du Y, Zhuang J C 2022 ACS Nano 16 2
[46] Ezawa M 2012 New J. Phys. 14 033003
Google Scholar
[47] Zhang R W, Ji W X, Zhang C W, Li S S, Li P, Wang P J 2016 J. Mater. Chem. C 4 2088
Google Scholar
[48] Xu Y, Yan B, Zhang H J, Wang J, Xu G, Tang P, Duan W, Zhang S C 2013 Phys. Rev. Lett. 111 136804
Google Scholar
[49] Zhao H, Zhang C W, Ji W X, Zhang R W, Li S S, Yan S S, Zhang B M, Li P, Wang P J 2016 Sci. Rep. 6 20152
Google Scholar
[50] Zhou L, Kou L, Sun Y, Felser C, Hu F, Shan G, Smith S C, Yan B, Frauenheim T 2015 Nano Lett. 15 7867
Google Scholar
[51] Weng H, Dai X, Fang Z 2014 Phys. Rev. X 4 011002
[52] Li X, Ying D, Ma Y, Wei W, Lin Y, Huang B 2015 Nano Res. 8 2954
Google Scholar
[53] Luo W, Xiang H 2015 Nano Lett. 15 3230
Google Scholar
[54] Jiang J W, Guo X Q, Ma Z, Wang G, Xu Y G, Zhang X W 2022 J. Mater. Chem. C 10 11329
Google Scholar
[55] Guo Z P, Yan D Y, Sheng H H, Nie S M, Shi Y G, Wang Z J 2021 Phys. Rev. B 103 115145
Google Scholar
[56] Wang X, Wan W H, Ge Y F, Zhang K C, Liu Y 2022 Physica E 143 115325
Google Scholar
[57] Perez M N R, Villaos R A B, Feng L Y, Maghirang A B, Cheng C P, Huang Z Q, Hsu C H, Bansil A, Chuang F C 2022 Appl. Phys. Rev. 9 011410
Google Scholar
[58] Li J, He C Y, Xiao H P, Tang C, Wei X L, Kim J, Kioussis N, Stocks M, Zhong J X 2015 Sci. Rep. 5 14115
Google Scholar
[59] Yuhara J, He B, Matsunami N, Nakatake M, Le Lay G 2019 Adv. Mater. 31 e1901017
Google Scholar
[60] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
Google Scholar
[61] Perdew J P, Burke K, Ernzerhof M 1998 Phys. Rev. Lett. 77 3865
[62] Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685
Google Scholar
[63] Wu Q S, Zhang S N, Song H F, Troyer M, Soluyanov A A 2018 Comput. Phys. Commun. 224 405
Google Scholar
[64] Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106
Google Scholar
[65] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
Google Scholar
[66] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
Google Scholar
[67] Zhang H J, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438
Google Scholar
[68] König M, Wiedmann S, Brüne C, Roth A, Buhmann H, W. Molenkamp L, Qi X L, Zhang S C 2007 Science 318 766
Google Scholar
[69] Liu Q, Guo Y, Freeman A 2013 Nano Lett. 13 5264
Google Scholar
[70] Gong Q, Zhang G L 2022 Int. J. Mol. Sci. 23 7629
Google Scholar
[71] Sino P A L, Feng L Y, Villaos R A B, Cruzado N H, Huang Z Q, Hsu C H, Chuang F C 2021 Nanoscale Adv. 3 6608
Google Scholar
[72] Hussain G, Samad A, Ur Rehman M, Guono G, Autieri C 2022 J. Magn. Magn. Mater. 563 169897
Google Scholar
[73] Xue W M, Li J, Peng X Y, He C Y, Ouyang T, Zhang C X, Tang C, Li Z Q, Lu D L, Zhong J X 2020 J. Phys. D: Appl. Phys 53 025302
Google Scholar
[74] Patel S, Dey U, Adhikari N P, Taraphder A 2022 Phys. Rev. B 106 035125
Google Scholar
[75] Xue W M, Li J, Peng X Y, He C Y, Ouyang T, Zhang C X, Tang C, Li Z Q, Liu H T, Zhong J X 2019 J. Phys. Condens. Matter 31 365002
Google Scholar
[76] Lee K, Yun W S, Lee J D 2015 Phys. Rev. B 91 125420
Google Scholar
[77] LaShell S, McDougall B, Jensen E 1996 Phys. Rev. Lett. 77 3419
Google Scholar
-
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