H-Pb-Cl中可调控的巨型Rashba自旋劈裂和量子自旋霍尔效应

薛文明; 李金; 何朝宇; 欧阳滔; 罗朝波; 唐超; 钟建新

doi:10.7498/aps.72.20221493

摘要

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(α_R = 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.

关键词:

Abstract

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 (α_R = 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:

作者及机构信息

1.
湖南工程学院计算科学与电子学院, 湘潭　411104

2.
湘潭大学物理与光电工程学院, 湘潭　411105

通信作者: 薛文明, xuewm@hnie.edu.cn ; 李金, lijin@xtu.edu.cn ;

基金项目: 国家自然科学基金 (批准号: 11874316, 11404275, 11474244)和湖南省自然科学基金(批准号: 2016JJ3118)资助的课题.

Authors and contacts

1.
School of Computational Science and Electronics, Hunan Institute of Engineering, Xiangtan 411104, China

2.
School of Physics and Optoelectronics Engineering, Xiangtan University, Xiangtan 411105, China

Corresponding author: Xue Wen-Ming, xuewm@hnie.edu.cn ; Li Jin, lijin@xtu.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874316, 11404275, 11474244) and the Natural Science Foundation of Hunan Province, China (Grant No. 2016JJ3118).

文章全文 : translate this paragraph

参考文献

[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 物理学报 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 物理学报 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

施引文献

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.

下载: 全尺寸图片幻灯片

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, p_{x, y}和p_z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, p_{x, y}, p_z orbitals of Pb atoms, respectively. The illustration in Figure (b) shows the band splitting near the Fermi surface.

下载: 全尺寸图片幻灯片

图 3 (a) 沿着k_y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 k_y, 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.

下载: 全尺寸图片幻灯片

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%.

下载: 全尺寸图片幻灯片

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α_R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 α_R 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.

下载: 全尺寸图片幻灯片

[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 物理学报 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 物理学报 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

[1]	王志梅, 王虹, 薛乃涛, 成高艳. 自旋轨道耦合量子点系统中的量子相干. 物理学报, 2022, 71(7): 078502. doi: 10.7498/aps.71.20212111
[2]	李家锐, 王梓安, 徐彤彤, 张莲莲, 公卫江. 一维${\cal {PT}}$对称非厄米自旋轨道耦合Su-Schrieffer-Heeger模型的拓扑性质. 物理学报, 2022, 71(17): 177302. doi: 10.7498/aps.71.20220796
[3]	薛海斌, 段志磊, 陈彬, 陈建宾, 邢丽丽. 自旋轨道耦合Su-Schrieffer-Heeger原子链系统的电子输运特性. 物理学报, 2021, 70(8): 087301. doi: 10.7498/aps.70.20201742
[4]	陈星, 薛潇博, 张升康, 马余全, 费鹏, 姜元, 葛军. 两体相互作用费米系统在自旋轨道耦合和塞曼场中的基态转变. 物理学报, 2021, 70(8): 083401. doi: 10.7498/aps.70.20201456
[5]	张爱霞, 姜艳芳, 薛具奎. 光晶格中自旋轨道耦合玻色-爱因斯坦凝聚体的非线性能谱特性. 物理学报, 2021, 70(20): 200302. doi: 10.7498/aps.70.20210705
[6]	施婷婷, 汪六九, 王璟琨, 张威. 自旋轨道耦合量子气体中的一些新进展. 物理学报, 2020, 69(1): 016701. doi: 10.7498/aps.69.20191241
[7]	梁滔, 李铭. 自旋轨道耦合系统中的整数量子霍尔效应. 物理学报, 2019, 68(11): 117101. doi: 10.7498/aps.68.20190037
[8]	李志强, 王月明. 一维谐振子束缚的自旋轨道耦合玻色气体. 物理学报, 2019, 68(17): 173201. doi: 10.7498/aps.68.20190143
[9]	杨圆, 陈帅, 李小兵. Rashba自旋轨道耦合下square-octagon晶格的拓扑相变. 物理学报, 2018, 67(23): 237101. doi: 10.7498/aps.67.20180624
[10]	耿虎, 计青山, 张存喜, 王瑞. 缀饰格子中时间反演对称破缺的量子自旋霍尔效应. 物理学报, 2017, 66(12): 127303. doi: 10.7498/aps.66.127303
[11]	赵正印, 王红玲, 李明. Al0.6Ga0.4N/GaN/Al0.3Ga0.7N/Al0.6Ga0.4N量子阱中的Rashba自旋劈裂. 物理学报, 2016, 65(9): 097101. doi: 10.7498/aps.65.097101
[12]	刘胜利, 厉建峥, 程杰, 王海云, 李永涛, 张红光, 李兴鳌. 强自旋轨道耦合化合物Sr2-xLaxIrO4的掺杂和拉曼谱学. 物理学报, 2015, 64(20): 207103. doi: 10.7498/aps.64.207103
[13]	陈东海, 杨谋, 段后建, 王瑞强. 自旋轨道耦合作用下石墨烯pn结的电子输运性质. 物理学报, 2015, 64(9): 097201. doi: 10.7498/aps.64.097201
[14]	龚士静, 段纯刚. 金属表面Rashba自旋轨道耦合作用研究进展. 物理学报, 2015, 64(18): 187103. doi: 10.7498/aps.64.187103
[15]	陈光平. 简谐+四次势中自旋轨道耦合旋转玻色-爱因斯坦凝聚体的基态结构. 物理学报, 2015, 64(3): 030302. doi: 10.7498/aps.64.030302
[16]	张磊, 李辉武, 胡梁宾. 二维自旋轨道耦合电子气中持续自旋螺旋态的稳定性的研究. 物理学报, 2012, 61(17): 177203. doi: 10.7498/aps.61.177203
[17]	李明, 张荣, 刘斌, 傅德颐, 赵传阵, 谢自力, 修向前, 郑有炓. AlGaN/GaN量子阱中子带的Rashba自旋劈裂和子带间自旋轨道耦合作用研究. 物理学报, 2012, 61(2): 027103. doi: 10.7498/aps.61.027103
[18]	杨杰, 董全力, 江兆潭, 张杰. 自旋轨道耦合作用对碳纳米管电子能带结构的影响. 物理学报, 2011, 60(7): 075202. doi: 10.7498/aps.60.075202
[19]	余志强, 谢泉, 肖清泉. 狭义相对论下电子自旋轨道耦合对X射线光谱的影响. 物理学报, 2010, 59(2): 925-931. doi: 10.7498/aps.59.925
[20]	周青春, 王嘉赋, 徐荣青. 自旋-轨道耦合对磁性绝缘体磁光Kerr效应的影响. 物理学报, 2002, 51(7): 1639-1644. doi: 10.7498/aps.51.1639

计量

文章访问数: 1073
PDF下载量: 48
被引次数: 0

全文HTML

1. 引　言

随着拓扑绝缘体(topological insulator, TI)的兴起与被广泛深入的研究^[1], 自旋轨道耦合(spin-orbit coupling, SOC)引起了人们极大的兴趣. SOC来源于电子的自旋与其在电场中的运动之间的相互作用. 根据相对论理论, 当静止参考系中的电子在电场中运动时, 通过相对论的洛伦兹变换, 电子会感受到一个和电场以及电子运动有关的等效磁场. 这个等效磁场和电子自旋的Zeeman相互作用将电子的自旋和轨道运动耦合在一起, 即SOC^[2,3]. SOC作用的强度与构成材料原子的原子序数密切相关, 电子平均速度较高的重原子, SOC的强度更大. 对于研究电子自旋行为的自旋电子学, SOC效应提供了控制电子自旋的可能性, 进而可以在具有强SOC作用的材料中诱发一系列新奇的特性, 如自旋弹道输运^[4]、电流诱导的自旋极化^[5]、自旋电流效应^[6]、超冷原子^[7-11]、量子电路^[12-15]等等. 在所有的与SOC有关的现象中, 由结构空间反演对称性破缺导致的Rashba类型自旋劈裂和量子自旋霍尔效应(quantum spin hall effect, QSHE)最受关注.

对于Rashba类型的SOC劈裂, 由于其最容易被外电场调控^[3,16], 且经常与材料内部反演对称性破缺导致的Dresselhaus型的自旋轨道耦合纠缠在一起^[17-20], 在材料的电子性质上诱导出现各向异性的自旋劈裂, 进而出现一系列有趣的物理现象. 此外, Rashba类型的SOC在实现无需外磁场作用的自旋电子器件方面具有很大的应用前景, 且巨型可调控的Rashba自旋劈裂更是对自旋场效应晶体管的实现具有重要意义. 在实际的操作中, 由于SOC诱导的Rashba效应和自旋电子器件的工作温度高度依赖于SOC的强度^[21,22], 因此, 实际的自旋电子应用对具有强Rashba 自旋轨道耦合的材料有很高的需求. 早期的研究中, 人们发现可以在重金属的表面^[23-26]或者合金表面^[27-31]诱导出较大的Rashba效应^[32], 但它们由于缺乏带隙, 不能广泛应用于许多自旋电子学器件^[33]. 在体半导体和铁电体系统^[34-40]中也发现了巨大的体Rashba效应, 这种效应甚至可以通过外部电场进行切换^[41], 但原子之间的强键作用使体系无法以稳定独立薄膜的形式存在, 这对于集成电路来说是非常不理想的. 因此, 寻找具有巨型可调控的Rashba自旋劈裂的材料依然是未来自旋电子学的核心问题.

对于QSHE, 其实现不需要外加磁场, 但需要物质本身有强的SOC, 以至于能在体系内形成能带翻转、产生带隙. 在QSHE中, 自旋方向相反的电子在沿着相反的方向运动, 在边缘出现自旋流, 但不存在电荷电流. 受时间反演对称性保护的自旋电流可以避免非磁性杂质的散射, 因此对于量子自旋霍尔系统, 时间反演对称性是不可或缺的. 所以对于能够实现QSHE的2D TI, 由于其具有受时间反演对称性保护的一维拓扑边缘态而在拓扑自旋电子器件方面拥有着极大的潜在应用价值. 然而, 目前实验上通过QSHE对量化霍尔电导的观察仅在少量二维体系材料中报道, 如HgTe/CdTe^[42](<10 K), InAs/GaSb^[43], Bi₄X₄ (X = Br和I)^[44,45]. 尤其是近期姚裕贵团队^[44]利用自助熔的方法制备高质量的Bi₄Br₄单晶样品, 并成功在300 K的室温下测得其受时间反演对称性保护的拓扑边缘态. 因此, 人们投入了大量精力来设计具有QSHE的新材料, 并提出了各种类型的2D TI, 包括硅烯^[46]、锗烯^[47]、锡烯^[48]、铅烯^[49]、过渡金属卤化物^[50]、ZrTe₅/HfTe₅^[51], III-V双层^[52], BiF^[53], X₂NaBi (X = K, Rb)^[54], Ta₂M₃Te₅ (M = Pd, Ni)^[55], MX₅ (M = Zr, Hf和X = S, Se, Te)^[56]和AM₂X₂ (A = Ca, Sr, Ba; M = Zn, Cd; X = Sb, Bi) ^[57]等等, 但目前这些预测的材料除了都没有在实验中得到直接证实外, 极大部分材料都存在拓扑带隙较小和易受基底的影响. 所以寻找具有巨大拓扑带隙且不受基底影响的2D TI至关重要.

Rashba自旋劈裂和QSHE的研究是2D强SOC材料近年来研究的两个重要热点, 但是目前二者的研究大部分都是独立开展, 并未将两种性质进行共同研究. 然而因为这两种性质在本质上并不存在互斥情况, 因此若能在同一材料中成功实现两种奇异性质的完美共存, 即在该材料中获得巨型Rashba劈裂的同时, 保证体系也存在受时间反演对称性保护的巨大拓扑带隙, 将可以极为有效地拓宽和增加该材料在自旋电子器件应用方面的广度和深度. 在近年来的一些研究中虽然也发现了在同一材料中Rashba自旋劈裂与QSHE的共存现象^[58]. 但是这些材料中的共存现象并不十分理想. 通常情况下, 体系中的Rashba自旋劈裂现象和拓扑带隙都很小, 这大大地限制了其在自旋电子器件方面的潜在应用. 因此, 是否可以设计一个空间反演对称性破缺的强SOC 2D材料, 使得巨型Rashba自旋劈裂和QSHE能够在该结构中完美共存呢? 根据Zhao等^[49]的结果, 我们注意到通过在强SOC的2D材料上吸附X(X = H, F, Cl, Br)原子可以极大地改变2D材料的电子性质, 甚至可以诱发拓扑相变. 而最近的研究报道显示, 已被实验成功制备的类石墨烯结构的铅烯^[59]是一个具有强SOC作用的普通绝缘体^[49]. 因此, 本文基于第一性原理计算, 从理论上提出了一种具有空间反转对称破缺的2D层状材料H—Pb—Cl. 根据计算结果, 注意到该材料在费米面附近有一个巨大的Rashba自旋劈裂(1.25 eV·Å), 并且在双轴应力(–16%)下, 劈裂可以进一步增强到3.78 eV·Å. 此外, 通过计算费米面附近的拓扑不变量和拓扑边态, 还发现该材料是一个具有巨大拓扑带隙(1.31 eV)的2D TI. 因此, 我们的研究相对于其他理论提出的模型, 具有更大的拓扑带隙, 且更不容易被基底效应影响, 此外, 巨型可调控的Rashba自旋劈裂和QSHE在2D H—Pb—Cl材料中的完美共存, 对于该材料在无磁场作用下的自旋电子器件应用以及在常温下观测受时间反演对称性保护的拓扑边缘态均具有极其重要的意义.

2. 计算方法

利用从头计算模拟程序包VASP(Vienna ab initio simulation package)^[60]进行了密度泛函理论计算. 计算中选用的交换关联能是带有范德瓦耳斯(van der Waals)修正的广义梯度近似(GGA)下的optPBE-vdW^[61]. 价电子与离子实之间的相互作用采用过投影缀加平面波(projected augmented wave, PAW)方法来描述. 平面波函数的截断能取为400 eV, 能量收敛标准设置为10^–6 eV. 采用Monkhorst-Pack方法, 布里渊区K点网格设置为9×9×1. 为了避免相邻胞的相互作用, 在异质结结构的z轴方向设置了20 Å的真空层. 利用共轭梯度方法对体系结构进行弛豫, 弛豫收敛条件为每个原子残余力小于0.001 eV/Å. 由于H—Pb—Cl为强SOC材料, 在电子结构的计算过程中也考虑了原子的SOC合作用. 通过利用wannier90^[62], wannier tools^[63]和PHONOPY^[64] 软件分别计算了H—Pb—Cl的拓扑不变量Z₂、拓扑边缘态以及声子谱.

4. 结　论

本文基于第一性原理计算预测了一个稳定的2D六角晶格结构H—Pb—Cl. 在SOC的影响下, 由于体系缺乏空间反转对称性, H—Pb—Cl在费米表面附近出现了明显的Rashba自旋劈裂现象, 通过计算该材料在不同应力下(–16%—16%)的电子性质, 发现其在费米面附近的Rashba自旋劈裂是随着应力增大而减小的, 且Rashba自旋劈裂值最高可达3.78 eV·Å, 这一发现对于实验实现并获得可调控的Rashba自旋劈裂具有重要意义. 此外, 还注意到在不考虑SOC作用时, 体系在费米面表现为半金属性质, 而在考虑SOC作用后, 体系打开了1.04 eV的巨大带隙, 在进一步考虑杂化泛函(HSE06)后, 体系带隙可高达1.31 eV. 进一步地, 通过计算其拓扑数Z₂和2D拓扑边缘态, 证明了该材料为2D TI. 这一发现表明, 巨型可调控的Rashba自旋劈裂和QSHE在2D H—Pb—Cl材料实现了完美共存, 这对于该材料在无磁场作用下的自旋电子器件应用, 以及在常温下观测受时间反演对称性保护的拓扑边缘态均具有极其重要的意义, 并且巨型可调控Rashba自旋劈裂和QSHE在2D H—Pb—Cl材料的共存更是有效地拓宽和增加了该材料在自旋电子器件方面的应用广度和深度.

参考文献 (77)

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

H-Pb-Cl中可调控的巨型Rashba自旋劈裂和量子自旋霍尔效应