锯齿型石墨烯纳米窄带中量子霍尔体系的电场调控

刘娜; 胡边; 魏鸿鹏; 刘红

doi:10.7498/aps.67.20180249

摘要

应用含自洽格点在位库仑作用的Kane-Mele模型，研究锯齿型石墨烯纳米窄带平面内横向电场对边界带能带结构和量子自旋霍尔（QSH）体系的影响.研究结果显示，当电场强度较弱时，外加电场的方向可以调控自旋向下的两个边界带一起朝不同方向移动，导致波矢q=0.5处自旋向下的两个纯边界态的能量简并劈裂方向可由电场调控；当电场强度进一步增强到超过0.69 V/nm，自旋向下的两个边界带出现较大带隙，能带反转，而自旋向上的电子结构无能隙，系统呈现半金属性，同时QSH体系不再是B类.特别当电场强度为1.17 V/nm时，在自旋向下能带的能隙中，q=0.5处存在自旋向上的纯边界态，意味着在8格点边界处可以产生自旋向上的纯边界电流.当电场强度持续增加时，QSH系统从B类到C类经历3个阶段的变化.当电场强度超过1.42 V/nm后，自旋向上的两个边界带也出现能带反转，分别成为导带和价带，系统成为C类的普通量子霍尔体系.

关键词:

Abstract

Using the tight binding Kane-Mele model including the self-consistent on-site Coulomb interactions (O-CIs), we study the influence of transverse electric field in the narrow zigzag graphene nanoribbon (ZGNR) plane on the edge band structure in order to investigate the way to control the type of quantum spin Hall (QSH) system in the ZGNR. The theoretical results show that when applying weak electric field intensity, the direction of electric field can adjust these two spin-down edge bands moving along the different directions in one-dimensional q space, which leads to the two different types of degenerative breakdown of two pure spin-down edge states at q=0.5. When applying positive electric field the energy of spin-down edge band at edge site 1 is higher than that at edge site 8. On the contrary, when applying negative electric field the energy of spin-down edge band at edge site 8 is higher than that at edge site 1. It shows that we can use the direction of electric field to control the two spin-down edge currents occurring at two different energies. Further, when the electric field intensity increases above 0.69 V/nm, the increased large band gap between the two spin-down edge bands leads to the inversion of these two spin-down edge bands. That is to say, there is a spin-down band gap, however, there is not a band gap for spin-up edge band in the region of spin-down band gap. Thus the system becomes half-metallic, and the QSH does not belong in the type B any longer. Specially, when the electric field intensity reaches 1.17 V/nm in the region of spin-down band gap, the pure spin-up edge state appears at q=0.5, which shows that the strong pure spin-up edge current along the edge site 8 can occur. With increasing the intensity of electric field, the QSH system undergoes three processes from the type B to the type C. When the electric field intensity is more than 1.42 V/nm, the two spin-up edge bands also present band inversion and turn into the conduction band and the valence band, respectively. Thus the system becomes semiconducting and the QSH system does not belong in the type C, ordinary quantum Hall system. Finally, according to the results discussed above, we can expect that using the direction and the intensity of the transverse electric field in plane we can adjust the properties of edge current, and control the type of QSH system varying from the type B to the type C.

Keywords:

作者及机构信息

1.
南京师范大学物理科学与技术学院, 南京 210023;

2.
安徽省铜陵市第一中学, 铜陵 244000

通信作者: 刘红, liuhong3@njnu.edu.cn

Authors and contacts

1.
School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China;

2.
No.1 High School of Tongling, Tongling 244000, China

Corresponding author: Liu Hong, liuhong3@njnu.edu.cn

参考文献

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[2]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[3]	Wallace P R 1947 Phys. Rev. 71 622
[4]	Neto A H C, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[5]	Fujita M, Wakabayashi K, Nakada K, Kusakabe K 1996 J. Phys. Soc. Jpn. 65 1920
[6]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[7]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
[8]	Dresselhaus G F, Dresselhaus M S, Mavroides J G 1966 Carbon 4 433
[9]	Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L, MacDonald A H 2006 Phys. Rev. B 74 165310
[10]	Qiao Z, Wang J 2007 Nanotechnology 18 435402
[11]	Zarea M, Sandler N 2009 Phys. Rev. B. 79 165442
[12]	Zarea M, Sandler N 2009 Phys. B: Condens. Matter 404 2694
[13]	Hatsugai Y 1993 Phys. Rev. Lett. 71 3697
[14]	Xu X Z, Yu J C, Zhang Z H, Liu K H 2017 Chin. Sci. Bull. 62 2220(in Chinese) [徐小志, 余佳晨, 张智宏, 刘开辉 2017 科学通报 62 2220]
[15]	Zhang Y B, Tang T T, Girit C, Hao Z, Martin M C, Zettl A, Crommie M F, Shen Y R, Wang F 2009 Nature 459 820
[16]	Son Y W, Cohen M L, Louie S G 2006 Nature 444 347
[17]	Wang Z G, Hao N N, Zhang P 2009 Phys. Rev. B 80 115420
[18]	Li H C, Sheng L, Xing D Y 2012 Phys. Rev. Lett. 108 196806
[19]	Guo J, Gunlycke D, White C T 2008 Appl. Phys. Lett. 92 163109
[20]	Gunlycke D, Areshkin D A, Li J, Mintmire J W, White C T 2007 Nano Lett. 7 3608
[21]	Hu B, Liu N, Liu H 2018 Journal of Nanjing Normal University 41 42 [胡边, 刘娜, 刘红 2018 南京师范大学学报 41 42]
[22]	Liu H, Hu B, Liu N 2016 Phys. Lett. A 380 3738
[23]	Sheng L, Sheng D N, Ting C S, Haldane F D M 2005 Phys. Rev. Lett. 95 136602

施引文献

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[2]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[3]	Wallace P R 1947 Phys. Rev. 71 622
[4]	Neto A H C, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[5]	Fujita M, Wakabayashi K, Nakada K, Kusakabe K 1996 J. Phys. Soc. Jpn. 65 1920
[6]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[7]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
[8]	Dresselhaus G F, Dresselhaus M S, Mavroides J G 1966 Carbon 4 433
[9]	Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L, MacDonald A H 2006 Phys. Rev. B 74 165310
[10]	Qiao Z, Wang J 2007 Nanotechnology 18 435402
[11]	Zarea M, Sandler N 2009 Phys. Rev. B. 79 165442
[12]	Zarea M, Sandler N 2009 Phys. B: Condens. Matter 404 2694
[13]	Hatsugai Y 1993 Phys. Rev. Lett. 71 3697
[14]	Xu X Z, Yu J C, Zhang Z H, Liu K H 2017 Chin. Sci. Bull. 62 2220(in Chinese) [徐小志, 余佳晨, 张智宏, 刘开辉 2017 科学通报 62 2220]
[15]	Zhang Y B, Tang T T, Girit C, Hao Z, Martin M C, Zettl A, Crommie M F, Shen Y R, Wang F 2009 Nature 459 820
[16]	Son Y W, Cohen M L, Louie S G 2006 Nature 444 347
[17]	Wang Z G, Hao N N, Zhang P 2009 Phys. Rev. B 80 115420
[18]	Li H C, Sheng L, Xing D Y 2012 Phys. Rev. Lett. 108 196806
[19]	Guo J, Gunlycke D, White C T 2008 Appl. Phys. Lett. 92 163109
[20]	Gunlycke D, Areshkin D A, Li J, Mintmire J W, White C T 2007 Nano Lett. 7 3608
[21]	Hu B, Liu N, Liu H 2018 Journal of Nanjing Normal University 41 42 [胡边, 刘娜, 刘红 2018 南京师范大学学报 41 42]
[22]	Liu H, Hu B, Liu N 2016 Phys. Lett. A 380 3738
[23]	Sheng L, Sheng D N, Ting C S, Haldane F D M 2005 Phys. Rev. Lett. 95 136602

[1]	贾亮广, 刘猛, 陈瑶瑶, 张钰, 王业亮. 单层二维量子自旋霍尔绝缘体1T'-WTe₂研究进展. 物理学报, 2022, 71(12): 127308. doi: 10.7498/aps.71.20220100
[2]	张振方, 郁殿龙, 刘江伟, 温激鸿. 内插扩张室声子晶体管路带隙特性研究. 物理学报, 2018, 67(7): 074301. doi: 10.7498/aps.67.20172383
[3]	底琳佳, 戴显英, 宋建军, 苗东铭, 赵天龙, 吴淑静, 郝跃. 基于锡组分和双轴张应力调控的临界带隙应变Ge1-xSnx能带特性与迁移率计算. 物理学报, 2018, 67(2): 027101. doi: 10.7498/aps.67.20171969
[4]	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
[5]	龙洋, 任捷, 江海涛, 孙勇, 陈鸿. 超构材料中的光学量子自旋霍尔效应. 物理学报, 2017, 66(22): 227803. doi: 10.7498/aps.66.227803
[6]	张勇, 施毅敏, 包优赈, 喻霞, 谢忠祥, 宁锋. 表面钝化效应对GaAs纳米线电子结构性质影响的第一性原理研究. 物理学报, 2017, 66(19): 197302. doi: 10.7498/aps.66.197302
[7]	李立明, 宁锋, 唐黎明. 量子局域效应和应力对GaSb纳米线电子结构影响的第一性原理研究. 物理学报, 2015, 64(22): 227303. doi: 10.7498/aps.64.227303
[8]	金峰, 张振华, 王成志, 邓小清, 范志强. 石墨烯纳米带能带结构及透射特性的扭曲效应. 物理学报, 2013, 62(3): 036103. doi: 10.7498/aps.62.036103
[9]	胡家光, 徐文, 肖宜明, 张丫丫. 晶格中心插入体的对称性及取向对二维声子晶体带隙的影响. 物理学报, 2012, 61(23): 234302. doi: 10.7498/aps.61.234302
[10]	许俊敏, 胡小会, 孙立涛. 铂掺杂扶手椅型石墨烯纳米带的电学特性研究. 物理学报, 2012, 61(2): 027104. doi: 10.7498/aps.61.027104
[11]	刘柱, 赵志飞, 郭浩民, 王玉琦. InAs/GaSb量子阱的能带结构及光吸收. 物理学报, 2012, 61(21): 217303. doi: 10.7498/aps.61.217303
[12]	马小凤, 王懿喆, 周呈悦. a-Si ∶H/SiO2多量子阱材料制备及其光学性能和微结构研究. 物理学报, 2011, 60(6): 068102. doi: 10.7498/aps.60.068102
[13]	林琦, 陈余行, 吴建宝, 孔宗敏. N掺杂对zigzag型石墨烯纳米带的能带结构和输运性质的影响. 物理学报, 2011, 60(9): 097103. doi: 10.7498/aps.60.097103
[14]	孙伟峰, 李美成, 赵连城. Ga和Sb纳米线声子结构和电子-声子相互作用的第一性原理研究. 物理学报, 2010, 59(10): 7291-7297. doi: 10.7498/aps.59.7291
[15]	王玮, 孙家法, 刘楣, 刘甦. β型烧绿石结构氧化物超导体AOs2O6(A=K,Rb,Cs)电子能带结构的第一性原理计算. 物理学报, 2009, 58(8): 5632-5639. doi: 10.7498/aps.58.5632
[16]	郝国郡, 傅秀军, 侯志林. 正方点阵上Fibonacci超元胞声子晶体的带结构. 物理学报, 2009, 58(12): 8484-8488. doi: 10.7498/aps.58.8484
[17]	邵明珠, 罗诗裕. 正弦平方势与带电粒子沟道效应的能带结构. 物理学报, 2007, 56(6): 3407-3410. doi: 10.7498/aps.56.3407
[18]	于威, 张立, 王保柱, 路万兵, 王利伟, 傅广生. 氢化纳米硅薄膜中氢的键合特征及其能带结构分析. 物理学报, 2006, 55(4): 1936-1941. doi: 10.7498/aps.55.1936
[19]	梁君武, 胡慧芳, 韦建卫, 彭平. 氧吸附对单壁碳纳米管的电子结构和光学性能的影响. 物理学报, 2005, 54(6): 2877-2882. doi: 10.7498/aps.54.2877
[20]	郭宝增. 用全带Monte Carlo方法模拟纤锌矿相GaN和ZnO材料的电子输运特性. 物理学报, 2002, 51(10): 2344-2348. doi: 10.7498/aps.51.2344

计量

文章访问数: 6208
PDF下载量: 122
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板