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耦合电磁场对石墨烯量子磁振荡的影响

卢亚鑫 马宁

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耦合电磁场对石墨烯量子磁振荡的影响

卢亚鑫, 马宁

The coupled electromagnetic field effects on quantum magnetic oscillations of graphene

Lu Ya-Xin, Ma Ning
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  • 我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应. 我们发现, 石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱, 且当电场与磁场比值超过某一临界值时, 量子磁振荡会突然消失, 这与非相对论二维电子气的情况显著不同. 这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释. 此外, 我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减. 我们的结果可用于分析石墨烯及其类似结构(硅烯、锗烯、锡烯等)的费米能级与朗道能谱的相互作用, 进而探测自旋轨道耦合引起的能隙.
    We have investigated the quantum magnetic oscillations of graphene subjected to the spin-orbit interaction(SOI) in the presence of crossed uniform electric and magnetic fields and scattered from impurities at finite temperatures. Landau levels are shown to be modified in an unexpected fashion by the spin-orbit interaction, the electrostatic potential and magnetic confinement; this is strikingly different from the non-relativistic 2D electron gas. Furthermore, we derive the analytical expressions of the thermodynamic quantities subject to the SOI, such as density of states, thermodynamic potential, magnetization, and magnetic susceptibility etc. At finite temperatures, the magnetization and magnetic susceptibility can both be predicted to oscillate periodically as a function of reciprocal field 1/B and shown to be modulated through the SOI and the dimensionless parameter ( = E/ F B). As approaches unity, the values of magnetization and magnetic susceptibility finally move to infinity, indicating a transformation of closed orbits into open trajectories, thereby, leading to the vanishing of magnetic oscillations. And, the magnetic susceptibility depends largely on the external fields, suggesting that graphene should be a non-linear magnetic medium. Besides, the associative effect of impurity scattering and temperature may make the standard 2D electron gas be deemed as the consequence of the relativistic type spectrum of low energy electrons and holes in graphene. Also, we comment on a possibility of using magnetic oscillations for detecting a gap that may open in the spectrum of quasiparticle excitations due to the SOI.
      通信作者: 马宁, maning@tyut.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11074196, 11304241)、太原理工大学引进人才基金(批准号: tyutrc-201273a)和太原理工大学校基金(批准号: 1205-04020102)资助的课题.
      Corresponding author: Ma Ning, maning@tyut.edu.cn
    • Funds: Project supported by the National Natural Science foundation of China (Grant Nos. 11074196, 11304241), the Qualified Personal Foundation of Taiyuan University of Technology (QPFT), China (Grant No. tyutrc-201273a), and the School Foundation of Taiyuan University of Technology, China (Grant No. 1205-04020102)
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    Gu N, Rudner M, Young A, Kim P, Levitov L 2011 Phys. Rev. Lett. 106 066601

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    Reis M S, Soriano S 2013 Appl. Phys. Lett. 102 112903

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    Alisultanov Z Z 2014 JETP Letters 99 232

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    Alisultanov Z Z 2014 Physica B 438 41

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    Alisultanov Z 2014 Phys. Letters A 378 2329

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    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802

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    Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L, MacDonald A H 2006 Phys. Rev. B 74 165310

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    Huertas-Hernando D, Guinea F, Brataas A 2006 Phys. Rev. B 74 155426

    [22]

    Gmitra M, Konschuh S, Ertler C, Ambrosch-Draxl C, Fabian J 2009 Phys. Rev. B 80 235431

    [23]

    Yao Y, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401(R)

    [24]

    Varykhalov A, Sanchez-Barriga J, Shikin A M, Biswas C, Vescovo E, Rybkin A, Marchenko D, Rader O 2008 Phys. Rev. Lett. 101 157601

    [25]

    Castro Neto A H, Guinea F 2009 Phys. Rev. Lett. 103 026804

    [26]

    Dresselhaus G 1955 Phys. Rev. 100 580

    [27]

    Yang Y E, Xiao Y, Yan X H, Dai C J 2015 Chin. Phys. B 24 117204

    [28]

    Cahangirov S, Topsakal M, Aktrk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804

    [29]

    Fang Y M, Hang Z Q, Hsu C H, Li X D, Xu Y X, Zhou Y H, Wu Z S, Chuang F C, Zhu Z Z 2015 Scientific Reports 5 14196

    [30]

    Landau L D, Diamagnetismus D M 1930 Z. Phys. 64 629

    [31]

    Landau L D, Lifshitz E M 1971 Relativistic Quantum Theory (New York: Pergamon Press) p100

    [32]

    Zutic I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323

    [33]

    Dresselhaus G, Dressehaus M S 1965 Phys. Rev. 140 A401

    [34]

    Meng L, Wang Y L, Zhang L Z, Du S X, Gao H J 2015 Chin. Phys. B 24 086803

  • [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]

    Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201

    [4]

    Sharapov S G, Gusynin V P, Beck H 2003 Phys. Rev. B 67 144509

    [5]

    Gusynin V P, Sharapov S G 2005 Phys. Rev. Lett. 95 146801

    [6]

    Gusynin V P, Sharapov S G 2005 Phys. Rev. B 71 125124

    [7]

    Gusynin V P, Sharapov S G 2006 Phys. Rev. B 73 245411

    [8]

    Lukose V, Shankar R, Baskaran G 2007 Phys. Rev. Lett. 98 116802

    [9]

    Gu N, Rudner M, Young A, Kim P, Levitov L 2011 Phys. Rev. Lett. 106 066601

    [10]

    Zhang S L, Ma N, Zhang E H 2010 J. Phys. Condens. Matter 22 115302

    [11]

    Ma N, Zhang S L, Liu D Q, Zhang E H 2011 Phys. Lett. A 375 3624

    [12]

    Reis M S, Soriano S 2013 Appl. Phys. Lett. 102 112903

    [13]

    Reis M S 2013 Solid State Commun. 161 19

    [14]

    Alisultanov Z Z 2014 JETP Letters 99 232

    [15]

    Alisultanov Z Z 2014 Physica B 438 41

    [16]

    Alisultanov Z 2014 Phys. Letters A 378 2329

    [17]

    Ji Q S, Hao H Y, Zhang C X, Wang R 2015 Acta Phys. Sin. 64 087302 (in Chinese) [季青山, 郝鸿雁, 张存熙, 王瑞 2015 物理学报 64 087302]

    [18]

    Dresselhaus G, Dressehaus M S 1965 Phys. Rev. 140 A401

    [19]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802

    [20]

    Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L, MacDonald A H 2006 Phys. Rev. B 74 165310

    [21]

    Huertas-Hernando D, Guinea F, Brataas A 2006 Phys. Rev. B 74 155426

    [22]

    Gmitra M, Konschuh S, Ertler C, Ambrosch-Draxl C, Fabian J 2009 Phys. Rev. B 80 235431

    [23]

    Yao Y, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401(R)

    [24]

    Varykhalov A, Sanchez-Barriga J, Shikin A M, Biswas C, Vescovo E, Rybkin A, Marchenko D, Rader O 2008 Phys. Rev. Lett. 101 157601

    [25]

    Castro Neto A H, Guinea F 2009 Phys. Rev. Lett. 103 026804

    [26]

    Dresselhaus G 1955 Phys. Rev. 100 580

    [27]

    Yang Y E, Xiao Y, Yan X H, Dai C J 2015 Chin. Phys. B 24 117204

    [28]

    Cahangirov S, Topsakal M, Aktrk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804

    [29]

    Fang Y M, Hang Z Q, Hsu C H, Li X D, Xu Y X, Zhou Y H, Wu Z S, Chuang F C, Zhu Z Z 2015 Scientific Reports 5 14196

    [30]

    Landau L D, Diamagnetismus D M 1930 Z. Phys. 64 629

    [31]

    Landau L D, Lifshitz E M 1971 Relativistic Quantum Theory (New York: Pergamon Press) p100

    [32]

    Zutic I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323

    [33]

    Dresselhaus G, Dressehaus M S 1965 Phys. Rev. 140 A401

    [34]

    Meng L, Wang Y L, Zhang L Z, Du S X, Gao H J 2015 Chin. Phys. B 24 086803

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出版历程
  • 收稿日期:  2015-06-25
  • 修回日期:  2015-10-27
  • 刊出日期:  2016-01-20

耦合电磁场对石墨烯量子磁振荡的影响

  • 1. 太原理工大学 物理与光电工程学院, 太原 030024
  • 通信作者: 马宁, maning@tyut.edu.cn
    基金项目: 国家自然科学基金(批准号: 11074196, 11304241)、太原理工大学引进人才基金(批准号: tyutrc-201273a)和太原理工大学校基金(批准号: 1205-04020102)资助的课题.

摘要: 我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应. 我们发现, 石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱, 且当电场与磁场比值超过某一临界值时, 量子磁振荡会突然消失, 这与非相对论二维电子气的情况显著不同. 这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释. 此外, 我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减. 我们的结果可用于分析石墨烯及其类似结构(硅烯、锗烯、锡烯等)的费米能级与朗道能谱的相互作用, 进而探测自旋轨道耦合引起的能隙.

English Abstract

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