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自旋轨道耦合作用下石墨烯pn结的电子输运性质

陈东海 杨谋 段后建 王瑞强

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自旋轨道耦合作用下石墨烯pn结的电子输运性质

陈东海, 杨谋, 段后建, 王瑞强

Electronic transport properties of graphene pn junctions with spin-orbit coupling

Chen Dong-Hai, Yang Mou, Duan Hou-Jian, Wang Rui-Qiang
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  • 本文研究了自旋轨道耦合作用下石墨烯纳米带pn结的电子输运性质. 当粒子的入射能量处于pn结两端势能之间时, 粒子将会以隧穿的形式通过石墨烯pn结, 同时伴随着电子空穴转换. 电导随费米能的变化曲线呈不等高阶梯状, 并在费米能位于pn结两端能量中点时取得最大值. 随着石墨烯pn结长度的增加, 电导以指数形式衰减. 自旋轨道耦合作用导致的能隙会使电导显著减小, 而边缘态的粒子则可以几乎毫无阻碍地通过pn结. 本文用一个简单的子带隧穿模型解释了上述特征. 最后还研究了在pn转换区中掺入替位杂质的情况. 在弱杂质下, 电导随费米能变化的曲线将不再对称; 当杂质较强时, 仅边界态的形成的电导台阶能够保持.
    We have investigated the electronic transport properties of graphene pn junction with spin-orbit coupling. If the incident energy lies between the potentials of the two ends of the pn junction, a particle can penetrate the graphene pn junction by tunneling accompanied by the electron-hole transition. The curve of conductance versus Fermi energy shows steps and reaches its maximum when the Fermi energy lies at the middle of the potentials of the p and n areas. As the length of graphene pn junction increases, the conductance decays exponentially. The spin-orbit coupling leads to a bulk energy gap and edge states; the gap reduces the conductance dramatically and the edge states result in an almost perfect conductance plateau. When the pn region is influenced by randomly doped impurities, the conductance curves are no longer symmetrical in the case of weak doping, while in the strong doping case, the step structures are destroyed but the conductance plateau contributed by the edge states survives well.
    • 基金项目: 国家自然科学基金(批准号: 11274124, 11474106)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11274124, 11474106).
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    Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620

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    Stander N, Huard B, Gordon C D 2009 Phys. Rev. Lett. 102 026807

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    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801

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    Jiang H, Qiao Z H, Liu H W, Shi J R, Niu Q 2012 Phys. Rev. Lett. 109 116803

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    Huang X Q, Lin C F, Yin X L, Zhao R G, Wang E G, Hu Z H 2014 Acta Phys. Sin. 63 197301 (in Chinese) [黄向前, 林陈昉, 尹秀丽, 赵汝光, 王恩哥, 胡宗海 2014 物理学报 63 197301]

    [13]

    Chen L, Liu C C, Feng B J, He X Y, Cheng P, Ding Z J, Meng S, Yao Y G, Wu K H 2012 Phys. Rev. Lett. 109 056804

    [14]

    Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett. 107 076802

    [15]

    Cai Y, Chuu C P, Wei C M, Chou M Y 2013 Phys. Rev. B 88 245408

    [16]

    Kim Y, Choi K, Ihm J, Jin H 2014 Phys. Rev. B 89 085429

    [17]

    Yokoyama T 2014 New J. Phys. 16 085005

    [18]

    Rachel S, Ezawa M 2014 Phys. Rev. B 89 195303

    [19]

    Wang S K, Wang J, Chan K S 2014 New J. Phys. 16 045015

    [20]

    Liu C C, Jiang H, Yao Y G 2011 Phys. Rev. B 84 195430

    [21]

    Chiu H Y, Perefleinos V, Lin Y M, Avouris P 2010 Nano Lett. 10 4634

    [22]

    Woszczyna M, Friedemann M, Dziomba T, Weimann T, Ahlers F J 2011 Appl. Phys. Lett. 99 022112

    [23]

    Silvestrov P G, Efetov K B 2007 Phys. Rev. Lett. 98 016802

    [24]

    Nakaharai S, Williams J R, Marcus C M 2011 Phys. Rev. Lett. 107 036602

    [25]

    Cheianov V V, Fal’ko V, Altshuler B L 2007 Science 315 1252

    [26]

    Gómez S, Burset P, Herrera W J, Yeyati L A 2012 Phys. Rev. B 85 115411

    [27]

    Williams J R, Marcus C M 2011 Phys. Rev. Lett. 107 046602

    [28]

    Williams J R, DiCarlo L, Marcus C M 2007 Science 317 638

    [29]

    Cheianov V V, Falko V I 2006 Phys. Rev. B 74 041403

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    Yang M, Ran X J, Cui Y, Wang R Q 2012 J. Appl. Phys. 111 083708

  • [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]

    Neto C A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109

    [4]

    Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620

    [5]

    Stander N, Huard B, Gordon C D 2009 Phys. Rev. Lett. 102 026807

    [6]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801

    [7]

    He W Y, He L 2013 Phys. Rev. B 88 085411

    [8]

    Jiang H, Qiao Z H, Liu H W, Shi J R, Niu Q 2012 Phys. Rev. Lett. 109 116803

    [9]

    Balakrishnan J, Koon G K W, Jaiswal M, Neto C A H, Ozyilmaz B 2013 Nat. Phys. 9 284

    [10]

    Hu J, Alicea J, Wu R Q, Franz M 2012 Phys. Rev. Lett. 109 266801

    [11]

    Liu Y, Yao J, Chen C, Miao L, Jiang J J 2013 Acta Phys. Sin. 62 63601 (in Chinese) [刘源, 姚洁, 陈驰, 缪灵, 江建军 2013 物理学报 62 63601]

    [12]

    Huang X Q, Lin C F, Yin X L, Zhao R G, Wang E G, Hu Z H 2014 Acta Phys. Sin. 63 197301 (in Chinese) [黄向前, 林陈昉, 尹秀丽, 赵汝光, 王恩哥, 胡宗海 2014 物理学报 63 197301]

    [13]

    Chen L, Liu C C, Feng B J, He X Y, Cheng P, Ding Z J, Meng S, Yao Y G, Wu K H 2012 Phys. Rev. Lett. 109 056804

    [14]

    Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett. 107 076802

    [15]

    Cai Y, Chuu C P, Wei C M, Chou M Y 2013 Phys. Rev. B 88 245408

    [16]

    Kim Y, Choi K, Ihm J, Jin H 2014 Phys. Rev. B 89 085429

    [17]

    Yokoyama T 2014 New J. Phys. 16 085005

    [18]

    Rachel S, Ezawa M 2014 Phys. Rev. B 89 195303

    [19]

    Wang S K, Wang J, Chan K S 2014 New J. Phys. 16 045015

    [20]

    Liu C C, Jiang H, Yao Y G 2011 Phys. Rev. B 84 195430

    [21]

    Chiu H Y, Perefleinos V, Lin Y M, Avouris P 2010 Nano Lett. 10 4634

    [22]

    Woszczyna M, Friedemann M, Dziomba T, Weimann T, Ahlers F J 2011 Appl. Phys. Lett. 99 022112

    [23]

    Silvestrov P G, Efetov K B 2007 Phys. Rev. Lett. 98 016802

    [24]

    Nakaharai S, Williams J R, Marcus C M 2011 Phys. Rev. Lett. 107 036602

    [25]

    Cheianov V V, Fal’ko V, Altshuler B L 2007 Science 315 1252

    [26]

    Gómez S, Burset P, Herrera W J, Yeyati L A 2012 Phys. Rev. B 85 115411

    [27]

    Williams J R, Marcus C M 2011 Phys. Rev. Lett. 107 046602

    [28]

    Williams J R, DiCarlo L, Marcus C M 2007 Science 317 638

    [29]

    Cheianov V V, Falko V I 2006 Phys. Rev. B 74 041403

    [30]

    Yang M, Ran X J, Cui Y, Wang R Q 2012 J. Appl. Phys. 111 083708

计量
  • 文章访问数:  3082
  • PDF下载量:  482
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-11-10
  • 修回日期:  2014-12-19
  • 刊出日期:  2015-05-05

自旋轨道耦合作用下石墨烯pn结的电子输运性质

  • 1. 广东省量子调控工程与材料重点实验室, 华南师范大学物理与电信工程学院, 广州 510006
    基金项目: 

    国家自然科学基金(批准号: 11274124, 11474106)资助的课题.

摘要: 本文研究了自旋轨道耦合作用下石墨烯纳米带pn结的电子输运性质. 当粒子的入射能量处于pn结两端势能之间时, 粒子将会以隧穿的形式通过石墨烯pn结, 同时伴随着电子空穴转换. 电导随费米能的变化曲线呈不等高阶梯状, 并在费米能位于pn结两端能量中点时取得最大值. 随着石墨烯pn结长度的增加, 电导以指数形式衰减. 自旋轨道耦合作用导致的能隙会使电导显著减小, 而边缘态的粒子则可以几乎毫无阻碍地通过pn结. 本文用一个简单的子带隧穿模型解释了上述特征. 最后还研究了在pn转换区中掺入替位杂质的情况. 在弱杂质下, 电导随费米能变化的曲线将不再对称; 当杂质较强时, 仅边界态的形成的电导台阶能够保持.

English Abstract

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