搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

具有p波超流的一维非公度晶格中迁移率边研究

刘通 高先龙

引用本文:
Citation:

具有p波超流的一维非公度晶格中迁移率边研究

刘通, 高先龙

Identifying the mobility edges in a one-dimensional incommensurate model with p-wave superfluid

Liu Tong, Gao Xian-Long
PDF
导出引用
  • 研究了具有p波超流的一维非公度晶格中迁移率边的性质. 发现适当的p波超流可以增加体系中的迁移率边的数目, 并且通过多分形分析确定了迁移率边所在的位置.
    The mobility edges which separate the localized energy eigenstates from the extended ones exist normally only in three dimensional systems. For one-dimensional systems with random on-site potentials, one never encounters mobility edges, where all the eigenstates are localized. However, there are two kinds of 1D systems such as correlated disordered models, and the systems of exponentially decaying hopping kinetics, features of mobility edges at some specific values become possible. We study in this paper the properties of the mobility edges in a one-dimensional p-wave superfluid on an incommensurate lattice with exponentially decaying hopping kinetics. Without the p-wave superluid, the system displays a single mobility edge, which separates the extended regime from the localized one at a certain energy. Without the exponentially decaying hopping term, the system displays a phase transition from a topological superconductor to an Anderson localization at a certain disorder strength, where no mobility edge exists. We are interested in the influence of the p-wave superfluid on the mobility edge. By solving the Bogoliubov-de Gennes equation, the eigenvalues and the eigenfunctions are obtained. In order to identify the extending or the localized properties of the eigenvectors, we define an inverse participation ratio IPR. For an extended state, IPRn~1/L which goes to zero at a large L, and for a localized one, IPRn being constant. Therefore, the IPR can be taken as a criterion to distinguish the extended state from the localized one, while the mobility edge is defined as the boundary between two different states. We find that, with a p-wave superfluid, the system changes from a single mobility edge to a multiple one, and the number of mobility edges increases with the increased superfluid pairing order parameter. To further obtain the energy or the location of the mobility edge, we investigate the scaling behavior of wave functions by using a multifractal analysis, which is calculated through the scaling index . The minimum value of the index, with the values min= 1, 0min1, and min= 0, mean the extended, critical, and localized states, respectively. For the two consecutive states, the minima of the scaling index min when extrapolating to the large size limit between 0 and 1 signal the mobility edge. By exploring the corresponding Bogoliubov quasi-particle wave functions for the system under open boundary conditions together with the multifractal analysis for the system under periodic boundary conditions, we identify two mobility edges for the system of the p-wave superfluid pairing. Furthermore, we will investigate how the existence of the mobility edges influences the p-wave superfluid, and identify the phase diagram at the given parameters. We will in the future try to understand the relationship between the topological superfluid and the mobility edges.
      通信作者: 高先龙, gaoxl@zjnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11374266)、新世纪优秀人才支持计划和浙江省自然科学基金(批准号: Z15A050001)资助的课题.
      Corresponding author: Gao Xian-Long, gaoxl@zjnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11374266), the Program for New Century Excellent Talents in University, and the Natural Science Foundation of Zhejiang Province, China (Grant No. Z15A050001).
    [1]

    Anderson P W 1958 Phys. Rev. 109 1492

    [2]

    Billy J, Josse V, Zuo Z, Bernard A, Hambrecht B, Lugan P, Clment D, Sanchez-Palencia L, Bouyer P, Aspect A 2008 Nature 453 891

    [3]

    Roati G, D' Errico C, Fallani L, Fattori M, Fort C, Zaccanti M, Modugno G, Modugno M, Inguscio M 2008 Nature 453 895

    [4]

    Aubry S, Andr G {1980 Ann. Isr. Phys. Soc. 3 18

    [5]

    Mott N 1987 J. Phys. C: Solid Stat. Phys. 20 3075

    [6]

    Hiramoto H, Kohmoto M 1989 Phys. Rev. B 40 8225

    [7]

    Zhou P Q, Fu X J, Guo Z Z, Liu Y Y 1995 Solid State Commun. 96 373

    [8]

    Ganeshan S, Pixley J H, Sarma S D 2015 Phys. Rev. Lett. 114 146601

    [9]

    Biddle J, Sarma S D 2010 Phys. Rev. Lett. 104 070601

    [10]

    Ivanov D A 2001 Phys. Rev. Lett. 86 268

    [11]

    Beenakker C W J 2013 Annu. Rev. Condens. Matter Phys. 4 113

    [12]

    Kitaev A Y 2001 Phys. Usp. 44 131

    [13]

    Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045

    [14]

    Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057

    [15]

    Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887

    [16]

    Motrunich O, Damle K, Huse D A 2001 Phys. Rev. B 63 224204

    [17]

    Brouwer P W, Furusaki A, Gruzberg I A, Mudry C 2000 Phys. Rev. Lett. 85 1064

    [18]

    Gruzberg I A, Read N, Vishveshwara S 2005 Phys. Rev. B 71 245124

    [19]

    Lobos A M, Lutchyn R M, Sarma S D 2012 Phys. Rev. Lett. 109 146403

    [20]

    Cai X M, Lang L J, Chen S, Wang Y P 2013 Phys. Rev. Lett. 110 176403

    [21]

    Ingold G L, Wobst A, Aulbach C, Hnggi P 2002 Eur. Phys. J. B 30 175

    [22]

    Thouless D J 1974 Phys. Rep. 13 93

    [23]

    Wang J, Liu X J, Gao X L, Hu H {2015 Phys. Rev. B 93 104504

    [24]

    Hiramoto H, Kohmoto M 1992 Int. J. Mod. Phys. B 06 281

    [25]

    Kohmoto M, Kadanoff L P, Tang C 1983 Phys. Rev. Lett. 50 1870

    [26]

    Ostlund S, Pandit R, Rand D, Schellnhuber H J, Siggia E D 1983 Phys. Rev. Lett. 50 1873

    [27]

    Kohmoto M 1983 Phys. Rev. Lett. 51 1198

    [28]

    Thouless D J 1983 Phys. Rev. B 28 4272

    [29]

    Kohmoto M, Tobe D 2008 Phys. Rev. B 77 134204

  • [1]

    Anderson P W 1958 Phys. Rev. 109 1492

    [2]

    Billy J, Josse V, Zuo Z, Bernard A, Hambrecht B, Lugan P, Clment D, Sanchez-Palencia L, Bouyer P, Aspect A 2008 Nature 453 891

    [3]

    Roati G, D' Errico C, Fallani L, Fattori M, Fort C, Zaccanti M, Modugno G, Modugno M, Inguscio M 2008 Nature 453 895

    [4]

    Aubry S, Andr G {1980 Ann. Isr. Phys. Soc. 3 18

    [5]

    Mott N 1987 J. Phys. C: Solid Stat. Phys. 20 3075

    [6]

    Hiramoto H, Kohmoto M 1989 Phys. Rev. B 40 8225

    [7]

    Zhou P Q, Fu X J, Guo Z Z, Liu Y Y 1995 Solid State Commun. 96 373

    [8]

    Ganeshan S, Pixley J H, Sarma S D 2015 Phys. Rev. Lett. 114 146601

    [9]

    Biddle J, Sarma S D 2010 Phys. Rev. Lett. 104 070601

    [10]

    Ivanov D A 2001 Phys. Rev. Lett. 86 268

    [11]

    Beenakker C W J 2013 Annu. Rev. Condens. Matter Phys. 4 113

    [12]

    Kitaev A Y 2001 Phys. Usp. 44 131

    [13]

    Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045

    [14]

    Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057

    [15]

    Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887

    [16]

    Motrunich O, Damle K, Huse D A 2001 Phys. Rev. B 63 224204

    [17]

    Brouwer P W, Furusaki A, Gruzberg I A, Mudry C 2000 Phys. Rev. Lett. 85 1064

    [18]

    Gruzberg I A, Read N, Vishveshwara S 2005 Phys. Rev. B 71 245124

    [19]

    Lobos A M, Lutchyn R M, Sarma S D 2012 Phys. Rev. Lett. 109 146403

    [20]

    Cai X M, Lang L J, Chen S, Wang Y P 2013 Phys. Rev. Lett. 110 176403

    [21]

    Ingold G L, Wobst A, Aulbach C, Hnggi P 2002 Eur. Phys. J. B 30 175

    [22]

    Thouless D J 1974 Phys. Rep. 13 93

    [23]

    Wang J, Liu X J, Gao X L, Hu H {2015 Phys. Rev. B 93 104504

    [24]

    Hiramoto H, Kohmoto M 1992 Int. J. Mod. Phys. B 06 281

    [25]

    Kohmoto M, Kadanoff L P, Tang C 1983 Phys. Rev. Lett. 50 1870

    [26]

    Ostlund S, Pandit R, Rand D, Schellnhuber H J, Siggia E D 1983 Phys. Rev. Lett. 50 1873

    [27]

    Kohmoto M 1983 Phys. Rev. Lett. 51 1198

    [28]

    Thouless D J 1983 Phys. Rev. B 28 4272

    [29]

    Kohmoto M, Tobe D 2008 Phys. Rev. B 77 134204

  • [1] 陆展鹏, 徐志浩. 具有平带的一维十字型晶格中重返局域化现象. 物理学报, 2024, 73(3): 037202. doi: 10.7498/aps.73.20231393
    [2] 吴瑾, 陆展鹏, 徐志浩, 郭利平. 由超辐射引起的迁移率边和重返局域化. 物理学报, 2022, 71(11): 113702. doi: 10.7498/aps.71.20212246
    [3] 徐志浩, 皇甫宏丽, 张云波. 一维准周期晶格中玻色子对的迁移率边. 物理学报, 2019, 68(8): 087201. doi: 10.7498/aps.68.20182218
    [4] 郭海君, 段宝兴, 袁嵩, 谢慎隆, 杨银堂. 具有部分本征GaN帽层新型AlGaN/GaN高电子迁移率晶体管特性分析. 物理学报, 2017, 66(16): 167301. doi: 10.7498/aps.66.167301
    [5] 张力, 林志宇, 罗俊, 王树龙, 张进成, 郝跃, 戴扬, 陈大正, 郭立新. 具有p-GaN岛状埋层耐压结构的横向AlGaN/GaN高电子迁移率晶体管. 物理学报, 2017, 66(24): 247302. doi: 10.7498/aps.66.247302
    [6] 安霞, 黄如, 李志强, 云全新, 林猛, 郭岳, 刘朋强, 黎明, 张兴. 高迁移率Ge沟道器件研究进展. 物理学报, 2015, 64(20): 208501. doi: 10.7498/aps.64.208501
    [7] 刘亚文, 陈亦望, 徐鑫, 刘宗信. 基于辅助差分方程的完全匹配层在时域多分辨率分析算法中的应用与性能分析. 物理学报, 2013, 62(3): 034101. doi: 10.7498/aps.62.034101
    [8] 张立超, 侯蓝田, 周桂耀. 八边形光子晶体光纤色散补偿特性分析. 物理学报, 2011, 60(5): 054217. doi: 10.7498/aps.60.054217
    [9] 罗世华, 曾九孙. 基于多分辨分析的高炉铁水含硅量波动多重分形辨识. 物理学报, 2009, 58(1): 150-157. doi: 10.7498/aps.58.150
    [10] 魏 巍, 郝 跃, 冯 倩, 张进城, 张金凤. AlGaN/GaN场板结构高电子迁移率晶体管的场板尺寸优化分析. 物理学报, 2008, 57(4): 2456-2461. doi: 10.7498/aps.57.2456
    [11] 李 潇, 张海英, 尹军舰, 刘 亮, 徐静波, 黎 明, 叶甜春, 龚 敏. 磷化铟复合沟道高电子迁移率晶体管击穿特性研究. 物理学报, 2007, 56(7): 4117-4121. doi: 10.7498/aps.56.4117
    [12] 代月花, 陈军宁, 柯导明, 孙家讹, 胡 媛. 纳米MOSFET迁移率解析模型. 物理学报, 2006, 55(11): 6090-6094. doi: 10.7498/aps.55.6090
    [13] 李志锋, 陆 卫, 叶红娟, 袁先璋, 沈学础, G.Li, S.J.Chua. GaN载流子浓度和迁移率的光谱研究. 物理学报, 2000, 49(8): 1614-1619. doi: 10.7498/aps.49.1614
    [14] 吕永良, 周世平, 徐得名. 光照下高电子迁移率晶体管特性分析. 物理学报, 2000, 49(7): 1394-1399. doi: 10.7498/aps.49.1394
    [15] 沈文忠, 唐文国, 沈学础, A.Dimoulas. δ掺杂的赝形高电子迁移率晶体管AlGaAs/InGaAs/GaAs结构的光谱研究. 物理学报, 1995, 44(5): 779-787. doi: 10.7498/aps.44.779
    [16] 沈文忠, 唐文国, 沈学础, A.Dimonlas. δ掺杂的赝形高电子迁移率晶体管AIGaAs/InGaAs/GaAs结构中的费密边奇异性研究. 物理学报, 1995, 44(5): 825-831. doi: 10.7498/aps.44.825
    [17] 王传奎, 孙金祚, 王继锁, 王文正. 一维无公度系统Aubry模型的迁移率边. 物理学报, 1993, 42(1): 95-100. doi: 10.7498/aps.42.95
    [18] 刘有延, 周义昌. 一维无公度势系统的迁移率边. 物理学报, 1988, 37(11): 1807-1813. doi: 10.7498/aps.37.1807
    [19] 郑兆勃, 朱凯. 一维无公度体系的电子谱和迁移率边. 物理学报, 1987, 36(5): 623-629. doi: 10.7498/aps.36.623
    [20] 周炳林, 陈正秀. 关于GaAs的低迁移率问题. 物理学报, 1985, 34(4): 537-541. doi: 10.7498/aps.34.537
计量
  • 文章访问数:  4586
  • PDF下载量:  179
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-01-22
  • 修回日期:  2016-03-28
  • 刊出日期:  2016-06-05

/

返回文章
返回