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本文利用一种新的数值方法研究了在较大的双层石墨烯样品中杂质的无序 效应对超导态特性的影响. 采用核多项式方法 (Kernel Polynomial Method) 来自洽求解双层石墨烯系统的Bogoliubov-de-Gennes (BdG) 方程, 从而得到了由无序效应所引起的超导序参量的空间涨落精确解. 进一步, 计算了系统处于超导态时的态密度、光电导和广义逆参与率 (inverse participation ratio) 等物理量, 并发现随着无序强度的不断增大态密度中的能隙被 完全抑制, 同时光电导的Drude权重也迅速减小并最终降为零, 这表明双层石墨烯中的低能电子态发生了安德森局域化, 系统因而发生了由无序效应诱导的超导-绝缘体相变.The kernel polynomial method is employed to study the disorder effects of impurities on the superconductivity of double-layer graphene. The Bogoliubov-de-Gennes equations are solved self-consistently by the kernel polynomial method, and the spatial fluctuations of the superconducting order parameters caused by disorder are obtained. Furthermore, we calculate the density of states, the optical conductivity and the general inverse participation ratio, and we find that the energy gap in the density of states can be constrained by increasing disorder, accompanied with the disappearance of the Drude weight in optical conductivity. We also find that the electron states are Anderson localized by disorder and the superconductor-insulator transition happens in double-layer graphene.
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Keywords:
- double-layer graphene /
- anderson localization /
- superconductor-insulator transition /
- kernel polynomial method
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[1] McChesney J L, Bostwick A, Ohta T, Seyller T, Horn K, González J, Rotenberg E 2010 Phys. Rev. Lett. 104 136803
[2] Heersche H B, Jarillo Herrero P, Oostinga J B, Vandersypen L M K, Morpurgo A 2007 Nature 446 56
[3] Castro E V, Novoselov K S, Morozov S V, Peres N M R, dos Santos J M B, Lopes N J Guinea F, Geim A K, Castro Neto A H 2007 Phys. Rev. Lett. 99 216802
[4] Zhang Y, Tang T T, Girit C, Hao Z, Martin M C, Zettl A, Crommie M F, Shen Y R, Wang F 2009 Nature 459 820
[5] Wang T, Guo Q, Liu Y, Sheng K 2012 Chin. Phys. B 21 67301
[6] Wang Z G, Zhang P, Li S S, Fu Z G 2011 Chin. Phys. B 20 058103
[7] Wang J J, Wang F, Yuan P F, Sun Q, Jia Y 2012 Acta Phys. Sin. 61 106801 (in Chinese) [王建军, 王飞, 原鹏飞, 孙强, 贾瑜 2012 61 106801]
[8] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[9] Anderson P W 1958 Phys. Rev. 109 1492
[10] Weiβe A, Wellein G, Alvermann A, Fehske H 2006 Rev. Mod. Phys. 78 275
[11] Castro E V, Novoselov K S, Morozov S V, Peres N M R, Lopes dos Santos J M B, Nilsson J, Guinea F, Geim A K, Castro Neto A H 2010 J. Phys: Condens. Matter 22 175503
[12] Ghosal A, Randeria M, Trivedi N 1998 Phys. Rev. Lett. 81 3940
[13] Ghosal A, Randeria M, Trivedi N 2000 Phys. Rev. B 65 014501
[14] Covaci L, Peeters F M, Berciu M 2010 Phys. Rev. Lett. 105 167006
[15] Nagai Y, Ota Y, Machida M 2012 J. Phys. Soc. Jpn. 81 024710
[16] Weiβe A 2004 Eur. Phys. J. B 40 125
[17] Partoens B, Peeters F M 2006 Phys. Rev. B 74 075404
[18] Sacépé B, Dubouchet T, Chapelier C, Sanquer M, Ovadia M, Shahar D, Feigel'man, Loffe L 2011 Nature Phys. 7 239
[19] Dubi Y, Meir Y, Avishai Y 2007 Nature 449 876
[20] Song Y, Song H K, Feng S P 2011 J. Phys.: Condens. Matter 23 205501
[21] Song Y, Wortis R, Atkinson W A 2008 Phys. Rev. B 77 054202
[22] Murphy N C, Wortis R, Atkinson W A 2011 Phys. Rev. B 83 184206
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