Localization behavior of Dirac particles in disordered graphene superlattices

Physical Review B - Condensed Matter and Materials Physics

Volumn 85, Issue 10, 2012, Pages

  Zhao, Qifang ^a   Gong, Jiangbin ^a   Müller, Cord A ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84858054345     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.85.104201     Document Type: Article

References (75)

1. J. C. Slonczewski and P. R. Weiss, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.272 109, 272 (1958).
2. G. W. Semenoff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53. 2449 53, 2449 (1984).
3. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 61.2015 61, 2015 (1988).
4. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.109 81, 109 (2009).
5. V. P. Gusynin and S. G. Sharapov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.125124 71, 125124 (2005). (Pubitemid 40777624)
6. M. S. Purewal, Y. Zhang, and P. Kim, Phys. Status Solidi B PSSBBD 0370-1972 10.1002/pssb.200669193 243, 3418 (2006). (Pubitemid 44787265)
7. O. Klein, Z. Phys. EPJAFV 1434-6001 10.1007/BF01339716 53, 157 (1929).
8. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat. Phys. 1745-2473 10.1038/nphys384 2, 620 (2006). (Pubitemid 44328348)
9. J. Schliemann, D. Loss, and R. M. Westervelt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.206801 94, 206801 (2005); (Pubitemid 41481102)
10. W. Zawadzki, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.085217 72, 085217 (2005); (Pubitemid 43406081)
11. R. Winkler, U. Zulicke, and J. Bolte, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.205314 75, 205314 (2007).
12. G. Juzeliunas, J. Ruseckas, M. Lindberg, L. Santos, and P. Ahberg, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.011802 77, 011802 (2008). (Pubitemid 351178661)
13. K. L. Lee, B. Grémaud, R. Han, B.-G. Englert, and C. Miniatura, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.043411 80, 043411 (2009).
14. Q. Zhang, J. B. Gong, and C. H. Oh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.023608 81, 023608 (2010).
15. E. Alba, X. Fernandez-Gonzalvo, J. Mur-Petit, J. J. Garcia-Ripoll, and J. K. Pachos, e-print arXiv: 1107.3673v1 (2011).
16. S. E. Savel'ev and A. S. Alexandrov, Phys. Rev. B 1098-0121 10.1103/PhysRevB.84.035428 84, 035428 (2011).
17. L. Lamata, J. Casanova, R. Gerritsma, C. F. Roos, J. J. García-Ripoll, and E. Solano, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/13/9/095003 13, 095003 (2011).
18. W. Zawadzki and T. M. Rusin, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/23/14/143201 23, 143201 (2011).
19. R. G. Unanyan, J. Otterbach, M. Fleischhauer, J. Ruseckas, V. Kudriasov, and G. Juzeliunas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105. 173603 105, 173603 (2010).
20. P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.1492 109, 1492 (1958).
21. B. Kramer and A. MacKinnon, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/56/12/001 56, 1469 (1993).
22. C. Bai and X. Zhang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76. 075430 76, 075430 (2007).
23. C.-H. Park, L. Yang, Y.-W. Son, M. Cohen, and S. G. Louie, Nat. Phys. 1745-2473 10.1038/nphys890 4, 213 (2008).
24. M. Barbier, F. M. Peeters, P. Vasilopoulos, and J. M. Pereira, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.115446 77, 115446 (2008).
25. C.-H. Park, Y.-W. Son, L. Yang, M. L. Cohen, and S. G. Louie, Nano Lett. NALEFD 1530-6984 10.1021/nl801752r 8, 2920 (2008).
26. J. H. Ho, Y. H. Chiu, S. J. Tsai, and M. F. Lin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.115427 79, 115427 (2009).
27. L. Brey and H. A. Fertig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.046809 103, 046809 (2009).
28. M. Barbier, P. Vasilopoulos, and F. M. Peeters, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.075438 81, 075438 (2010).
29. L.-G. Wang and S.-Y. Zhu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.205444 81, 205444 (2010).
30. C.-H. Park, L. Z. Tan, and S. G. Louie, Physica E PELNFM 1386-9477 10.1016/j.physe.2010.07.022 43, 651 (2011).
31. M. RamezaniMasir, P. Vasilopoulos, A. Matulis, and F. M. Peeters, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.235443 77, 235443 (2008).
32. M. Ramezani Masir, P. Vasilopoulos, and F. M. Peeters, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.035409 79, 035409 (2009).
33. S. Ghosh and M. Sharma, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/21/29/292204 21, 292204 (2009).
34. L. Dell'Anna and A. De Martino, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.045420 79, 045420 (2009).
35. Q.-S. Wu, S.-N. Zhang, and S.-J. Yang, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/20/48/485210 20, 485210 (2008).
36. I. Snyman, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.054303 80, 054303 (2009).
37. L. Z. Tan, C.-H. Park, and S. G. Louie, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.195426 81, 195426 (2010).
38. S. Gattenlöhner, W. Belzig, and M. Titov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.155417 82, 155417 (2010).
39. A. Isacsson, L. M. Jonsson, J. M. Kinaret, and M. Jonson, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.035423 77, 035423 (2008).
40. F. Guinea, M. I. Katsnelson, and M. A. H. Vozmediano, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.075422 77, 075422 (2008).
41. T. O. Wehling, A. V. Balatsky, M. I. Katsnelson, and A. I. Lichtenstein, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/84/17003 84, 17003 (2008).
42. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science SCIEAS 0036-8075 10.1126/science.1102896 306, 666 (2004). (Pubitemid 39440910)
43. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature (London) NATUAS 0028-0836 10.1038/nature04233 438, 197 (2005). (Pubitemid 41599867)
44. Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature (London) NATUAS 0028-0836 10.1038/nature04235 438, 201 (2005). (Pubitemid 41599868)
45. J. C. Meyer, C. O. Girit, and M. F. Crommie, A. Zettl, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2901147 92, 123110 (2008). (Pubitemid 351451677)
46. S. Marchini, S. Günther, and J. Wintterlin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.075429 76, 075429 (2007).
47. A. L. Vazquez de Parga, F. Calleja, B. Borca, M. C. G. Passeggi, J. J. Hinarejos, F. Guinea, and R. Miranda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.056807 100, 056807 (2008). (Pubitemid 351230698)
48. P. W. Sutter, J.-I. Flege, and E. A. Sutter, Nat. Mater. 1476-1122 10.1038/nmat2166 7, 406 (2008). (Pubitemid 351585230)
49. D. Martoccia, P. R. Willmott, T. Brugger, M. Björck, S. Günther, C. M. Schlepütz, A. Cervellino, S. A. Pauli, B. D. Patterson, S. Marchini, J. Wintterlin, W. Moritz, and T. Greber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.126102 101, 126102 (2008).
50. J. Coraux, A. T. N'Diaye, C. Busse, and T. Michely, Nano Lett. NALEFD 1530-6984 10.1021/nl0728874 8, 565 (2008). (Pubitemid 351346018)
51. A. T. N'Diaye 1, J. Coraux, T. N. Plasa, C. Busse, and T. Michely, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/4/043033 10, 043033 (2008).
52. I. Pletikosić, M. Kralj, P. Pervan, R. Brako, J. Coraux, A. T. N'Diaye, C. Busse, and T. Michely, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.056808 102, 056808 (2009).
53. A. Avsar, Nano Lett. NALEFD 1530-6984 10.1021/nl200714q 11, 2363 (2011).
54. W. G. Cullen, M. Yamamoto, K. M. Burson, J. H. Chen, C. Jang, L. Li, M. S. Fuhrer, and E. D. Williams, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.215504 105, 215504 (2010).
55. A. De Martino, L. Dell'Anna, and R. Egger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.066802 98, 066802 (2007). (Pubitemid 46220747)
56. L. Dell'Anna and A. De Martino, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.155449 83, 155449 (2011).
57. V. M. Pereira and A. H. Castro Neto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.046801 103, 046801 (2009).
58. M. R. Masir, P. Vasilopoulos, and F. M. Peeters, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/11/9/095009 11, 095009 (2009).
59. S.-L. Zhu, D.-W. Zhang, and Z. D. Wang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.210403 102, 210403 (2009).
60. Y. P. Bliokh, V. Freilikher, S. Savel'ev, and F. Nori, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.075123 79, 075123 (2009).
61. P. Marko and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, Princeton and Oxford, 2008), Chap. 1-4.
62. C. A. Müller and D. Delande, in Disorder and interference: localization phenomena, edited by, C. Miniatura, L.-C. Kwek, M. Ducloy, B. Grémaud, B.-G. Englert, L. Cugliandolo, A. Ekert, and, K. K. Phua, Proceedings of the Les Houches Summer School of Theoretical Physics, XCI, 2009 (Oxford University Press, Oxford, 2011).
63. A. Galindo and P. Pascual, Quantum Mechanics I (Springer, Berlin, 1990).
64. H. Furstenberg and H. Kesten, Ann. Math. Statist. AASTAD 0003-4851 10.1214/aoms/1177705909 31, 457 (1960);
65. H. Furstenberg, Trans. Amer. Math. Soc. TAMTAM 0002-9947 10.1090/S0002-9947-1963-0163345-0 108, 377 (1963).
66. A. A. Abrikosov, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(81)91203-5 37, 997 (1981). (Pubitemid 11506436)
67. M. V. Berry and S. Klein, Eur. J. Phys. EJPHD4 0143-0807 10.1088/0143-0807/18/3/017 18, 222 (1997).
68. B. Derrida, K. Mecheri, and J. Pichard, J. Phys. (France) JPRAAJ 0368-3842 10.1051/jphys:01987004805073300 48, 733 (1987).
69. B. Derrida and E. Gardner, J. Phys. (France) JPRAAJ 0368-3842 10.1051/jphys:019840045080128300 45, 1283 (1984).
70. F. M. Izrailev, S. Ruffo, and L. Tessieri, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/31/23/008 31, 5263 (1998). (Pubitemid 128083112)
71. M. Barbier, P. Vasilopoulos, and F. M. Peeters, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.205415 80, 205415 (2009).
72. F. M. Izrailev, A. A. Krokhin, and S. E. Ulloa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.63.041102 63, 041102 (2001).
73. A. Krokhin, F. M. Izrailev, U. Kuhl, H.-J. Stöckmann, and S. E. Ulloa, Physica E PELNFM 1386-9477 10.1016/S1386-9477(02)00261-8 13, 695 (2002). (Pubitemid 34648798)
74. P. Lugan, A. Aspect, L. Sanchez-Palencia, D. Delande, B. Grémaud, C. A. Müller, and C. Miniatura, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.023605 80, 023605 (2009).
75. A. Zhang, Z. Dai, L. Shi, Y. P. Feng, and C. Zhang, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3511782 133, 224705 (2010).