Character of electronic states in graphene antidot lattices: Flat bands and spatial localization

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 4, 2009, Pages

  Vanević, Mihajlo ^a   Stojanović, Vladimir M ^b,c   Kindermann, Markus ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

^c UNIVERSITY OF BASEL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 69949170591     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.045410     Document Type: Article

References (71)

1. For a review, see A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). 10.1103/RevModPhys. 81.109
2. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004). 10.1126/science.1102896
3. S. Y. Zhou, G. H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D. H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, Nature Mater. 6, 770 (2007). 10.1038/nmat2003
4. X. Wu, X. Li, Z. Song, C. Berger, and W. A. de Heer, Phys. Rev. Lett. 98, 136801 (2007). 10.1103/PhysRevLett.98.136801
5. S. Y. Zhou, D. A. Siegel, A. V. Fedorov, F. ElGabaly, A. K. Schmid, A. H. Castro Neto, and A. Lanzara, Nature Mater. 7, 259 (2008). 10.1038/nmat2154b
6. J. Tworzydlo, B. Trauzettel, M. Titov, A. Rycerz, and C. W. J. Beenakker, Phys. Rev. Lett. 96, 246802 (2006). 10.1103/PhysRevLett.96.246802
7. N. M. R. Peres, A. H. Castro Neto, and F. Guinea, Phys. Rev. B 73, 195411 (2006). 10.1103/PhysRevB.73.195411
8. Y. W. Son, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 97, 216803 (2006) 10.1103/PhysRevLett.97.216803
9. M. Wimmer, I. Adagideli, S. Berber, D. Tománek, and K. Richter, Phys. Rev. Lett. 100, 177207 (2008). 10.1103/PhysRevLett.100.177207
10. V. V. Cheianov and V. I. Fal'ko, Phys. Rev. B 74, 041403 (R) (2006). 10.1103/PhysRevB.74.041403
11. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat. Phys. 2, 620 (2006). 10.1038/nphys384
12. E. H. Hwang, S. Adam, and S. Das Sarma, Phys. Rev. Lett. 98, 186806 (2007) 10.1103/PhysRevLett.98.186806
13. E. H. Hwang and S. Das Sarma, Phys. Rev. B 75, 205418 (2007). 10.1103/PhysRevB.75.205418
14. B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, Nat. Phys. 3, 192 (2007). 10.1038/nphys544
15. J. Milton Pereira, P. Vasilopoulos, and F. M. Peeters, Nano Lett. 7, 946 (2007). 10.1021/nl062967s
16. P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, Phys. Rev. B 76, 235404 (2007). 10.1103/PhysRevB.76.235404
17. T. Stauber, N. M. R. Peres, and A. H. Castro Neto, Phys. Rev. B 78, 085418 (2008). 10.1103/PhysRevB.78.085418
18. G. W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984) 10.1103/PhysRevLett.53. 2449
19. D. P. DiVincenzo and E. J. Mele, Phys. Rev. B 29, 1685 (1984). 10.1103/PhysRevB.29.1685
20. C. W. J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008). 10.1103/RevModPhys. 80.1337
21. N. Stander, B. Huard, and D. Goldhaber-Gordon, Phys. Rev. Lett. 102, 026807 (2009). 10.1103/PhysRevLett.102.026807
22. A. Rycerz, J. Tworzydlo, and C. W. J. Beenakker, Nat. Phys. 3, 172 (2007) 10.1038/nphys547
23. L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. W. Hill, K. S. Novoselov, and A. K. Geim, Science 320, 356 (2008) 10.1126/science.1154663
24. X. Du, I. Skachko, and E. Y. Andrei, Phys. Rev. B 77, 184507 (2008) 10.1103/PhysRevB.77.184507
25. V. Pereira and A. Castro Neto, arXiv:0810.4539 (unpublished).
26. X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo, and H. Dai, Phys. Rev. Lett. 100, 206803 (2008). 10.1103/PhysRevLett.100.206803
27. Y.-M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, Nano Lett. 9, 422 (2009). 10.1021/nl803316h
28. For a review, see P. Avouris, Z. Chen, and V. Perebeinos, Nat. Nanotechnol. 2, 605 (2007). 10.1038/nnano.2007.300
29. C. Berger, Science 312, 1191 (2006); 10.1126/science.1125925
30. M. D. Fischbein and M. Drndić, Appl. Phys. Lett. 93, 113107 (2008). 10.1063/1.2980518
31. F. Molitor, J. Güttinger, C. Stampfer, D. Graf, T. Ihn, and K. Ensslin, Phys. Rev. B 76, 245426 (2007). 10.1103/PhysRevB.76.245426
32. A. J. M. Giesbers, G. Rietveld, E. Houtzager, U. Zeitler, R. Yang, K. S. Novoselov, A. K. Geim, and J. C. Maan, Appl. Phys. Lett. 93, 222109 (2008). 10.1063/1.3043426
33. D.-K. Ki, D. Jeong, J.-H. Choi, H.-J. Lee, and K.-S. Park, Phys. Rev. B 78, 125409 (2008). 10.1103/PhysRevB.78.125409
34. A. K. Geim and K. S. Novoselov, Nature Mater. 6, 183 (2007). 10.1038/nmat1849
35. M. Y. Han, B. Ozyilmaz, Y. Zhang, and P. Kim, Phys. Rev. Lett. 98, 206805 (2007). 10.1103/PhysRevLett.98.206805
36. Y.-M. Lin, V. Perebeinos, Z. Chen, and P. Avouris, Phys. Rev. B 78, 161409 (R) (2008). 10.1103/PhysRevB.78.161409
37. C. Stampfer, J. Güttinger, S. Hellmüller, F. Molitor, K. Ensslin, and T. Ihn, Phys. Rev. Lett. 102, 056403 (2009). 10.1103/PhysRevLett. 102.056403
38. S. Russo, J. B. Oostinga, D. Wehenkel, H. B. Heersche, S. S. Sobhani, L. M. K. Vandersypen, and A. F. Morpurgo, Phys. Rev. B 77, 085413 (2008). 10.1103/PhysRevB.77.085413
39. T. G. Pedersen, C. Flindt, J. Pedersen, N. A. Mortensen, A.-P. Jauho, and K. Pedersen, Phys. Rev. Lett. 100, 136804 (2008). 10.1103/PhysRevLett.100. 136804
40. T. G. Pedersen, C. Flindt, J. Pedersen, A.-P. Jauho, N. A. Mortensen, and K. Pedersen, Phys. Rev. B 77, 245431 (2008). 10.1103/PhysRevB.77.245431
41. T. Shen, Y. Q. Wu, M. A. Capano, L. P. Rokhinson, L. W. Engel, and P. D. Ye, Appl. Phys. Lett. 93, 122102 (2008). 10.1063/1.2988725
42. J. Eroms and D. Weiss, arXiv:0901.0840 (unpublished).
43. O. V. Yazyev, Phys. Rev. Lett. 101, 037203 (2008). 10.1103/PhysRevLett. 101.037203
44. J. J. Palacios, J. Fernández-Rossier, and L. Brey, Phys. Rev. B 77, 195428 (2008) 10.1103/PhysRevB.77.195428
45. J. Fernández-Rossier and J. J. Palacios, Phys. Rev. Lett. 99, 177204 (2007). 10.1103/PhysRevLett.99.177204
46. S. Hikami, A. I. Larkin, and Y. Nagaoka, Prog. Theor. Phys. 63, 707 (1980) 10.1143/PTP.63.707
47. F. Pierre and N. O. Birge, Phys. Rev. Lett. 89, 206804 (2002). 10.1103/PhysRevLett.89.206804
48. E. H. Lieb, Phys. Rev. Lett. 62, 1201 (1989). 10.1103/PhysRevLett.62.1201
49. M. Inui, S. A. Trugman, and E. Abrahams, Phys. Rev. B 49, 3190 (1994). 10.1103/PhysRevB.49.3190
50. N. Shima and H. Aoki, Phys. Rev. Lett. 71, 4389 (1993). 10.1103/PhysRevLett.71.4389
51. S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejón, Phys. Rev. B 66, 035412 (2002). 10.1103/PhysRevB.66.035412
52. K. Hannewald, V. M. Stojanović, J. M. T. Schellekens, P. A. Bobbert, G. Kresse, and J. Hafner, Phys. Rev. B 69, 075211 (2004). 10.1103/PhysRevB.69.075211
53. G. Binnig and H. Rohrer, Rev. Mod. Phys. 71, S324 (1999). 10.1103/RevModPhys.71.S324
54. See, for example, G. Grosso and G. P. Parravicini, Solid State Physics (Academic, New York, 2003), p. 20.
55. P. Fazekas, Lecture Notes on Electron Correlation and Magnetism (World Scientific, New York, 1999).
56. M. Fujita, K. Wakabayashi, K. Nakada, and K. Kusakabe, J. Phys. Soc. Jpn. 65, 1920 (1996). 10.1143/JPSJ.65.1920
57. K. Nakada, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B 54, 17954 (1996). 10.1103/PhysRevB.54.17954
58. K. Kusakabe and M. Maruyama, Phys. Rev. B 67, 092406 (2003). 10.1103/PhysRevB.67.092406
59. Similar midgap states have recently been shown to lead to an order-of-magnitude increase in conductance in graphene; see S. Jafri, K. Carva, E. Widenkvist, T. Blom, B. Sanyal, J. Fransson, O. Eriksson, U. Jansson, H. Grennberg, O. Karis, R. Quinlan, B. Holloway, and K. Leifer, arXiv:0905.1346 (unpublished).
60. R. E. Peierls, Z. Phys. 80, 763 (1933). 10.1007/BF01342591
61. D. A. Bahamon, A. L. C. Pereira, and P. A. Schulz, Phys. Rev. B 79, 125414 (2009). 10.1103/PhysRevB.79.125414
62. This is, indeed, intuitively plausible from the point of view of the standard first-order Rayleigh-Schrödinger perturbation theory of a degenerate energy level; see, for example, L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Course of Theoretical Physics Vol. 3 (Pergamon, Oxford, 1991).
63. S. Nishino, M. Goda, and K. Kusakabe, J. Phys. Soc. Jpn. 72, 2015 (2003) 10.1143/JPSJ.72.2015
64. S. Miyahara, K. Kubo, H. Ono, Y. Shimomura, and N. Furukawa, J. Phys. Soc. Jpn. 74, 1918 (2005). 10.1143/JPSJ.74.1918
65. Z. Liu, K. Suenaga, P. J. F. Harris, and S. Iijima, Phys. Rev. Lett. 102, 015501 (2009). 10.1103/PhysRevLett.102.015501
66. H. A. Mizes and J. S. Foster, Science 244, 559 (1989). 10.1126/science.244.4904.559
67. P. Ruffieux, O. Gröning, P. Schwaller, L. Schlapbach, and P. Gröning, Phys. Rev. Lett. 84, 4910 (2000). 10.1103/PhysRevLett.84.4910
68. G. M. Rutter, J. N. Crain, N. P. Guisinger, T. Li, P. N. First, and J. A. Stroscio, Science 317, 219 (2007). 10.1126/science.1142882
69. Y. Kobayashi, K.-I. Fukui, T. Enoki, and K. Kusakabe, Phys. Rev. B 73, 125415 (2006). 10.1103/PhysRevB.73.125415
70. Y. Hasegawa and P. Avouris, Phys. Rev. Lett. 71, 1071 (1993). 10.1103/PhysRevLett.71.1071
71. P. Mallet, F. Varchon, C. Naud, L. Magaud, C. Berger, and J.-Y. Veuillen, Phys. Rev. B 76, 041403 (R) (2007). 10.1103/PhysRevB.76.041403