Evaluation of the Green's function of disordered graphene

Physical Review B - Condensed Matter and Materials Physics

Volumn 82, Issue 15, 2010, Pages

  Zhu, W ^a,b   Shi, Q W ^a,b   Wang, X R ^b,c   Wang, X P ^a   Yang, J L ^a   Chen, J ^d,e   Hou, J G ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c SHANDONG UNIVERSITY   (China)

^d UNIVERSITY OF ALBERTA   (Canada)

^e NATIONAL RESEARCH COUNCIL CANADA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78149272879     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.82.153405     Document Type: Article

References (48)

1. K. S. Novoselov, Science 306, 666 (2004). 10.1126/science.1102896
2. Y. Zhang, Nature (London) 438, 201 (2005). 10.1038/nature04235
3. A. K. Geim, Nature Mater. 6, 183 (2007). 10.1038/nmat1849
4. A. H. Castro Neto, Rev. Mod. Phys. 81, 109 (2009). 10.1103/RevModPhys.81. 109
5. S. Das Sarma, S. Adam, E. Hwang, and E. Rossi, arXiv:1003.4731 (unpublished).
6. Z. F. Wang, R. Xiang, Q. W. Shi, J. Yang, X. Wang, J. G. Hou, and J. Chen, Phys. Rev. B 74, 125417 (2006). 10.1103/PhysRevB.74.125417
7. Y. Y. Zhang, J. Hu, B. A. Bernevig, X. R. Wang, X. C. Xie, and W. M. Liu, Phys. Rev. Lett. 102, 106401 (2009) 10.1103/PhysRevLett.102.106401
8. Y. Zhang, J. P. Hu, B. A. Bernevig, X. R. Wang, X. C. Xie, and W. M. Liu, Phys. Rev. B 78, 155413 (2008). 10.1103/PhysRevB.78.155413
9. E. N. Economou, Green's Functions in Quantum Physics (Springer, New York, 2006).
10. E. H. Hwang and S. Das Sarma, Phys. Rev. B 77, 195412 (2008). 10.1103/PhysRevB.77.195412
11. M. I. Katsnelson, Philos. Trans. R. Soc. London, Ser. A 366, 195 (2008). 10.1098/rsta.2007.2157
12. P. A. Lee, Rev. Mod. Phys. 57, 287 (1985). 10.1103/RevModPhys.57.287
13. X. R. Wang, Phys. Rev. B 51, 9310 (1995) 10.1103/PhysRevB.51.9310
14. X. R. Wang, Phys. Rev. B 53, 12035 (1996). 10.1103/PhysRevB.53.12035
15. M. C. W. van Rossum, Rev. Mod. Phys. 71, 313 (1999). 10.1103/RevModPhys. 71.313
16. M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Phys. Rev. Lett. 66, 3132 (1991). 10.1103/PhysRevLett.66.3132
17. T. Ando, J. Phys. Soc. Jpn. 75, 074716 (2006) 10.1143/JPSJ.75.074716
18. N. H. Shon and T. Ando, J. Phys. Soc. Jpn. 67, 2421 (1998). 10.1143/JPSJ.67.2421
19. S. Wu, L. Jing, Q. Li, Q. W. Shi, J. Chen, H. Su, X. Wang, and J. Yang, Phys. Rev. B 77, 195411 (2008) 10.1103/PhysRevB.77.195411
20. V. M. Pereira, F. Guinea, J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, Phys. Rev. Lett. 96, 036801 (2006) 10.1103/PhysRevLett.96. 036801
21. B. L. Huang,, EPL 88, 68005 (2009) 10.1209/0295-5075/88/68005
22. and N. M. R. Peres, F. Guinea, and A. H. Castro Neto, Phys. Rev. B 73, 125411 (2006). 10.1103/PhysRevB.73.125411
23. Resonant states will lead to some new physical features, which needs further study.
24. Other uncorrelated short-range impurity potential (such as Anderson disorder) produces similar results.
25. J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Problem (Birkhäuser, Boston, 1985).
26. E. Dagotto, Rev. Mod. Phys. 66, 763 (1994) 10.1103/RevModPhys.66.763
27. L. C. Davis, Phys. Rev. B 28, 6961 (1983) 10.1103/PhysRevB.28.6961
28. B. Bäuml, G. Wellein, and H. Fehske, Phys. Rev. B 58, 3663 (1998) 10.1103/PhysRevB.58.3663
29. S. M. Anlage and D. L. Smith, Phys. Rev. B 34, 2336 (1986). 10.1103/PhysRevB.34.2336
30. A small artificial cut-off energy η is used to simulate the infinitesimal imaginary energy in Green's function. We chose η ∼ 0.01 meV in this Brief Report, which is much less than the energy resolution in recent angle-resolved photoemission spectroscopy experiments (Ref.).
31. It has been checked that the averaged Green's functions do not change when the sample size is doubled to 4800 × 4800 or reduced to 1200 × 1200.
32. A. Altland and B. Simons, Condensed Matter Field Theory (Cambridge University Press, Cambridge, 2006).
33. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B 74, 235443 (2006). 10.1103/PhysRevB.74.235443
34. T. Fukuzawa, J. Phys. Soc. Jpn. 78, 094714 (2009). 10.1143/JPSJ.78.094714
35. I. L. Aleiner and K. B. Efetov, Phys. Rev. Lett. 97, 236801 (2006) 10.1103/PhysRevLett.97.236801
36. it is found that SCBA neglects most terms of equal order in perturbation theory.
37. M. Calandra and F. Mauri, Phys. Rev. B 76, 205411 (2007). 10.1103/PhysRevB.76.205411
38. K. Nomura and A. H. MacDonald, Phys. Rev. Lett. 96, 256602 (2006) 10.1103/PhysRevLett.96.256602
39. K. Nomura and A. H. MacDonald, Phys. Rev. Lett. 98, 076602 (2007). 10.1103/PhysRevLett.98.076602
40. G. D. Mahan, Many-Particle Physics, 3rd ed. (Kluwer Academic, New York, 2000).
41. K. Tarafder, A. Chakrabarti, K. K. Saha, and A. Mookerjee, Phys. Rev. B 74, 144204 (2006). 10.1103/PhysRevB.74.144204
42. C. H. Park, F. Giustino, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 99, 086804 (2007). 10.1103/PhysRevLett.99.086804
43. L.-W. Wang, L. Bellaiche, S.-H. Wei, and A. Zunger, Phys. Rev. Lett. 80, 4725 (1998) 10.1103/PhysRevLett.80.4725
44. Y. Zhang, A. Mascarenhas, and L.-W. Wang, Phys. Rev. Lett. 101, 036403 (2008). 10.1103/PhysRevLett.101.036403
45. E. A. Henriksen, P. Cadden-Zimansky, Z. Jiang, Z. Q. Li, L.-C. Tung, M. E. Schwartz, M. Takita, Y.-J. Wang, P. Kim, and H. L. Stormer, Phys. Rev. Lett. 104, 067404 (2010) 10.1103/PhysRevLett.104.067404
46. for details please see our interpretation to this cyclotron resonance experiment (Ref.).
47. A. Damascelli, Rev. Mod. Phys. 75, 473 (2003). 10.1103/RevModPhys.75.473
48. W. Zhu, Q. W. Shi, J. G. Hou, and X. R. Wang, Phys. Rev. Lett. 105, 159703 (2010). 10.1103/PhysRevLett.105.159703