Dirac boundary condition at the reconstructed zigzag edge of graphene

Physical Review B - Condensed Matter and Materials Physics

Volumn 84, Issue 19, 2011, Pages

  Van Ostaay, J A M ^a   Akhmerov, A R ^a   Beenakker, C W J ^a   Wimmer, M ^a  

^a UNIVERSITEIT LEIDEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 82655166466     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.84.195434     Document Type: Article

References (36)

1. 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).
2. L. Brey and H. A. Fertig, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.73.235411 73, 235411 (2006). (Pubitemid 44943452)
3. M. Fujita, K. Wakabayashi, K. Nakada, and K. Kusakabe, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.65.1920 65, 1920 (1996).
4. K. Nakada, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.54.17954 54, 17954 (1996).
5. Y.-W. Son, M. L. Cohen, and S. G. Louie, Nature (London) NATUAS 0028-0836 10.1038/nature05180 444, 347 (2006). (Pubitemid 44764106)
6. K. A. Ritter and J. W. Lyding, Nat. Mater. 1476-1122 10.1038/nmat2378 8, 235 (2009).
7. Y. Niimi, T. Matsui, H. Kambara, K. Tagami, M. Tsukada, and H. Fukuyama, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.73.085421 73, 085421 (2006). (Pubitemid 43297066)
8. Y. Kobayashi, K. I. Fukui, T. Enoki, and K. Kusakabe, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.73.125415 73, 125415 (2006). (Pubitemid 43429362)
9. C. Tao, L. Jiao, O. V. Yazyev, Y.-C. Chen, J. Feng, X. Zhang, R. B. Capaz, J. M. Tour, A. Zettl, S. G. Louie, H. Dai, and M. F. Crommie, Nat. Phys. 1745-2473 10.1038/nphys1991 7, 616 (2011).
10. P. Koskinen, S. Malola, and H. Häkkinen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.115502 101, 115502 (2008).
11. T. Wassmann, A. P. Seitsonen, A. M. Saitta, M. Lazzeri, and F. Mauri, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.096402 101, 096402 (2008).
12. B. Huang, M. Liu, N. Su, J. Wu, W. Duan, B.-L. Gu, and F. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.166404 102, 166404 (2009).
13. J. Li, Z. Li, G. Zhou, Z. Liu, J. Wu, B.-L. Gu, J. Ihm, and W. Duan, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.82.115410 82, 115410 (2010).
14. G.-D. Lee, C. Z. Wang, E. Yoon, N.-M. Hwang, and K. M. Ho, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.81.195419 81, 195419 (2010).
15. C. K. Gan and D. J. Srolovitz, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.81.125445 81, 125445 (2010).
16. J. M. H. Kroes, M. A. Akhukov, J. H. Los, N. Pineau, and A. Fasolino, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.83.165411 83, 165411 (2011).
17. P. Koskinen, S. Malola, and H. Häkkinen, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.80.073401 80, 073401 (2009).
18. C. Girit, J. C. Meyer, R. Erni, M. D. Rossell, C. Kisielowski, L. Yang, C.-H. Park, M. F. Crommie, M. L. Cohen, S. G. Louie, and A. Zettl, Science SCIEAS 0036-8075 10.1126/science.1166999 323, 1705 (2009).
19. P. Rakyta, A. Kormányos, J. Cserti, and P. Koskinen, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.81.115411 81, 115411 (2010).
20. S. M.-M. Dubois, A. Lopez-Bezanilla, A. Cresti, F. Triozon, B. Biel, J.-C. Charlier, and S. Roche, ACS Nano SCIEAS 1936-0851 10.1021/nn100028q 4, 1971 (2010).
21. J. N. B. Rodrigues, P. A. D. Gonçalves, N. F. G. Rodrigues, R. M. Ribeiro, J. M. B. Lopes dos Santos, and N. M. R. Peres, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.84.155435 84, 155435 (2011).
22. J. W. McClure, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.104.666 104, 666 (1956).
23. D. P. DiVincenzo and E. J. Mele, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.29.1685 29, 1685 (1984).
24. A. R. Akhmerov and C. W. J. Beenakker, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.77.085423 77, 085423 (2008).
25. V. A. Volkov and I. V. Zagorodnev, Low Temp. Phys. LTPHEG 1063-777X 10.1063/1.3064694 35, 2 (2009).
26. Reference 21 reaches a different conclusion that the decay lengths into the bulk differ for the two sublattices in the case of a reczag edge. In their tight-binding approach, the Dirac and boundary modes are not easily separated. While we find that the former have a sublattice independent decay length 1 / k, the latter modes do introduce a sublattice dependence on the scale of the lattice constant, in accordance with Eq..
27. M. Wimmer, A. R. Akhmerov, and F. Guinea, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.82.045409 82, 045409 (2010).
28. J. Wurm, K. Richter, and I. Adagideli, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.84.075468 84, 075468 (2011).
29. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
30. T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.74.777 74, 777 (2005). (Pubitemid 41282624)
31. L. Brey and H. A. Fertig, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.73.195408 73, 195408 (2006). (Pubitemid 43702100)
32. A. R. Akhmerov and C. W. J. Beenakker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.157003 98, 157003 (2007). (Pubitemid 46582693)
33. K. Sasaki, S. Murakami, and R. Saito, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2181274 88, 113110 (2006).
34. S. Bhowmick and V. B. Shenoy, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.82.155448 82, 155448 (2010).
35. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College, London, 2003).
36. K. I. Sasaki, Y. Shimomura, Y. Takane, and K. Wakabayashi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.146806 102, 146806 (2009).