Multiple magnetic barriers in graphene

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 4, 2009, Pages

  Dell'Anna, Luca ^a   De Martino, Alessandro ^b,c  

^a SISSA   (Italy)

^b UNIVERSITY OF COLOGNE   (Germany)

^c HEINRICH HEINE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 60349084637     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.045420     Document Type: Article

References (42)

1. For recent reviews, see A. K. Geim and K. S. Novoselov, Nature Mater. 6, 183 (2007) 10.1038/nmat1849
2. 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
3. A. De Martino, L. Dell'Anna, and R. Egger, Phys. Rev. Lett. 98, 066802 (2007) 10.1103/PhysRevLett.98.066802
4. A. De Martino, L. Dell'Anna, and R. Egger, Solid State Commun. 144, 547 (2007). 10.1016/j.ssc.2007.03.062
5. S. Park and H. S. Sim, Phys. Rev. B 77, 075433 (2008). 10.1103/PhysRevB.77.075433
6. L. Oroszlany, P. Rakyta, A. Kormanyos, C. J. Lambert, and J. Cserti, Phys. Rev. B 77, 081403 (R) (2008). 10.1103/PhysRevB.77.081403
7. T. K. Ghosh, A. De Martino, W. Häusler, L. Dell'Anna, and R. Egger, Phys. Rev. B 77, 081404 (R) (2008) 10.1103/PhysRevB.77.081404
8. W. Häusler, A. De Martino, T. K. Ghosh, and R. Egger, Phys. Rev. B 78, 165402 (2008). 10.1103/PhysRevB.78.165402
9. F. Zhai and K. Chang, Phys. Rev. B 77, 113409 (2008). 10.1103/PhysRevB.77.113409
10. M. Tahir and K. Sabeeh, Phys. Rev. B 77, 195421 (2008). 10.1103/PhysRevB.77.195421
11. M. Ramezani Masir, P. Vasilopoulos, A. Matulis, and F. M. Peeters, Phys. Rev. B 77, 235443 (2008). 10.1103/PhysRevB.77.235443
12. Hengyi Xu, T. Heinzel, M. Evaldsson, and I. V. Zozoulenko, Phys. Rev. B 77, 245401 (2008). 10.1103/PhysRevB.77.245401
13. A. Kormányos, P. Rakyta, L. Oroszlány, and J. Cserti, Phys. Rev. B 78, 045430 (2008). 10.1103/PhysRevB.78.045430
14. S. Ghosh and M. Sarma, arXiv:0806.2951 (unpublished).
15. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat. Phys. 2, 620 (2006) 10.1038/nphys384
16. V. V. Cheianov and V. I. Fal'ko, Phys. Rev. B 74, 041403 (R) (2006). 10.1103/PhysRevB.74.041403
17. 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) 438, 197 (2005) 10.1038/nature04233
18. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature (London) 438, 201 (2005). 10.1038/nature04235
19. V. P. Gusynin and S. G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005). 10.1103/PhysRevLett.95.146801
20. See, for example, M. Cerchez, S. Hugger, T. Heinzel, and N. Schulz, Phys. Rev. B 75, 035341 (2007) for a recent work, and references therein. 10.1103/PhysRevB.75.035341
21. M. L. Leadbeater, C. L. Foden, J. H. Burroughes, M. Pepper, T. M. Burke, L. L. Wang, M. P. Grimshaw, and D. A. Ritchie, Phys. Rev. B 52, R8629 (1995). 10.1103/PhysRevB.52.R8629
22. S. J. Bending, K. von Klitzing, and K. Ploog, Phys. Rev. Lett. 65, 1060 (1990). 10.1103/PhysRevLett.65.1060
23. M. Johnson, B. R. Bennett, M. J. Yang, M. M. Miller, and B. V. Shanabrook, Appl. Phys. Lett. 71, 974 (1997) 10.1063/1.119704
24. V. Kubrak, A. Neumann, B. L. Gallagher, P. C. Main, M. Henini, C. H. Marrows, and B. J. Hickey, J. Appl. Phys. 87, 5986 (2000). 10.1063/1.372588
25. H. A. Carmona, A. K. Geim, A. Nogaret, P. C. Main, T. J. Foster, M. Henini, S. P. Beaumont, and M. G. Blamire, Phys. Rev. Lett. 74, 3009 (1995) 10.1103/PhysRevLett.74.3009
26. P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995). 10.1103/PhysRevLett.74. 3013
27. A. Nogaret, S. J. Bending, and M. Henini, Phys. Rev. Lett. 84, 2231 (2000). 10.1103/PhysRevLett.84.2231
28. K. S. Novoselov, A. K. Geim, S. V. Dubonos, Y. G. Cornelissens, F. M. Peeters, and J. C. Maan, Phys. Rev. B 65, 233312 (2002). 10.1103/PhysRevB.65. 233312
29. F. M. Peeters and A. Matulis, Phys. Rev. B 48, 15166 (1993) 10.1103/PhysRevB.48.15166
30. J. Reijniers, F. M. Peeters and A. Matulis, Phys. Rev. B 59, 2817 (1999) 10.1103/PhysRevB.59.2817
31. For a recent review, see also S. J. Lee, S. Souma, G. Ihm, and K. J. Chang, Phys. Rep. 394, 1 (2004) and references therein. 10.1016/j.physrep.2003. 11.004
32. B. Huard, J. A. Sulpizio, N. Stander, K. Todd, B. Yang, and D. Goldhaber-Gordon, Phys. Rev. Lett. 98, 236803 (2007). 10.1103/PhysRevLett.98. 236803
33. J. R. Williams, L. Di Carlo, and C. M. Marcus, Science 317, 638 (2007). 10.1126/science.1144657
34. In all cases discussed in this paper, the transmission probability is the same at the two valleys.
35. From now on the magnetic flux always refers to the unit length in the y direction.
36. B. H. J. McKellar and G. J. Stephenson, Jr., Phys. Rev. C 35, 2262 (1987). 10.1103/PhysRevC.35.2262
37. M. Barbier, F. M. Peeters, P. Vasilopoulos, and J. M. Pereira, Phys. Rev. B 77, 115446 (2008). 10.1103/PhysRevB.77.115446
38. Note that according to the usual definition, our T̂ is actually the inverse of the transfer matrix.
39. I. S. Ibrahim and F. M. Peeters, Phys. Rev. B 52, 17321 (1995). 10.1103/PhysRevB.52.17321
40. A. Matulis, F. M. Peeters, and P. Vasilopoulos, Phys. Rev. Lett. 72, 1518 (1994). 10.1103/PhysRevLett.72.1518
41. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).
42. V. V. Cheianov, V. Fal'ko, and B. L. Altschuler, Science 315, 1252 (2007). 10.1126/science.1138020