Quantum transport via evanescent waves in undoped graphene

Journal of Computational and Theoretical Nanoscience

Volumn 8, Issue 6, 2011, Pages 912-918

  Katsnelson, M I ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Aharonov bohm effect; Conformal mapping; Dirac equation; Graphene; Minimal conductivity; Pseudodiffusive transport

Indexed keywords

AHARONOV-BOHM EFFECTS; CONDENSED MATTER; CORBINO GEOMETRY; DIRAC EQUATION; DIRAC FERMIONS; DIRAC OPERATORS; EVANESCENT WAVE; MAPPING TECHNIQUES; MATHEMATICAL TOOLS; MINIMAL CONDUCTIVITY; PSEUDODIFFUSIVE TRANSPORT; QUANTUM TRANSPORT; QUASIPARTICLES; RELATIVISTIC EFFECTS; ZERO CHARGE;

CARRIER CONCENTRATION; GRAPHENE; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; QUANTUM CHEMISTRY; QUANTUM ELECTRONICS;

CONFORMAL MAPPING;

EID: 79955456961     PISSN: 15461955     EISSN: None     Source Type: Journal    
DOI: 10.1166/jctn.2011.1770     Document Type: Article

References (61)

1. A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (2007).
2. M. I. Katsnelson, Mater. Today 10, 20 (2007).
3. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 80, 315 (2008).
4. C. W. J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008).
5. A. K. Geim, Science 324, 1530 (2009).
6. S. D. Sarma, S. Adam, E. H. Hwang, and E. Rossi, arXiv: 1003.4731.
7. M. A. H. Vozmediano, M. I. Katsnelson, and F. Guinea, Phys. Rep. 496, 109 (2010).
8. 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 438, 197 (2005).
9. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 (2005).
10. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat. Phys. 2, 620 (2006).
11. N. Stander, B. Huard, and D. Goldhaber-Gordon, Phys. Rev. Lett. 102, 026807 (2009).
12. A. F. Young and P. Kim, Nat. Phys. 5, 222 (2009).
13. E. Fradkin, Phys. Rev. B 33, 3263 (1986).
14. P. A. Lee, Phys. Rev. Lett. 71, 1887 (1993).
15. A. W. W. Ludwig, M. P. A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B 50, 7526 (1994).
16. A. A. Nersesyan, A. M. Tsvelik, and F. Wenger, Phys. Rev. Lett. 72, 2628 (1994).
17. K. Ziegler, Phys. Rev. Lett. 80, 3113 (1998).
18. N. H. Shon and T. Ando, J. Phys. Soc. Japan 67, 2421 (1998).
19. E. V. Gorbar, V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Phys. Rev. B 66, 045108 (2002).
20. X. Yang and C. Nayak, Phys. Rev. B 65, 064523 (2002).
21. M. I. Katsnelson, Eur. Phys. J. B 51, 157 (2006).
22. J. Tworzydlo, B. Trauzettel, M. Titov, A. Rycerz, and C. W. J. Beenakker, Phys. Rev. Lett. 96, 246802 (2006).
23. S. Ryu, C. Mudry, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 75, 205344 (2007).
24. E. Schrodinger, Sitz. Preuss. Akad. Wiss. Phys.-Math. 24,418 (1930).
25. C. W. J. Beenakker and H. van Houten, Solid State Phys. 44, 1 (1991).
26. Y. M. Blanter and M. Buttiker, Phys. Rep. 336, 1 (2000).
27. E. Prada, P. San-Jose, B. Wunsch, and F. Guinea, Phys. Rev. B 75, 113407 (2007).
28. M. I. Katsnelson and F. Guinea, Phys. Rev. B 78, 075417 (2008).
29. A. Rycerz, P. Recher, and M. Wimmer, Phys. Rev. B 80, 125417 (2009).
30. A. Schuessler, P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B 79, 075405 (2009).
31. M. I. Katsnelson, Europhys. Lett. 89, 17001 (2010).
32. F. Miao, S. Wijeratne, Y. Zhang, U. C. Coskun, W. Bao, and C. N. Lau, Science 317, 1530 (2007).
33. R. Danneau, F. Wu, M. F. Craciun, S. Russo, M. Y. Tomi, J. Salmilehto, A. F. Morpurgo, and P. J. Hakonen, Phys. Rev. Lett. 100, 196802 (2008).
34. M. Auslender and M. I. Katsnelson, Phys. Rev. B 76, 235425 (2007).
35. R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, Nature 463, 68 (2010).
36. J. Cserti and G. David, Phys. Rev. B 74, 172305 (2006).
37. T. M. Rusin and W. Zawadzki, Phys. Rev. B 78, 125419 (2008).
38. T. M. Rusin and W. Zawadzki, Phys. Rev. B 80, 045416 (2009).
39. A. A. Abrikosov, Phys. Rev. B 58, 2788 (1998).
40. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Relativistic Quantum Theory, Oxford etc., Pergamon (1971), Vol. 1.
41. A. S. Davydov, Quantum Mechanics, Oxford etc., Pergamon (1976).
42. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics, Consultants Bureau, New York (1974).
43. K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Falko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, Nat. Phys. 2, 177 (2006).
44. E. McCann and V. I. Falko, Phys. Rev. Lett. 96, 086805 (2006).
45. A. C. Hewson, The Kondo Problem to Heavy Fermions, Cambridge University Press, Cambridge, (1993).
46. W. Tian and S. Datta, Phys. Rev. B 49, 5097 (1994).
47. L. Chico, L. X. Benedict, S. G. Louie, and M. L. Cohen, Phys. Rev. B 54, 2600 (1996).
48. C. W. J. Beenakker and M. Büttiker, Phys. Rev. B 46, 1889 (1992).
49. K. E. Nagaev, Phys. Lett. A 169, 103 (1992).
50. M. I. Katsnelson, Eur. Phys. J. B 52, 151 (2006).
51. I. Snyman and C. W. J. Beenakker, Phys. Rev. B 75, 045322 (2007).
52. J. Cserti, A. Csordäs, and G. David, Phys. Rev. Lett. 99, 066802 (2007).
53. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
54. S. Olariu and I. I. Popescu, Rev. Mod. Phys. 57, 339 (1985).
55. P. Recher, B. Trauzettel, A. Rycerz, Ya. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, Phys. Rev. B 76, 235404 (2007).
56. R. Jackiw, A. I. Milstein, S.-Y. Pi, and I. S. Terekhov, Phys. Rev. B 80, 033413 (2009).
57. J. Wurm, M. Wimmer, H. U. Baranger, and K. Richter, Semicond. Sei. Tech. 25, 034003 (2010).
58. 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).
59. M. Huefner, F. Molitor, A. Jacobsen, A. Pioda, C. Stampfer, K. Ensslin, and T. Ihn, Phys. Stat. Sol. (b) 246, 2756 (2009).
60. Y. Aharonov and A. Casher, Phys. Rev. A 19, 2461 (1979).
61. A. Rycerz, Phys. Rev. B 81, 121404 (2010).