Characteristics of level-spacing statistics in chaotic graphene billiards

Chaos

Volumn 21, Issue 1, 2011, Pages

  Huang, Liang ^a,b   Lai, Ying Cheng ^a,c,d   Grebogi, Celso ^d  

^a AZ 85281   (United States)

^b LANZHOU UNIVERSITY   (China)

^c ARIZONA STATE UNIVERSITY   (United States)

^d UNIVERSITY OF ABERDEEN   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPHITE;

ARTICLE; CHEMISTRY; MAGNETISM; NONLINEAR SYSTEM; STATISTICAL MODEL; THERMODYNAMICS;

GRAPHITE; MAGNETICS; MODELS, STATISTICAL; NONLINEAR DYNAMICS; THERMODYNAMICS;

EID: 79953276130     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3537814     Document Type: Article

References (54)

1. Bohigas G. Giannoni M.-J. Bohigas G. Giannoni M.-J. Schmit C. Bohigas G. Giannoni M.-J. Bohigas G. Giannoni M.-J. Schmit C. Phys. Rev. Lett. 1984, 52:1. 10.1103/PhysRevLett.52.1, 10.1103/PhysRevLett.52.1, and in Lecture Notes in Physics, Vol. (Springer, Berlin, );, and and Vol. (Springer, Berlin, );, and.
2. Berry M.V. Proc. R. Soc. London, Ser. A 1985, 400:229. 10.1098/rspa.1985.0078.
3. Gutzwiller M. Chaos in Classical and Quantum Mechanics 1990, (Springer, Berlin, ).
4. Haake F. Quantum Signatures of Chaos 2001, 2nd ed. (Springer, Berlin, ).
5. Weidenmüller H.A. Mitchell G.E. Rev. Mod. Phys. 2009, 81:539. 10.1103/RevModPhys.81.539, and.
6. A requirement for the applicability of random-matrix theory is that the system possess no geometric symmetry. 10.1103/RevModPhys.81.539.
7. Berry M.V. Robnik M. J. Phys. A 1986, 19:649. 10.1088/0305-4470/19/5/019, and.
8. Stöckmann H.J. Quantum Chaos: An Introduction 1999, (Cambridge University Press, Cambridge, England, ).
9. Stoffregen U. Stein J. Stöckmann H.-J. Kuś M. Haake F. Phys. Rev. Lett. 1995, 74:2666. 10.1103/PhysRevLett.74.2666, and.
10. So P. Anlage S.M. Ott E. Oerter R.N. Phys. Rev. Lett. 1995, 74:2662. 10.1103/PhysRevLett.74.2662, and.
11. Berry M.V. Mondragon R.J. Proc. R. Soc. London, Ser. A 1987, 412:53. 10.1098/rspa.1987.0080, and.
12. Karagiorgi G. Aguilar-Arevalo A. Conrad J.M. Shaevitz M.H. Whisnant K. Sorel M. Barger V. Phys. Rev. D 2007, 75:013011. 10.1103/PhysRevD.75.013011, Neutrinos have a minuscule, but nonzero mass. See and.
13. Novoselov K.S. Geim A.K. Morozov S.V. Jiang D. Zhang Y. Dubonos S.V. Grigorieva I.V. Firsov A.A. Science 2004, 306:666. 10.1126/science.1102896, and.
14. Miao F. Wijeratne S. Zhang Y. Coskun U.C. Bao W. Lau C.N. Science 2007, 317:1530. 10.1126/science.1144359, and.
15. Ponomarenko L.A. Schedin F. Katsnelson M.I. Yang R. Hill E.W. Novoselov K.S. Geim A.K. Science 2008, 320:356. 10.1126/science.1154663, and.
16. Libisch F. Stampfer C. Burgdörfer J. Phys. Rev. B 2009, 79:115423. 10.1103/PhysRevB.79.115423, and.
17. Amanatidis I. Evangelou S.N. Phys. Rev. B 2009, 79:205420. 10.1103/PhysRevB.79.205420, and.
18. Huang L. Lai Y.-C. Grebogi C. Phys. Rev. E 2010, 81:055203(R). 10.1103/PhysRevE.81.055203, and.
19. Suzuura H. Ando T. Phys. Rev. Lett. 2002, 89:266603. 10.1103/PhysRevLett.89.266603, and.
20. Robnik M. Berry M.V. Robnik M. Robnik M. Berry M.V. Robnik M. Quantum Chaos and Statistical Nuclear Physics, Lecture Notes in Physics 1986, 263:669. 10.1088/0305-4470/19/5/020, 10.1088/0305-4470/19/5/020, and ;, in Lecture Notes in Physics, Vol. (Springer-Verlag, Berlin, )., and ;, in Vol. (Springer-Verlag, Berlin, ).
21. Wurm J. Rycerz A. Adagideli I. Wimmer M. Richter K. Baranger H.U. Phys. Rev. Lett. 2009, 102:056806. 10.1103/PhysRevLett.102.056806, and.
22. Ryu S. Mudry C. Obuse H. Furusaki A. Phys. Rev. Lett. 2007, 99:116601. 10.1103/PhysRevLett.99.116601, and.
23. Nomura K. Koshino M. Ryu S. Phys. Rev. Lett. 2007, 99:146806. 10.1103/PhysRevLett.99.146806, and.
24. Ostrovsky P.M. Gornyi I.V. Mirlin A.D. Phys. Rev. Lett. 2007, 98:256801. 10.1103/PhysRevLett.98.256801, and.
25. Beenakker C.W. J. Rev. Mod. Phys. 2008, 80:1337. 10.1103/RevModPhys.80.1337.
26. Bena C. Phys. Rev. Lett. 2008, 100:076601. 10.1103/PhysRevLett.100.076601.
27. Brihuega I. Mallet P. Bena C. Bose S. Michaelis C. Vitali L. Varchon F. Magaud L. Kern K. Veuillen J.Y. Phys. Rev. Lett. 2008, 101:206802. 10.1103/PhysRevLett.101.206802, and.
28. Ando T. Nakanishi T. Saito R. J. Phys. Soc. Jpn. 1998, 67:2857. 10.1143/JPSJ.67.2857, and.
29. Morozov S.V. Novoselov K.S. Katsnelson M.I. Schedin F. Ponomarenko L.A. Jiang D. Geim A.K. Phys. Rev. Lett. 2006, 97:016801. 10.1103/PhysRevLett.97.016801, and.
30. McCann E. Kechedzhi K. Falko V.I. Suzuura H. Ando T. Altshuler B.L. Phys. Rev. Lett. 2006, 97:146805. 10.1103/PhysRevLett.97.146805, and.
31. Morpurgo A.F. Guinea F. Phys. Rev. Lett. 2006, 97:196804. 10.1103/PhysRevLett.97.196804, and.
32. Wu X. Li X. Song Z. Berger C. de Heer W.A. Phys. Rev. Lett. 2007, 98:136801. 10.1103/PhysRevLett.98.136801, and.
33. Kharitonov M.Y. Efetov K.B. Phys. Rev. B 2008, 78:033404. 10.1103/PhysRevB.78.033404, and.
34. Castro Neto A.H. Guinea F. Peres N.M. R. Novoselov K.S. Geim A.K. Rev. Mod. Phys. 2009, 81:109. 10.1103/RevModPhys.81.109, and.
35. Saito R. Dresselhaus G. Dresselhaus M.S. Rycerz A. TworzydŁo J. Beenakker C.W. J. Cheianov V.V. Fal'ko V. Altshuler B.L. Garcia-Pomar J.L. Cortijo A. Nieto-Vesperinas M. Phys. Rev. Lett. 2008, 100:236801. 10.1103/PhysRevB.61.2981, 10.1038/nphys547, 10.1126/science.1138020, 10.1103/PhysRevLett.100.236801, and ;, and ;, and ;, and.
36. 10.1103/RevModPhys.81.109, The magnetic field can be scaled down for larger confinements to yield similar effects.
37. Baltes H.P. Hilf E.R. Spectra of Finite Systems 1976, and (B.-I. Wissenschaftseverlag, Mannheim, ).
38. Brey L. Fertig H.A. Phys. Rev. B 2006, 73:235411. 10.1103/PhysRevB.73.235411, and.
39. Berry M.V. Tabor M. Proc. R. Soc. 1977, 356:375. and London.
40. Mehta M.L. Random Matrices 1967, (Academic, New York, ).
41. Bohr A. Mottelson B.R. Nuclear Structure 1969, 1:294-301. and Vol. (Benjamin, New York, ), Appendix 2C, pp.
42. Here we do not consider GSE since it is irrelevant to our studies. 10.1103/PhysRevB.73.235411.
43. Dyson F.J. Mehta M.L. J. Math. Phys. 1963, 4:701. 10.1063/1.1704008, and.
44. Bohigas O. Giannoni M.J. Ann. Phys. 1975, 89:393. 10.1016/0003-4916(75)90187-6, and.
45. Liu B. Zhang G.-C. Ding L. Dai J.-H. Zhang H.-J. Phys. Lett. A 1999, 260:406. 10.1016/S0375-9601(99)00537-X, and.
46. Wright A.R. Liu F. Zhang C. Nanotechnology 2009, 20:405203. 10.1088/0957-4484/20/40/405203, and.
47. Son Y.-W. Cohen M.L. Louie S.G. Phys. Rev. Lett. 2006, 97:216803. 10.1103/PhysRevLett.97.216803, and.
48. Kane C.L. Mele E.J. Phys. Rev. Lett. 2005, 95:146802. 10.1103/PhysRevLett.95.146802, and.
49. Zhou S.Y. Gweon G.-H. Fedorov A.V. First P.N. de Heer W.A. Lee D.-H. Guinea F. Castro Neto A.H. Lanzara A. Nature Mater. 2007, 6:770. 10.1038/nmat2003, and.
50. MacDonald A.H. Phys. Rev. B 1984, 29:6563. 10.1103/PhysRevB.29.6563.
51. Huang L. Lai Y.-C. Ferry D.K. Goodnick S.M. Akis R. Phys. Rev. Lett. 2009, 103:054101. 10.1103/PhysRevLett.103.054101, and.
52. Alhassid Y. Lewenkopf C.H. Phys. Rev. Lett. 1995, 75:3922. 10.1103/PhysRevLett.75.3922, and.
53. Robnik M. Berry M.V. Robnik M. Robnik M. Berry M.V. Robnik M. J. Phys. 1986, 19:3619. 10.1088/0305-4470/18/9/019, 10.1088/0305-4470/19/17/025, 10.1088/0305-4470/18/9/019, 10.1088/0305-4470/19/17/025, and ;, in (Adam-Hilger, Bristol, );, and ;, in Malvern Physics Series (Adam-Hilger, Bristol, );.
54. Robnik M. Batistić B. Robnik M. J. Phys. A: Math. Theor. 2010, 43:215101. 10.1088/1751-8113/43/21/215101, and.