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Quantum oscillations and wave packet revival in conical graphene structure

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Abstract

We present analytical expressions for the eigenstates and eigenvalues of electrons confined in a graphene monolayer in which the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square or heptagon. The calculations are performed in the continuum limit approximation in the vicinity of the Dirac points, solving Dirac equation by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearance of Aharonov-Bohm oscillations and find out the conditions of gapped and gapless states in the spectrum. We show that the gauge field due to a disclination lifts the orbital degeneracy originating from the existence of two valleys. The broken valley degeneracy has a clear signature on quantum oscillations and wave packet dynamics.

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References

  1. M. Vozmediano, M. Katsnelson, F. Guinea, Phys. Rep. 496, 109 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  2. G.E. Volovik, The Universe in a Helium Droplet, in International Series of Monographs on Physics (Oxford University Press, 2003)

  3. E.R. Pereira, S. Fumeron, F. Moraes, Phys. Rev. E 87, 049904 (2013)

    Article  ADS  Google Scholar 

  4. D. Sinha, Eur. Phys. J. B 88, 83 (2015)

    Article  ADS  Google Scholar 

  5. M.O. Katanaev, I.V. Volovich, Ann. Phys. 216, 1 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  6. S. Yeganeh, M.A. Ratner, E. Medina, V. Mujica, J. Chem. Phys. 131, 014707 (2009)

    Article  ADS  Google Scholar 

  7. E. Medina, L.A. González-Arraga, D. Finkelstein-Shapiro, B. Berche, V. Mujica, J. Chem. Phys. 142, 194308 (2015)

    Article  ADS  Google Scholar 

  8. D. Schmeltzer, New J. Phys. 14, 063025 (2012)

    Article  ADS  Google Scholar 

  9. M. Buongiorno Nardelli, B.I. Yakobson, J. Bernholc, Phys. Rev. B 57, R4277 (1998)

    Article  ADS  Google Scholar 

  10. A.H. Castro Neto, F. Guinea, N.M.R.. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  11. T. Ando, J. Phys. Soc. Jpn 74, 777 (2005)

    Article  ADS  Google Scholar 

  12. A. Krishnan, E. Dujardin, M.M.J. Treacy, J. Hugdahl, S. Lynum, T.W. Ebbesen, Nature 388, 451 (1997)

    Article  ADS  Google Scholar 

  13. S.N. Naess, A. Elgsaeter, G. Helgesen, K.D. Knudsen, Sci. Technol. Adv. Mater. 10, 065002 (2009)

    Article  Google Scholar 

  14. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  15. Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  16. E. Medina, A. López, B. Berche, Europhys. Lett. 83, 47005 (2008)

    Article  ADS  Google Scholar 

  17. E. Lipparini, Modern Many-Particle Physics (World Scientific, Singapore, 2008)

  18. P. Recher, B. Trauzettel, A. Rycerz, Y.M. Blanter, C.W.J. Beenakker, A.F. Morpurgo, Phys. Rev. B. 76, 235404 (2007)

    Article  ADS  Google Scholar 

  19. M. Zarenia, J. Milton Pereira, A. Chaves, F.M. Peeters, G.A. Farias, Phys. Rev. B 81, 045431 (2010)

    Article  ADS  Google Scholar 

  20. M. Zarenia, J. Milton Pereira, A. Chaves, F.M. Peeters, G.A. Farias, Erratum, Phys. Rev. B 82, 119906(E) (2010)

    Article  ADS  Google Scholar 

  21. N. Bolívar, E. Medina, B. Berche, Phys. Rev. B 89, 125413 (2014)

    Article  ADS  Google Scholar 

  22. T. García, S. Rodríguez-Bolívar, N.A. Cordero, E. Romera, J. Phys: Condens. Matter 25, 235301 (2013)

    ADS  Google Scholar 

  23. J. Gonzalez, F. Guinea, M.A.H. Vozmediano, Nucl. Phys. B 406, 771 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  24. P.E. Lammert, V.H. Crespi, Phys. Rev. Lett. 85, 5190 (2000)

    Article  ADS  Google Scholar 

  25. A. Cortijo, M.A.H. Vozmediano, Nucl. Phys. B 763, 293 (2007)

    Article  ADS  Google Scholar 

  26. O.V. Yazyev, S.G. Louie, Phys. Rev. B 81, 195420 (2010)

    Article  ADS  Google Scholar 

  27. E. Cockayne, G.M. Rutter, N.P. Guisinger, J.N. Crain, P.N. First, J.A. Stroscio, Phys. Rev. B. 83, 195425 (2011)

    Article  ADS  Google Scholar 

  28. B. An, S. Fukuyama, K. Yokogawaa, M. Yoshimura, M. Egashira, Y. Korai, I. Mochida, Appl. Phys. Lett. 78, 3696 (2001)

    Article  ADS  Google Scholar 

  29. A. Hashimoto, K. Suenaga, A. Gloter, K. Urita, S. Iijima, Nature 430, 870 (2004)

    Article  ADS  Google Scholar 

  30. E.J. Duplock, M. Scheffler, P.J.D. Lindan, Phys. Rev. Lett. 92, 225502 (2004)

    Article  ADS  Google Scholar 

  31. A. Ruegg, C. Lin, Phys. Rev. Lett 110, 046401 (2013)

    Article  ADS  Google Scholar 

  32. E. McCann, V.I. Fal’ko, Phys. Rev. Lett. 96, 086805 (2006)

    Article  ADS  Google Scholar 

  33. P. Recher, J. Nilsson, G. Burkard, B. Trauzettel, Phys. Rev. B 79, 085407 (2009)

    Article  ADS  Google Scholar 

  34. F. Guinea, M.I. Katsnelson, A.K. Geim, Nat. Phys. 6, 30 (2010)

    Article  Google Scholar 

  35. P. Ghaemi, J. Cayssol, D.N. Sheng, A. Viswanath, Phys. Rev. Lett. 108, 266801 (2012)

    Article  ADS  Google Scholar 

  36. A. Ruegg, C. Lin, Phys. Rev. Lett 110, 046401 (2013)

    Article  ADS  Google Scholar 

  37. L. Brey, H.A. Fertig, Phys. Rev. B 73, 235411 (2006)

    Article  ADS  Google Scholar 

  38. F.E. Meijer, A.F. Morpurgo, T.M. Klapwijk, Phys. Rev. B 66, 033107 (2002)

    Article  ADS  Google Scholar 

  39. B. Berche, C. Chatelain, E. Medina, Eur. J. Phys. 31, 1267 (2010)

    Article  Google Scholar 

  40. U.C. Coskun, T.-C. Wei, S. Vishveshwara, P.M. Goldbart, A. Bezryadin, Science 304, 1132 (2004)

    Article  ADS  Google Scholar 

  41. G. Fedorov, P. Barbara, D. Smirnov, D. Jiménez, S. Roche, Appl. Phys. Lett. 96, 132101 (2010)

    Article  ADS  Google Scholar 

  42. M. Trushin, J. Schliemann, Phys. Rev. Lett. 107, 156801 (2011)

    Article  ADS  Google Scholar 

  43. M. Mecklenburg, B.C. Regan, Phys. Rev. Lett. 106, 116803 (2011)

    Article  ADS  Google Scholar 

  44. G. Rempe, H. Walther, N. Klein, Phys. Rev. Lett. 58, 353 (1987)

    Article  ADS  Google Scholar 

  45. J.A. Yeazell, M. Mallalieu, C.R. Stroud, Jr., Phys. Rev. Lett. 64, 2007 (1990)

    Article  ADS  Google Scholar 

  46. M.J.J. Vrakking, D.M. Villeneuve, A. Stolow, Phys. Rev. A 54, R37 (1996)

    Article  ADS  Google Scholar 

  47. G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, S. Longh, Phys. Rev. Lett. 102, 180402 (2009)

    Article  ADS  Google Scholar 

  48. E.A. Shapiro, M. Spanner, M.Y. Ivanov, Phys. Rev. Lett. 91, 237901 (2003)

    Article  ADS  Google Scholar 

  49. M. Spanner, E.A. Shapiro, M.Y. Ivanov, Phys. Rev. Lett. 92, 093001 (2004)

    Article  ADS  Google Scholar 

  50. K.F. Lee, D.M. Villeneuve, P.B. Corkum, E.A. Shapiro, Phys. Rev. Lett. 93, 233601 (2004)

    Article  ADS  Google Scholar 

  51. M. Mehring, K. Müller, I.Sh. Averbukh, W. Merkel, W.P. Schleich, Phys. Rev. Lett. 98, 120502 (2007)

    Article  ADS  Google Scholar 

  52. M. Gilowski, T. Wendrich, T. Müller, Ch. Jentsch, W. Ertmer, E.M. Rasel, W.P. Schleich, Phys. Rev. Lett. 100, 030201 (2008)

    Article  ADS  Google Scholar 

  53. D. Bigourd, B. Chatel, W.P. Schleich, B. Girard, Phys. Rev. Lett. 100, 030202 (2008)

    Article  ADS  Google Scholar 

  54. I. Sh. Averbukh, J.F. Perelman, Phys. Lett. A 139, 449 (1989)

    Article  ADS  Google Scholar 

  55. V. Krueckl, T. Kramer, New J. Phys. 11, 093010 (2009)

    Article  ADS  Google Scholar 

  56. R.W. Robinett, Phys. Rep. 392, 1 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  57. E. Romera, F. de los Santos, Phys. Rev. B 80, 165416 (2009)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. TIFR Centre for Interdisciplinary Sciences, 500075, Hyderabad, India

    Debabrata Sinha

  2. Statistical Physics Group, Institut Jean Lamour, UMR CNRS No 7198, Université de Lorraine, B.P. 70239, 54506, Vandœuvre les Nancy, France

    Bertrand Berche

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  1. Debabrata Sinha
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  2. Bertrand Berche
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Correspondence to Debabrata Sinha.

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Sinha, D., Berche, B. Quantum oscillations and wave packet revival in conical graphene structure. Eur. Phys. J. B 89, 57 (2016). https://doi.org/10.1140/epjb/e2016-60907-y

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  • DOI: https://doi.org/10.1140/epjb/e2016-60907-y

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