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Electron-polaron—electron-polaron bound states in mass-gap graphene-like planar quantum electrodynamics: s-wave bipolarons

Abstract

A Lorentz invariant version of a mass-gap graphene-like planar quantum electrodynamics, the parity-preserving U(1) × U(1) massive QED3, exhibits attractive interaction in low-energy electron-polaron–electron-polaron s-wave scattering, favoring quasiparticles bound states, the s-wave bipolarons.

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References

  1. 1.

    J.F. Schonfeld, Nucl. Phys. B 185, 157 (1981)

  2. 2.

    R. Jackiw, S. Templeton, Phys. Rev. D 23, 2291 (1981)

  3. 3.

    S. Deser, R. Jackiw, S. Templeton, Ann. Phys. 140, 372 (1982)

  4. 4.

    S. Deser, R. Jackiw, S. Templeton, Phys. Rev. Lett. 48, 975 (1982)

  5. 5.

    S. Deser, R. Jackiw, S. Templeton, Ann. Phys. 281, 409 (2000)

  6. 6.

    M. Franz, Z. Tešanović, O. Vafek, Phys. Rev. B 66, 054535 (2002)

  7. 7.

    I.F. Herbut, Phys. Rev. B 66, 094504 (2002)

  8. 8.

    H.R. Christiansen, O.M. Del Cima, M.M. Ferreira Jr., J.A. Helayël-Neto, Int. J. Mod. Phys. A 18, 725 (2003)

  9. 9.

    R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

  10. 10.

    A.M.J. Schakel, Phys. Rev. D 43, 1428 (1991)

  11. 11.

    A. Raya, E.D. Reyes, J. Phys. A: Math. Theor. 41, 355401 (2008)

  12. 12.

    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)

  13. 13.

    C.L. Kane, J.E. Moore, Phys. World 24, 32 (2011)

  14. 14.

    J.M. Fonseca, W.A. Moura-Melo, A.R. Pereira, J. Appl. Phys. 111, 064913 (2012)

  15. 15.

    M. Leijnse, K. Flensberg, Semicond. Sci. Technol. 27, 124003 (2012)

  16. 16.

    S. Yonezawa, AAPPS Bull. 26, 3 (2016)

  17. 17.

    M. Sato, Y. Ando, Rep. Prog. Phys. 80, 076501 (2017)

  18. 18.

    V.P. Gusynin, V.A. Miransky, I.A. Shovkovy, Phys. Rev. Lett. 73, 3499 (1994)

  19. 19.

    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438, 197 (2005)

  20. 20.

    V.P. Gusynin, S.G. Sharapov, J.P. Carbotte, Int. J. Mod. Phys. B 21, 4611 (2007)

  21. 21.

    R. Jackiw, S.-Y. Pi, Phys. Rev. Lett. 98, 266402 (2007)

  22. 22.

    R. Jackiw, S.-Y. Pi, Phys. Rev. B 78, 132104 (2008)

  23. 23.

    M.I. Katsnelson, K.S. Novoselov, Solid State Commun. 143, 3 (2007)

  24. 24.

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

  25. 25.

    A. Shytov, M. Rudner, N. Gu, M.I. Katsnelson, L. Levitov, Solid State Commun. 149, 1087 (2009)

  26. 26.

    V.P. Gusynin, Graphene and Quantum Electrodynamics, in International Jubilee Seminar Current problems in Solid State Physics, November (2011), Kharkov, Ukraine (2011)

  27. 27.

    E.M.C. Abreu, M.A. De Andrade, L.P.G. De Assis, J.A. Helayël- Neto, A.L.M.A. Nogueira, R.C. Paschoal, J. High Energy Phys. 1105, 001 (2011)

  28. 28.

    D.V. Khveshchenko, Phys. Rev. Lett. 87, 246802 (2001)

  29. 29.

    D.V. Khveshchenko, H. Leal, Nucl. Phys. B 687, 323 (2004)

  30. 30.

    L. Covaci, M. Berciu, Phys. Rev. Lett. 100, 256405 (2008)

  31. 31.

    D.A. Siegel, C. Hwang, A.V. Fedorov, A. Lanzara, New J. Phys. 14, 095006 (2012)

  32. 32.

    M.S. Fuhrer, Science 340, 1413 (2013)

  33. 33.

    P. Kumar, R. Skomski, P. Manchanda, A. Kashyap, P.A. Dowben, Curr. Appl. Phys. 14, S136 (2014)

  34. 34.

    A. Sharma, V.N. Kotov, A.H. Castro Neto, Phys. Rev. B 95, 235124 (2017)

  35. 35.

    J.P. Hagues, Phys. Rev. B 86, 064302 (2012)

  36. 36.

    G.Q. Hai, L. Cândido, B.G.A. Brito, F.M. Peeters, J. Phys. Commun. 2, 035017 (2018)

  37. 37.

    C. Chen, J. Avila, S. Wang, Y. Wang, C. Shen, R. Yang, B. Nosarzewski, T.P. Devereaux, G. Zhang, M.C. Asensio, Nano Lett. 18, 1082 (2018)

  38. 38.

    J.T. Devreese, Z. Phys. B 104, 601 (1997)

  39. 39.

    J.T. Devreese, A.S. Alexandrov, Rep. Prog. Phys. 72, 066501 (2009)

  40. 40.

    D.A. Siegel, C. Hwang, A.V. Fedorov, A. Lanzara, New J. Phys. 14, 095006 (2012)

  41. 41.

    J.C. Johannsen, S. Ulstrup, M. Bianchi, R. Hatch, D. Guan, F. Mazzola, L. Hornekær, F. Fromm, C. Raidel, T. Seyller, P. Hofmann, J. Phys.: Condens. Matter 25, 094001 (2013)

  42. 42.

    C. Chen, J. Avila, E. Frantzeskakis, A. Levy, M.C. Asensio, Nat. Commun. 6, 8585 (2015)

  43. 43.

    L.D. Landau, Phys. Z. Sowjetunion 3, 644 (1933)

  44. 44.

    K. Chadan, N.N. Khuri, A. Martin, T.T. Wu, Phys. Rev. D 58, 025014 (1998)

  45. 45.

    K. Chadan, N.N. Khuri, A. Martin, T.T. Wu, J. Math. Phys. 44, 406 (2003)

  46. 46.

    T. Kato,Perturbation theory for linear operators (Springer-Verlag, Heidelberg, 1976)

  47. 47.

    N. Setô, Publ. RIMS 9, 429 (1974)

  48. 48.

    B. Simon, Ann. Phys. 97, 279 (1976)

  49. 49.

    R.G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982)

  50. 50.

    V. Bargmann, Proc. Nat. Acad. Sci. U.S.A. 38, 961 (1952)

  51. 51.

    B. Simon, On the number of bound states of two-body Schrödinger operators: A review, in Studies in Mathematical Physics, Essays in Honour of Valentine Bargmann (Princeton University Press, Princeton, 1976), p. 305

  52. 52.

    B. Binegar, J. Math. Phys. 23, 1511 (1982)

  53. 53.

    J.J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Reading, 1967)

  54. 54.

    C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1988)

  55. 55.

    E.S. Miranda, Electron-electron attractive potential in parity-preserving Maxwell-Chern-Simons QED3, M.Sc. Thesis, UFV, 2016

  56. 56.

    O.M. Del Cima, E.S. Miranda, On the emergence of electron-electron attractive interaction in parity-preserving U(1) × U(1) massive QED3, in progress

  57. 57.

    M. Chaichian, J. Fischer, Yu.S. Vernov, Nucl. Phys. B 383, 152 (1992)

  58. 58.

    O.M. Del Cima, Mod. Phys. Lett. A 9, 1695 (1994)

  59. 59.

    K. Chadan, N.N. Khuri, A. Martin, T.T. Wu, Phys. Rev. D 58, 025014 (1998)

  60. 60.

    W.B. De Lima, O.M. Del Cima, D.H.T. Franco, An estimate for the number of bound states in planar quantum field theories, in progress

  61. 61.

    M. Kim, D. Jeong, G.-H. Lee, Y.-S. Shin, H.-W. Lee, H.-J. Lee, Sci. Rep. 5, 8715 (2015)

  62. 62.

    S. Ichinokura, K. Sugawara, A. Takayama, T. Takahashi, S. Hasegawa, ACS Nano 10, 2761 (2016)

  63. 63.

    Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, P. Jarillo-Herrero, Nature 556, 43 (2018)

  64. 64.

    Y. Cao, V. Fatemi, A. Demir, S. Fang, S.L. Tomarken, J.Y. Luo, J.D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R.C. Ashoori, P. Jarillo-Herrero, Nature 556, 80 (2018)

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Correspondence to Oswaldo M. Del Cima.

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Del Cima, O.M., Miranda, E.S. Electron-polaron—electron-polaron bound states in mass-gap graphene-like planar quantum electrodynamics: s-wave bipolarons. Eur. Phys. J. B 91, 212 (2018). https://doi.org/10.1140/epjb/e2018-90252-0

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Keywords

  • Solid State and Materials