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Quantum holonomies in graphene wormholes

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Abstract

In this paper, a discussion about quantum holonomies around a possible bridge between two graphene sheets has been made. That bridge is widely known as a graphene wormhole, and some of its characteristics are also showed up here. As well as their build as a zigzag junction between a baggy nanotube and the graphene lattices. And how the localized electronic states could be mimicked by gauge fields in a low-energy regime. Further, the possibility to build holonomies handle by an effective flux from topological defects in junctions of that bridge has been discussed.

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Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. R. Jackiw, Lower dimensional gravity. Nucl. Phys. B 252, 343 (1985)

    Article  ADS  Google Scholar 

  2. S. Deser, R. Jackiw, Three-dimensional einstein gravity: dynamics of flat space, G. ’t Hooft. Ann. Phys. (N. Y.) 152, 220 (1984)

    Article  ADS  Google Scholar 

  3. M.I. Katsnelson, Graphene - carbon in two dimensions (Cambridge University Press, 2012)

    Book  Google Scholar 

  4. H. Suzuura, T. Ando, Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice. Phys. Rev. Lett. 89, 266603 (2002)

    Article  ADS  Google Scholar 

  5. A. Fasolino, J.H. Los, M.I. Katsnelson, Intrinsic ripples in graphene. Nature Materials 6, 858–861 (2007)

    Article  ADS  Google Scholar 

  6. M.I. Katsnelson, A.K. Geim, Electron scattering on microscopic corrugations in graphene. Philos. Trans. R. Soc. A 366, 195 (2008)

    Article  ADS  Google Scholar 

  7. V. Volterra, Sur l’équilibre des corps élastiques multiplement connexes. Annales scientifiques de l’École normale supérieure 24, 401–517 (1907)

    Article  MathSciNet  MATH  Google Scholar 

  8. M.O. Katanaev, I.V. Volovich, Theory of defects in solids and three-dimensional gravity. Ann. Phys. 216(1), 1–28 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. I.V. Fialkovsky, D.V. Vassilevich, Quantum field theory in graphene. Int. J. Mod. Phys. A 27(15), 1260007 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, C60: Buckminsterfullerene. Nature 328, 162 (1985)

    Article  ADS  Google Scholar 

  11. J. Gonzalez, F. Guinea, M.A.H. Vozmediano, Continuum approximation to fullerene molecules. Phys. Rev. Lett. 69, 1 (1992)

    Article  Google Scholar 

  12. J. Gonzalez, F. Guinea, M.A.H. Vozmediano, The electronic spectrum of fullerenes from the Dirac equation. Nucl. Phys. B 406, 771 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. E. Cavalcante, C. Carvalho, Geometric model for Fullerene Molecule in the presence of Aharonov-Bohm flux. J. Phys. Chem. Solids 75, 1265–1268 (2014)

    Article  ADS  Google Scholar 

  14. G.Q. Garcia, E. Cavalcante, A.M. de M. Carvalho, C. Furtado, The geometric theory of defects description for \(C_{60}\) fullerenes in a rotating frame. Eur. Phys. J. Plus 132, 183 (2017)

    Article  Google Scholar 

  15. J. Gonzalez, J. Herrero, Graphene wormholes: a condensed matter illustration of Dirac fermions in curved space. Nucl. Phys. B 825, 426–443 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. G.D. Garcia, P.J. Porfírio, D.C. Moreira, C. Furtado, Graphene wormhole trapped by external magnetic field. Nucl. Phys. B 950, 114853 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  17. A. Einstein, N. Rosen, The particle problem in the general theory of relativity. Phys. Rev. 48(1), 73 (1935)

    Article  ADS  MATH  Google Scholar 

  18. M.S. Morris, K.S. Thorne, Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity. Amer. J. Phys. 56, 395 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. J. Gonzalez, F. Guinea, J. Herrero, Propagating, evanescent, and localized states in carbon nanotube-graphene junctions. Phys. Rev. B 79(16), 165434 (2009)

    Article  ADS  Google Scholar 

  20. T.F. Souza, A.C.A. Ramos, R.N. Costa Filho, J. Furtado, Generalized Ellis-Bronnikov graphene wormhole, e-print arXiv:2208.06869 (gr-qc) (2022)

  21. J.E.G. Ramos, J. Furtado, T.M. Santiago, A.C.A. Ramos, D.R. da Costa, Electronic properties of bilayer graphene catenoid bridge. Phys. Lett. A 384, 126458 (2020)

    Article  MathSciNet  Google Scholar 

  22. H. Kleinert, Gauge fields in condensed matter (World Scientific, Berlim 2, 1989)

    Book  MATH  Google Scholar 

  23. A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, J. Zwanziger, The geometric phase in quantum systems: foundation, mathematical concepts and applications in molecular and condensed Matter Physics Springer, New-York (2003)

  24. P. Zanardi, M. Rasetti, Holonomic quantum computation. Phys. Lett. A 264, 94–99 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. V.I. Kuvshinov, A.V. Kuzmin, Stability of holonomic quantum computations. Phys. Lett. A 316, 391–394 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. C. Monroe, D.M. Meekhof, B.E. King, W.M. Itano, D.J. Wineland, Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. J. Pachos, Topological features in ion-trap holonomic computation. Phys. Rev. A 66, 042318 (2002)

    Article  ADS  Google Scholar 

  28. M. Cholascinski, Quantum holonomies with Josephson-junction devices. Phys. Rev. B 69, 134516 (2004)

    Article  ADS  Google Scholar 

  29. A. Recati, T. Calarco, P. Zanardi, J.I. Cirac, P. Zoller, Holonomic quantum computation with neutral atoms. Phys. Rev. A 66, 032309 (2002)

    Article  ADS  Google Scholar 

  30. J. Pachos, S. Chountasis, Optical holonomic quantum computer. Phys. Rev. A 62, 052318 (2000)

    Article  ADS  Google Scholar 

  31. K. Bakke, C. Furtado, S. Sergeenkov, Holonomic quantum computation associated with a defect structure of conical graphene. Europhysics Letters 87, 30002 (2009)

    Article  ADS  Google Scholar 

  32. J.A. Jones, V. Vedral, A. Ekert, G. Castagnoli, Geometric quantum computation using nuclear magnetic resonance. Nature 403, 869871 (2000)

    Article  Google Scholar 

  33. J. Teles et al., Experimental implementation of quantum information processing by Zeeman-perturbed nuclear quadrupole resonance. Quantum Inf. Process 14, 18891906 (2015)

    Article  Google Scholar 

  34. E. Cavalcante, C. Furtado, Quantum Holonomy based in a Kaluza-Klein description for defects in \(C_{60}\) fullerenes. Int. J. Geom. Methods Mod. Phys. 18(10), 2150163 (2021)

    Article  Google Scholar 

  35. C. Bena, G. Montambaux, Remarks on the tight-binding model of graphene. New J. Phys. 11(9), 095003 (2009)

    Article  ADS  Google Scholar 

  36. M. Visser, Lorentzian Wormholes: from Einstein to Hawking, AIP (1995)

  37. C.W. Misner, J.A. Wheeler, Classical physics as geometry. Annals Phys. 2, 525 (1957)

    Article  ADS  MATH  Google Scholar 

  38. H.G. Ellis, Ether flow through a drainhole: a particle model in general relativity. J. Math. Phys. 14(1), 104–118 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  39. K.A. Bronnikov, Scalar-tensor theory and scalar charge. A. Phys. Pol. B 4, 251–266 (1973)

    MathSciNet  Google Scholar 

  40. M.S. Morris, K.S. Thorne, U. Yurtsever, Wormholes, times machines and weak energy conditions. Phys. Rev. Lett. 61, 1446–1449 (1988)

    Article  ADS  Google Scholar 

  41. N. Godani, G.C. Samanta, Non violation of energy conditions in wormholes modeling. Mod. Phys. Lett. A 34(28), 1950266 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  42. N. Godani, D.V. Singh, G.C. Samanta, Phys. Dark Univ. 35, 100952 (2022)

    Article  Google Scholar 

  43. K. Sasaki, J. Jiang, R. Saito, S. Onari, Y. Tanaka, Theory of superconductivity of carbon nanotubes and graphene. J. Phys. Soc. Jpn. 76, 033704 (2007)

    Article  ADS  Google Scholar 

  44. Y.M. Xie, D.K. Efetov, T. Law, Valley-polarized state induced \(\phi _{0}\)-Josephson junction in twisted Bilayer-Graphene, e-print arXiv:2202.05663v2 (cond-mat.mes-hall) (2022)

  45. I. Takesue, J. Haruyama, N. Kobayashi, S. Chiashi, S. Maruyama, T. Sugai, H. Shinohara, Superconductivity in entirely end-bonded multiwalled carbon nanotubes. Phys. Rev. Lett. 96, 057001 (2006)

    Article  ADS  Google Scholar 

  46. Y. Cao, V. Fateni, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018)

    Article  ADS  Google Scholar 

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Acknowledgements

I thank CAPES and CNPQ for financial support.

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Authors and Affiliations

  1. Departamento de Física, Centro de Ciências e Tecnologia, Universidade Estadual da Paraíba, Campina Grande, PB, Brazil

    Everton Cavalcante

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Correspondence to Everton Cavalcante.

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Cavalcante, E. Quantum holonomies in graphene wormholes. Eur. Phys. J. Plus 137, 1351 (2022). https://doi.org/10.1140/epjp/s13360-022-03527-4

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