Skip to main content
Log in

Position-dependent mass effects on a bilayer graphene catenoid bridge

  • Regular Article – Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We study the electronic properties of a position-dependent effective mass electron on a bilayer graphene catenoid bridge. We propose a position-dependent mass (PDM) as a function of both Gaussian and mean curvature. The Hamiltonian exhibits parity and time-reversal steaming from the bridge symmetry. The effective potential contains the da Costa, centrifugal, and PDM terms which are concentrated around the catenoid bridge. For zero angular momentum states, the PDM term provides a transition between a reflectionless to a double-well potential. As a result, the bound states undergo a transition from a single state around the bridge throat into two states each one located at rings around the bridge. Above some critical value of the PDM coupling constant, the degeneracy is restored due to double-well tunneling resonance.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All the data is in the paper.]

References

  1. A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)

    Article  ADS  Google Scholar 

  2. 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 

  3. M. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, Cambridge, 2012)

    Book  Google Scholar 

  4. S. Berber, Y.K. Kwon, D. Tomanek, Phys. Rev. Lett. 84, 4613 (2000)

    Article  ADS  Google Scholar 

  5. A. Carvalho, M. Wang, X. Zhu, A.S. Rodin, H. Su, A.H. Castro Neto, Nat. Rev. Mater. 1, 11 (2016)

    Article  Google Scholar 

  6. C. Furtado, F. Moraes, A.M. de M. Carvalho, Phys. Lett. A 372, 5368 (2008)

    Article  ADS  Google Scholar 

  7. R. Dandoloff, T.T. Truong, Phys. Lett. A 325, 233 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  8. V. Atanasov, R. Dandoloff, A. Saxena, Phys. Rev. B 79, 033404 (2009)

    Article  ADS  Google Scholar 

  9. V. Atanasov, A. Saxena, Phys. Rev. B 92, 035440 (2015)

    Article  ADS  Google Scholar 

  10. F. Guinea, A.K. Geim, M.I. Katsnelson, K.S. Novoselov, Phys. Rev. B 81, 035408 (2010)

    Article  ADS  Google Scholar 

  11. F. de Juan, A. Cortijo, M.A.H. Vozmediano, Phys. Rev. B 76, 165409 (2007)

    Article  ADS  Google Scholar 

  12. V. Atanasov, A. Saxena, Phys. Rev. B 81, 205409 (2010)

    Article  ADS  Google Scholar 

  13. H. Jensen, H. Koppe, Ann. Phys. 63, 586 (1971)

    Article  ADS  Google Scholar 

  14. R.C.T. da Costa, Phys. Rev. A 23, 1982 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  15. R.C.T. da Costa, Phys. Rev. A 25, 2893 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  16. S. Matsutani, J. Phys. Soc. Jpn. 61, 3825 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  17. Luiz C.B. da Silva, Cristiano C. Bastos, Fábio G. Ribeiro, Ann. Phys. 379, 13 (2017)

    Article  ADS  Google Scholar 

  18. G. Ferrari, G. Cuoghi, Phys. Rev. Lett. 100, 230403 (2008)

    Article  ADS  Google Scholar 

  19. Y.L. Wang, L. Du, C.T. Xu, X.J. Liu, H.S. Zong, Phys. Rev. A 90, 042117 (2014)

    Article  ADS  Google Scholar 

  20. Mark Burgess, B. Jensen, Phys. Rev. A. 48(3), 1861 (1993)

    Article  ADS  Google Scholar 

  21. J. González, J. Herrero, Nucl. Phys. B 825, 426 (2010)

    Article  ADS  Google Scholar 

  22. R. Pincak, J. Smotlacha, Quantum Matter 5, 114 (2016)

    Article  Google Scholar 

  23. R. Dandoloff, Phys. Lett. A 373, 2667–2669 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  24. R. Dandoloff, A. Saxena, B. Jensen, Phys. Rev. A 81, 014102 (2010)

    Article  ADS  Google Scholar 

  25. M. Spivak, A Comprehensive Introduction to Differential Geometry (Publish or Perish, Houston, 1999)

    MATH  Google Scholar 

  26. H. Terrones, A.L. Mackay, Chem. Phys. Lett. 207, 45 (1993)

    Article  ADS  Google Scholar 

  27. J.E.G. Silva et al., Phys. Lett. A 384, 126458 (2020)

    Article  MathSciNet  Google Scholar 

  28. Y.N. Joglekar, A. Saxena, Phys. Rev. B 80, 153405 (2009)

    Article  ADS  Google Scholar 

  29. A. Sinner, K. Ziegler, Ann. Phys. 400, 262–278 (2019)

    Article  ADS  Google Scholar 

  30. M.G. Burt, J. Phys. Condens. Matter 4(32), 6651 (1992)

    Article  ADS  Google Scholar 

  31. S.Y. Ren, Y.-C. Chang, Ann. Phys. 325(5), 937–947 (2010)

    Article  ADS  Google Scholar 

  32. J.M. Lévi-Le-Blond, Phys. Rev. A 52, 1845 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  33. Gang Chen, Zi-dong Chen, Phys. Lett. A 331, 312 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  34. F. Serafim et al., Phys. E 108, 139 (2019)

    Article  Google Scholar 

  35. Pedro H. Souza et al., Ann. Phys. 530, 1800112 (2018)

    Article  MathSciNet  Google Scholar 

  36. T.J. Willmore, J. Lond. Math. Soc. 3, 307 (1971)

    Article  Google Scholar 

  37. W. Helfrich, Z. Nat. C 28, 693 (1973)

    Google Scholar 

  38. M.A. Khamehchi et al., Phys. Rev. Lett. 118, 155301 (2017)

    Article  ADS  Google Scholar 

  39. D. Yiqun et al., Phys. Rev. Lett. 99, 093904 (2007)

    Article  ADS  Google Scholar 

  40. D. Strasser et al., Phys. Rev. Lett. 89, 283204 (2002)

    Article  Google Scholar 

  41. C.M. Bender, Rept. Prog. Phys. 70, 947 (2007)

    Article  ADS  Google Scholar 

  42. C.M. Bender, S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  43. H.F. Jones, J. Mateo, Phys. Rev. D 73, 085002 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  44. A.A. Andrianov, Phys. Rev. D 76, 025003 (2007)

    Article  ADS  Google Scholar 

  45. A.A. Andrianov, Ann. Phys. 140, 82 (1982)

    Article  ADS  Google Scholar 

  46. A.C.A. Ramos, G.A. Farias, N.S. Almeida, Phys. E 43, 1878 (2011)

    Article  Google Scholar 

  47. M. Novaes, N. Studart, Mecânica Quântica Básica - São Paulo: Editora Livraria da Física (Série MNPEF), (2016)

Download references

Acknowledgements

J. E. G. Silva thanks the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Grants n\(^{\underline{\hbox {o}}}\) 312356/2017-0 for financial support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Furtado.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Silva, J.E.G., Furtado, J. & Ramos, A.C.A. Position-dependent mass effects on a bilayer graphene catenoid bridge. Eur. Phys. J. B 94, 127 (2021). https://doi.org/10.1140/epjb/s10051-021-00138-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-021-00138-3

Navigation