Skip to main content
Log in

Exciton energies and wave functions in hexagonal boron nitride using Miller and Good’s uniform approach

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

Abstract

In this paper we revisit the work of Miller and Good, which describes an uniform JWKB type of approximation to the solution of quantum problems. This paper, very well known in atomic physics in the 1970’s 1980’s of the last century, did not attract the same attention from the condensed matter community. Contrary to the usual JWKB approach, Miller and Good’s method yields wave functions that do not diverge at the classical turning points. We apply the method in the context of two-dimensional excitons, an important condensed matter system. In particular, we apply our results to excitons in hexagonal boron nitride, solving the corresponding Wannier equation. We compare the semiclassical results with others from the literature and find good agreement.

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

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This work is of theoretical nature and therefore no data exists to store. The codes that led to the figures are available from the authors.]

References

  1. H. Jeffreys, Proc. Lond. Math. Soc. 2(1), 428 (1923)

    Article  MathSciNet  Google Scholar 

  2. D. Gough, Astronomische Nachrichten 328(3–4), 273 (2007)

    Article  ADS  Google Scholar 

  3. R. Blumel, Advanced Quantum Mechanics: The Classical-Quantum Connection (Jones & Bartlett Publishers, Burlington, 2011)

    Google Scholar 

  4. M. Vandyck, Eur. J. Phys. 12(3), 112 (1991)

    Article  Google Scholar 

  5. S.K. Adhikari, M.S. Hussein, Am. J. Phys. 76(12), 1108 (2008)

    Article  ADS  Google Scholar 

  6. M.S. Child, Semiclassical Mechanics with Molecular Applications (Oxford University Press, New York, 2014)

    Book  Google Scholar 

  7. M.V. Berry, K. Mount, Rep. Prog. Phys. 35(1), 315 (1972)

    Article  ADS  Google Scholar 

  8. A. Amthong, Eur. J. Phys. 35(6), 065009 (2014)

  9. M. Arzamasovs, B. Liu, Eur. J. Phys. 38(6), 065405 (2017)

  10. S.C. Miller Jr., R. Good Jr., Phys. Rev. 91(1), 174 (1953)

    Article  ADS  MathSciNet  Google Scholar 

  11. S. Miller Jr., Phys. Rev. 94(5), 1345 (1954)

    Article  ADS  MathSciNet  Google Scholar 

  12. R. Good Jr., Phys. Rev. 90(1), 131 (1953)

    Article  ADS  MathSciNet  Google Scholar 

  13. M. Berry, A.O. de Almeida, J. Phys. A 6(10), 1451 (1973)

    Article  ADS  Google Scholar 

  14. G. Wang, A. Chernikov, M.M. Glazov, T.F. Heinz, X. Marie, T. Amand, B. Urbaszek, Rev. Mod. Phys. 90, 021001 (2018)

    Article  ADS  Google Scholar 

  15. A. Chaves, R. Ribeiro, T. Frederico, N. Peres, 2D Mater. 4(2), 025086 (2017)

    Article  Google Scholar 

  16. K. Zhang, Y. Feng, F. Wang, Z. Yang, J. Wang, J. Mater. Chem. C 5(46), 11992 (2017)

    Article  Google Scholar 

  17. J.D. Caldwell, I. Aharonovich, G. Cassabois, J.H. Edgar, B. Gil, D. Basov, Nat. Rev. Mater. 4(8), 552 (2019)

    Article  Google Scholar 

  18. J. Henriques, G. Ventura, C. Fernandes, N. Peres, J. Phys. Condens. Matter 32(2), 025304 (2020)

    Article  ADS  Google Scholar 

  19. S. Rytova, Mosc. Univ. Phys. Bull. 22, 30 (1967)

    Google Scholar 

  20. L. Keldysh, Sov. J. Exp. Theor. Phys. Lett. 29, 658 (1979)

    ADS  Google Scholar 

  21. T. Galvani, F. Paleari, H.P.C. Miranda, A. Molina-Sánchez, L. Wirtz, S. Latil, H. Amara, F.M.C. Ducastelle, Phys. Rev. B 94, 125303 (2016)

    Article  ADS  Google Scholar 

  22. A.K. Ghatak, R. Gallawa, I. Goyal, NIST 92, 20427 (1991)

    Google Scholar 

  23. I. Goyal, R. Gallawa, A. Ghatak, J. Electromagn. Waves Appl. 5(6), 623 (1991)

    Article  Google Scholar 

  24. J.P. Dahl, W.P. Schleich, J. Phys. Chem. A 108(41), 8713 (2004)

    Article  Google Scholar 

  25. A. Sinha, R. Roychoudhury, Y. Varshni, Phys. B Cond. Matt. 325, 214 (2003)

    Article  ADS  Google Scholar 

  26. M.V. Berry, K. Burke, Eur. J. Phys. 40(6), 065403 (2019)

    Article  Google Scholar 

  27. X. Yang, S. Guo, F. Chan, K. Wong, W. Ching, Phys. Rev. A 43(3), 1186 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  28. S. Ullah, F. Sato, M.G. Menezes, R.B. Capaz, Phys. Rev. B 100, 085427 (2019)

    Article  ADS  Google Scholar 

  29. J.C.G. Henriques, G. Catarina, A.T. Costa, J. Fernández-Rossier, N.M.R. Peres, Phys. Rev. B 101, 045408 (2020)

    Article  ADS  Google Scholar 

  30. M. Selig, G. Berghäuser, A. Raja, P. Nagler, C. Schüller, T.F. Heinz, T. Korn, A. Chernikov, E. Malic, A. Knorr, Nat. Commun. 7, 13279 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge Mike Belsley for carefully reading the manuscript and for comments that allowed to improve the overall presentation. N.M.R.P. acknowledges support from the European Commission through the project “Graphene-Driven Revolutions in ICT and Beyond” (Ref. no. 881603 – core 3), and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2019. In addition, N.M.R.P. acknowledges COMPETE2020, PORTUGAL2020, FEDER and the Portuguese Foundation for Science and Technology (FCT) through projects POCI-01-0145-FEDER-028114, POCI-01-0145-FEDER- 029265, PTDC/NAN-OPT/29265/2017, and POCI-01-0145-FEDER-02888.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. M. R. Peres.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Henriques, J.C.G., Peres, N.M.R. Exciton energies and wave functions in hexagonal boron nitride using Miller and Good’s uniform approach. Eur. Phys. J. B 94, 7 (2021). https://doi.org/10.1140/epjb/s10051-020-00014-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-020-00014-6

Navigation