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Zeeman-Stark problem in a two-dimensional disk

Thomas Garm Pedersen*

  • Department of Materials and Production, Aalborg University, DK-9220 Aalborg Øst, Denmark

  • *tgp@mp.aau.dk
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Phys. Rev. A 107, 052207 – Published 9 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.052207

Abstract

Under a perpendicular magnetic field, electrons in two-dimensional disks occupy quantum-confined Landau levels. By analyzing the electric polarizability of such states, we reveal an extreme sensitivity to confinement. Hence, an exponential increase with magnetic field or disk size is found and ascribed to the linear Zeeman effect. In contrast, if the balance between linear and quadratic Zeeman terms is slightly reduced, due to, e.g., addition of a nonmagnetic parabolic potential, the polarizability varies nonmonotonically with field strength and eventually vanishes. The analysis is based on a compact exact expression for the polarizability valid for arbitrary magnetic field, disk size, and linear Zeeman strength.

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References (26)

  1. R. C. Ashoori, Nature (London) 379, 413 (1996).
  2. H. R. Hasse, Proc. Cambridge Philos. Soc. 26, 542 (1930).
  3. K. Tanaka, M. Kobashi, T. Shichiri, T. Yamabe, D. M. Silver, and H. J. Silverstone, Phys. Rev. B 35, 2513 (1987).
  4. T. G. Pedersen, Solid State Commun. 141, 569 (2007).
  5. T. G. Pedersen, H. Mera, and B. K. Nikolić, Phys. Rev. A 93, 013409 (2016).
  6. T. G. Pedersen, S. Latini, K. S. Thygesen, H. Mera, and B. K. Nikolic, New J. Phys. 18, 073043 (2016).
  7. P. Szabó, S. Góger, J. Charry, M. R. Karimpour, D. V. Fedorov, and A. Tkatchenko, Phys. Rev. Lett. 128, 070602 (2022).
  8. T. G. Pedersen, New J. Phys. 19, 043011 (2017).
  9. T. G. Pedersen, Phys. Rev. A 99, 063410 (2019).
  10. M. E. Rensink, Am. J. Phys. 37, 900 (1969).
  11. G. Li, S. V. Branis, and K. K. Bajaj, Phys. Rev. B 47, 15735 (1993).
  12. N. C. van der Vaart, M. P. de Ruyter van Steveninck, L. P. Kouwenhoven, A. T. Johnson, Y. V. Nazarov, C. J. P. M. Harmans, and C. T. Foxon, Phys. Rev. Lett. 73, 320 (1994).
  13. P. C. Main, A. S. G. Thornton, R. J. A. Hill, S. T. Stoddart, T. Ihn, L. Eaves, K. A. Benedict, and M. Henini, Phys. Rev. Lett. 84, 729 (2000).
  14. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1993).
  15. V. C. Aguilera-Navarro, J. F. Gomes, A. H. Zimerman, and K. Ley Koo, J. Phys. A: Math. Gen. 16, 2943 (1983).
  16. S. M. Al-Jaber, Int. J. Theor. Phys. 47, 1853 (2008).
  17. H. G. Laguna and R. P. Sagar, Ann. Phys. 526, 555 (2014).
  18. A. Michels, J. de Boer, and A. Bijl, Physica (Amsterdam) 4, 981 (1937).
  19. C. Laughlin, J. Phys. B 37, 4085 (2004).
  20. B. L. Burrows and M. Cohen, Phys. Rev. A 72, 032508 (2005).
  21. N. L. Manakov, S. I. Marmo, and V. D. Ovsyannikov, JETP 64, 236 (1986).
  22. T. G. Pedersen, Phys. Rev. A 107, 022804 (2023).
  23. T. G. Pedersen, Phys. Lett. A. 382, 1837 (2018).
  24. A. Dalgarno and J. T. Lewis, Proc. R. Soc. London A 233, 70 (1955).
  25. H. A. Mavromatis, Am. J. Phys. 59, 738 (1991).
  26. T. G. Pedersen, Phys. Rev. B 96, 115432 (2017).

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Phys. Rev. A 107, 052207– Published 9 May, 2023
  • Received 27 March 2023
  • Accepted 26 April 2023
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