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Coulomb Interaction in Finite-Width Quantum Rings

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Physics of Quantum Rings

Part of the book series: NanoScience and Technology ((NANO))

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Abstract

Due to the particular confinement and reduced dimensionality of quantum rings, Coulomb interaction plays an important role for their electronic structure. In this chapter, we discuss the dependency of the ground state of an idealized quantum ring contained a small number of interacting electrons on geometric parameters like ring radius, radial confinement and eccentricity. The ring geometry affects both the charge distribution and the spin configuration in a quantum ring. Numerically exact results obtained from path-integral quantum Monte Carlo demonstrate the strong connection between the structure and the total spin of the ground state emerging from the interplay between confinement and Coulomb interaction.

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References

  1. P. Singha Deo, P. Koskinen, M. Koskinen, M. Manninen, Europhys. Lett. 63(6), 846–852 (2003)

    Article  ADS  Google Scholar 

  2. M. Szelag, M. Szopa, J. Phys. Conf. Ser. 104, 012006–012014 (2008)

    Article  Google Scholar 

  3. Y.V. Pershin, C. Piermarocchi, Phys. Rev. B 72(12), 125348 (2005)

    Article  ADS  Google Scholar 

  4. N. Yang, J.-L. Zhu, Z. Dai, J. Phys. Condens. Matter 20(29), 295202–295213 (2008)

    Article  Google Scholar 

  5. T. Chakraborty, P. Pietiläinen, Phys. Rev. B 52, 1932–1935 (1995)

    Article  ADS  Google Scholar 

  6. K. Niemelä, P. Pietiläinen, P. Hyvönen, T. Chakraborty, Europhys. Lett. 36(7), 533–538 (1996)

    Article  ADS  Google Scholar 

  7. F. Pederiva, A. Emperador, E. Lipparini, Phys. Rev. B 66(16), 165314 (2002)

    Article  ADS  Google Scholar 

  8. P. Borrmann, J. Harting, Phys. Rev. Lett. 86(14), 3120–3123 (2001)

    Article  ADS  Google Scholar 

  9. V.M. Fomin (ed.), J. Nanoelectron. Optoelectron. 6(1) (2011)

    Google Scholar 

  10. Y. Saiga, D.S. Hirashima, J. Usukura, Phys. Rev. B 75(4), 045343–045354 (2007)

    Article  ADS  Google Scholar 

  11. P. Koskinen, M. Koskinen, M. Manninen, Eur. Phys. J. B 28(4), 483–489 (2002)

    Article  ADS  Google Scholar 

  12. L.A. Lavenere-Wanderley, A. Bruno-Alfonso, A. Latge, J. Phys. Condens. Matter 14(2), 259–270 (2002)

    Article  ADS  Google Scholar 

  13. D. Gridin, A.T.I. Adamou, R.V. Craster, Phys. Rev. B 69(15), 155317 (2004)

    Article  ADS  Google Scholar 

  14. A. Lorke, J.R. Luyken, A.O. Govorov, J.P. Kotthaus, J.M. Garcia, P.M. Petroff, Phys. Rev. Lett. 84(10), 2223–2226 (2000)

    Article  ADS  Google Scholar 

  15. D.M. Ceperley, Rev. Mod. Phys. 67(2), 279–355 (1995)

    Article  ADS  Google Scholar 

  16. B. Baxevanis, D. Pfannkuche, J. Nanoelectron. Optoelectron. 6(1), 76–80 (2011)

    Article  Google Scholar 

  17. M. Takahashi, M. Imada, J. Phys. Soc. Jpn. 53(3), 963–974 (1984)

    Article  ADS  Google Scholar 

  18. R. Egger, W. Häusler, C.H. Mak, H. Grabert, Phys. Rev. Lett. 83(2), 462 (1999)

    Article  ADS  Google Scholar 

  19. R. Pauncz, The Construction of Spin Eigenfunctions: An Exercise Book (Kluwer Academic/Plenum, New York, 2001)

    Google Scholar 

  20. A.P. Lyubartsev, P.N. Vorontsov-Velyaminov, Phys. Rev. A 48(6), 4075–4083 (1993)

    Article  ADS  Google Scholar 

  21. M. Hamermesh, Group Theory and Its Application to Physical Problems (Dover, New York, 1989)

    Google Scholar 

  22. L. Wendler, V.M. Fomin, A.V. Chaplik, A.O. Govorov, Z. Phys. B, Condens. Matter 100, 211–221 (1996)

    Article  ADS  Google Scholar 

  23. E. Wigner, Phys. Rev. 46(11), 1002–1011 (1934)

    Article  ADS  Google Scholar 

  24. M. Koskinen, M. Manninen, B. Mottelson, S.M. Reimann, Phys. Rev. B 63(20), 205323 (2001)

    Article  ADS  Google Scholar 

  25. P. Hawrylak, D. Pfannkuche, Phys. Rev. Lett. 70(4), 485–488 (1993)

    Article  ADS  Google Scholar 

  26. P.A. Maksym, Phys. Rev. B 53(16), 10871–10886 (1996)

    Article  ADS  Google Scholar 

  27. P.A. Maksym, Physica B, Condens. Matter 184(1–4), 385–393 (1993)

    Article  ADS  Google Scholar 

  28. R. Courant, D. Hilbert, Methods of Mathematical Physics, vol. I (Interscience, New York, 1953)

    Google Scholar 

  29. C. Herring, Phys. Rev. B 11(5), 2056–2061 (1975)

    Article  ADS  Google Scholar 

  30. M. Aizenman, E.H. Lieb, Phys. Rev. Lett. 65(12), 1470–1473 (1990)

    Article  ADS  Google Scholar 

  31. E.H. Lieb, D. Mattis, J. Math. Phys. 3(4), 749–751 (1962)

    Article  ADS  MATH  Google Scholar 

  32. J. Planelles, F. Rajadell, J.I. Climente, Nanotechnology 18(37), 375402–375413 (2007)

    Article  Google Scholar 

  33. A. Bruno-Alfonso, A. Latgé, Phys. Rev. B 77(20), 205303 (2008)

    Article  ADS  Google Scholar 

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Correspondence to Benjamin Baxevanis .

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Baxevanis, B., Pfannkuche, D. (2014). Coulomb Interaction in Finite-Width Quantum Rings. In: Fomin, V. (eds) Physics of Quantum Rings. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39197-2_15

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