Abstract
We study the impact of surface defects on a condensate of electron pairs in a quantum wire. Based on previous results, we formulate a simple mathematical model accounting for such surface effects. For a system of noninteracting pairs, we prove the destruction of the condensate in the bulk. Finally, taking repulsive interactions between the pairs into account, we show that the condensate is recovered for pair densities greater than a critical density if the number of the surface defects is not too large.
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References
J. Kerner, “On pairs of interacting electrons in a quantum wire”, J. Math. Phys., 59, 063504 (2018); arXiv:1801.00696v1 [math-ph] (2018).
J. Kerner, “On bound electron pairs on the half-line”, Rep. Math. Phys., 83, 129–138 (2019).
P. G. de Gennes, “Boundary effects in superconductors”, Rev. Modern Phys., 36, 225–237 (1964).
S. T. Sekula and J. H. Barrett, “Surface effects and low frequency losses in hard superconductors”, Appl. Phys. Lett., 17, 204–205 (1970).
L. Burlachkov, A. E. Koshelev, and V. M. Vinokur, “Transport properties of high-temperature superconductors: Surface vs bulk effect”, Phys. Rev. B, 54, 6750–6757 (1996).
S. Kashiwaya and Y. Tanaka, “Tunnelling effects on surface bound states in unconventional superconductors”, Rep. Progr. Phys., 63, 1641–1724 (2000).
L. V. Belevtsov, “Interplay between surface effects and the magnetic properties in polycrystalline superconductors”, J. Low Temperature Phys., 131, 37–49 (2003).
A. V. Narlikar, The Oxford Handbook of Small Superconductors, Oxford Univ. Press, Oxford (2017).
S. Alexander, “Superconductivity of networks: A percolation approach to the effects of disorder”, Phys. Rev. B, 27, 1541–1557 (1983).
F. R. K. Chung, Spectral Graph Theory (CBMS Regl. Conf. Ser. Math.), Vol. 92, Amer. Math. Soc., Providence, R. I. (1997).
F. Schwabl, Statistical Mechanics, Springer, Berlin (2006).
A. Verbeure, Many-Body Boson Systems: Half a Century Later, Springer, London (2011).
D. Ruelle, Statistical Mechanics: Rigorous Results, W. A. Benjamin, New York (1969).
P. A. Martin and F. Rothen, Many-Body Problems and Quantum Field Theory, Springer, Berlin (2004).
J. Blank, P. Exner, and M. Havliček, Hilbert Space Operators in Quantum Physics, Springer, Berlin (2008).
T. Michoel and A. Verbeure, “Non-extensive Bose-Einstein condensation model”, J. Math. Phys., 40, 1268–1279 (1999).
L. J. Landau and I. F. Wilde, “On the Bose-Einstein condensation of an ideal gas”, Commun. Math. Phys., 70, 43–51 (1979).
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 2, pp. 300–310, May, 2020
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Kerner, J. Impact of surface defects on a condensate of electron pairs in a quantum wire. Theor Math Phys 203, 691–699 (2020). https://doi.org/10.1134/S0040577920050104
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DOI: https://doi.org/10.1134/S0040577920050104