Superconductivity: Quantum Uncertainty of the Number of Carriers and Stability of the Superconducting Phase
( Pp. 312-321)
More about authors
Rakhimov Rustam Kh.
Dr. Sci. (Eng.); Head, Laboratory No. 4, Institute of Materials Science; Academy of Sciences of the Republic of Uzbekistan; Tashkent, Republic of Uzbekistan
Академия наук Республики Узбекистан
г. Ташкент, Республика Узбекистан Yermakov Vladimir P. senior research, Laboratory No. 4, Institute of Materials Science; Academy of Sciences of the Republic of Uzbekistan; Tashkent, Republic of Uzbekistan
Академия наук Республики Узбекистан
г. Ташкент, Республика Узбекистан Yermakov Vladimir P. senior research, Laboratory No. 4, Institute of Materials Science; Academy of Sciences of the Republic of Uzbekistan; Tashkent, Republic of Uzbekistan
Abstract:
The article addresses the conceptual link between quantum uncertainty in the number of charge carriers and the stability of the macroscopic superconducting phase. It is shown that a condensate of Cooper pairs characterized by a well-defined global phase is mathematically equivalent to a superposition of states with different pair numbers, so that local charge is effectively delocalized across the condensate. Building on this premise, the paper develops the notion of superconductor polarizability as a parameter governing the energetic cost of charge redistribution and, consequently, the critical characteristics of the material – critical current Ic and critical field Hc. Four classes of systems in which number-phase fluctuations are particularly pronounced are examined: thin films, granular superconductors, cuprates, and high-pressure hydrides. Experimental techniques for detecting these fluctuations (STM/STS spectroscopy, impedance spectroscopy, noise measurements) and the relevant theoretical frameworks (BCS theory, Ginzburg–Landau theory, strong-correlation models) are reviewed. The conclusion argues that superconductivity stability is governed by the balance between phase coherence and the energetic penalty for charge localization, and justifies the requirement for a comprehensive assessment of phase stiffness when evaluating claims of high-temperature superconductivity.
How to Cite:
Rakhimov R.Kh. and Yermakov V.P. Superconductivity: Quantum uncertainty of the number of carriers and stability of the superconducting phase. Computational Nanotechnology. 13, 2 (2026), 312–321. DOI: 10.33693/2313-223X-2026-13-2-312-321. EDN: XERUIY
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Bardeen J., Cooper L.N., Schrieffer J.R. Theory of superconductivity. Physical Review. 1957. Vol. 108. Pp. 1175–1204. DOI: 10.1103/PhysRev.108.1175.
Blatter G. et al. Vortices in high-temperature superconductors. Reviews of Modern Physics. 1994. Vol. 66. Pp. 1125–1388. DOI: 10.1103/RevModPhys.66.1125.
Dagotto E. Complexity in strongly correlated electronic systems. Science. 2005. Vol. 309. Pp. 257–262. DOI: 10.1126/science.1107559.
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Emery V.J., Kivelson S.A. Importance of phase fluctuations in superconductors with small superfluid density. Nature. 1995. Vol. 374. Pp. 434–437. DOI: 10.1038/374434a0.
Fischer O. et al. Scanning tunneling spectroscopy of high-temperature superconductors. Reviews of Modern Physics. 2007. Vol. 79. Pp. 353–419. DOI: 10.1103/RevModPhys.79.353.
Gantmakher V.F., Dolgopolov V.T. Superconductor – insulator quantum phase transition. Physics-Uspekhi. 2010. Vol. 53. Pp. 1–49. DOI: 10.3367/UFNe.0180.201002a.0025.
Ginzburg V.L., Landau L.D. On the theory of superconductivity. JETF. 1950. Vol. 20. Pp. 1064–1082.
Goldman A.M., Marković N. Superconductor – insulator transitions in the two-dimensional limit. Physics Today. 1998. Vol. 51. Pp. 39–44. DOI: 10.1063/1.881145.
Haviland D.B., Liu Y., Goldman A.M. Onset of superconductivity in the two-dimensional limit. Physical Review Letters. 1989. Vol. 62. Pp. 2180–2183. DOI: 10.1103/PhysRevLett.62.2180.
Ioffe L.B., Millis A.J. Phase fluctuations and the pseudo gap in cuprates. arXiv. DOI: cond-mat/9808005,
Lee P.A., Nagaosa N., Wen X.-G. Doping a Mott insulator: Physics of high-temperature superconductivity. Reviews of Modern Physics. 2006. Vol. 78. Pp. 17–85. DOI: 10.1103/RevModPhys.78.17. arXiv: cond-mat/0410445
Nambu Y. Quasi-particles and gauge invariance in the theory of superconductivity. Physical Review. 1960. Vol. 117. Pp. 648–663. DOI: 10.1103/PhysRev.117.648.
Sondhi S.L., Girvin S.M., Carini J.P., Shahar D. Continuous quantum phase transitions. Reviews of Modern Physics. 1997. Vol. 69. Pp. 315–333. DOI: 10.1103/RevModPhys.69.315.
Tinkham M. Introduction to superconductivity. 2nd ed. Dover Publications, 2004. ISBN: 978-0486435039.
Keywords:
superconductivity, number-phase uncertainty relation, charge fluctuations, polarizability, critical current, super insulator, Cooper pairs, thin films.
