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2004 | 2 | 1 | 220-240
Tytuł artykułu

Critical fields of a superconducting cylinder

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Języki publikacji
EN
Abstrakty
EN
The self-consistent solutions of the nonlinear Ginzburg-Landau equations, which describe the behavior of a superconducting mesoscopic cylinder in an axial magnetic field H (provided there are no vortices inside the cylinder), are studied. Different, vortex-free states (M-, e-, d-, p-), which exist in a superconducting cylinder, are described. The critical fields (H 1, H 2, H p, H i, H r), at which the first or second order phase transitions between different states of the cylinder occur, are found as functions of the cylinder radius R and the GL-parameter $$\kappa $$ . The boundary $$\kappa _c (R)$$ , which divides the regions of the first and second order (s, n)-transitions in the icreasing field, is found. It is found that at R→∞ the critical value, is $$\kappa _c = 0.93$$ . The hysteresis phenomena, which appear when the cylinder passes from the normal to superconducting state in the decreasing field, are described. The connection between the self-consistent results and the linearized theory is discussed. It is shown that in the limiting case $$\kappa \to {1 \mathord{\left/ {\vphantom {1 {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }}$$ and R ≫ λ (λ is the London penetration length) the self-consistent solution (which correponds to the socalled metastable p-state) coincides with the analitic solution found from the degenerate Bogomolnyi equations. The reason for the existence of two critical GL-parameters $$\kappa _0 = 0.707$$ and $$\kappa _0 = 0.93$$ in, bulk superconductors is discussed.
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Wydawca

Czasopismo
Rocznik
Tom
2
Numer
1
Strony
220-240
Opis fizyczny
Daty
wydano
2004-03-01
online
2004-03-01
Twórcy
autor
  • P.N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky pr., 53, 119991, Moscow, Russia
Bibliografia
  • [1] V.L. Ginzburg and L.D. Landau: “To the theory of superconductivity”, Zh. Exp. Teor. Fyz., Vol. 20, (1950), pp. 1064–1082.
  • [2] A.A. Abrikosov: Fundamentals of the Theory of Metals, North-Holland, Amsterdam, 1988.
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  • [4] P.G. deGennes, Superconductivity of Metals and Alloys, Addison-Wesley, New York, 1989.
  • [5] D. Saint-James, G. Sarma, E.J. Thomas, Type II superconductivity, Pergamon, Oxford, 1969.
  • [6] G.F. Zharkov: “First and second order phase transitions and magnetic hysteresis in a superconducting plate”, J. Low Temp. Phys., Vol. 130, (2003), pp. 45–67. http://dx.doi.org/10.1023/A:1021845418088[Crossref]
  • [7] A.Yu. Tsvetkov, G.F. Zharkov, V.G. Zharkov: “Superconducting plate in a magnetic field”, Krat. Soob. Fyz. FIAN, Vol. 2, (2003), pp. 42–50.
  • [8] G.F. Zharkov, V.G. Zharkov, A.Yu. Tsvetkov: “GL-calculations, for superconducting cylinder in a magnetic field”, Phys. Rev. B, Vol. 61, (2000), pp. 12293–12312. http://dx.doi.org/10.1103/PhysRevB.61.12293[Crossref]
  • [9] G.F. Zharkov: “The emergence of superconductivity and hysteresis in a type-I superconducting cylinder”, Zh. Exp. Teor. Fyz., Vol. 122, (2002), pp. 600–609.
  • [10] G.F., Zharkov, V.G. Zharkov, A.Yu. Tsvetkov: “Self-consistent solutions of GL-equations and superconducting edge-states in a magnetic field” Krat. Soob. Fyz. FIAN, (2001), pp. 35–48; “One-dimensional solutions of GL-equations for superconducting cylinder in magnetic field”, ibid, N 12, pp. 31–38 (2001).
  • [11] G.F. Zharkov: “Transitions of I- and II-order in magnetic field for superconducting cylinder obtained from self-consistent solution of GL-equations”, Phys. Rev. B, Vol. 63, (2001), pp. 224513–224519. http://dx.doi.org/10.1103/PhysRevB.63.224513[Crossref]
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  • [16] E.B. Bogomolnyi: “Stability of classical solutions”, Yad Phys., Vol. 24, (1976), pp. 861–870.
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  • [18] A.M. Gulian and G.F. Zharkov: Nonequilibrium Electrons and Phonons in Superconductors, Kluwer/Plenum, New York, 1999.
  • [19] H.J. Fink and A.G. Presson: “Superheating, of the Meissner state and the giant vortex state of a cylinder of finite extent”, Phys. Rev., Vol. 168, (1968), pp. 399–402. http://dx.doi.org/10.1103/PhysRev.168.399[Crossref]
  • [20] H.J. Fink, D.S. McLachlan and B. Rothberg-Bibby: “First and second order phase transitions in moderately small superconductors in a magnetic field”, In: Prog. in Low Temp. Phys.”, (Ed.): Vol. VIIb, D. F. Brewer North Holland, Amsterdam, 1978, pp. 435–516.
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  • [22] F.M., Peeters et. al: Superlatt. and Microstruct., Vol. 25, (1999), pp. 1195; “Hysteresis in mesoscopic superconducting disks”, Phys. Rev. B, Vol. 59 (1999), pp. 6039–6042; “Vortex structure of thin, mesoscopic disks with enhanced surface superconductivity”, ibid, Vol. 62, (2000), pp. 9663–9687; “Superconducting properties of mesoscopic cylinders with enhanced surface superconductivity”, ibid, Vol. 65, (2002), pp. 024510(10). http://dx.doi.org/10.1006/spmi.1999.0734[Crossref]
  • [23] J.J. Palacios: “Vortex matter in, superconducting mesoscopic disks”, Phys. Rev. B, Vol. 58, (1998), pp. R5948-R5951; “Flux penetration and expulsion in thin superconducting disks”, Phys. Rev. Lett., Vol. 83, (1999), pp. 2409–2412; “Stability and paramagnetism in superconducting mesoscopic disks”, Phys. Rev. Lett., Vol. 84, (2000), pp. 1796–1880. http://dx.doi.org/10.1103/PhysRevB.58.R5948[Crossref]
  • [24] V.V. Moshchalkov et al.: “Effect of sample topology on the critical fields of mesoscopic superconductors”, Nature, Vol. 373, (1995), pp. 319–322; “Symmetry-induced formation of antivortices in mesoscopic superconductors”, Nature, Vol. 408, (2000), pp. 833–835. http://dx.doi.org/10.1038/373319a0[Crossref]
  • [25] A.K. Geim et. al.: “Phase transitions in individual sub-micrometer superconductors”. Nature, Vol. 390 (1997), pp. 259–262; “Paramagnetic Meissner effect in small superconductors”, Nature, Vol. 396, (1998), pp. 144–146; “Non-quantized penetration of magnetic field in the vortex state of superconductors”, Nature, Vol. 407, (2000), pp. 55–57; “Fine structure in magnetization of individual fluxoid states”, Phys. Rev. Lett., Vol. 85, (2000), pp 1528–1532. http://dx.doi.org/10.1038/36797[Crossref]
  • [26] D.S. McLachlan: “Quantum oscillations and the order of the phase charge in a low \(\kappa \) type-II superconducting microcylinder”, Solid State Commun., Vol 8, (1970), pp. 1589–1593; “(II) Quantum oscillations, pinning and the superheating and other critical fields in a low \(\kappa \) type-II superconducting microcylinder”, ibid, pp. 1595–1599. http://dx.doi.org/10.1016/0038-1098(70)90470-9[Crossref]
  • [27] O. Buisson, et al.: “Magnetization oscillations of a superconducting disk”, Phys. Lett. A., Vol. 150, (1990), pp. 36–42. http://dx.doi.org/10.1016/0375-9601(90)90056-T[Crossref]
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Bibliografia
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