We shall discuss the magnetic behaviors associated with the boundary effects for type-Ⅱ superconductors in general orientations. Using previous results, we speculate that the relation among the lower critical field Hc1, the thermodynamic critical field Hc and the upper critical field Hc2, namely Hc2～Hc1Hc2, is still approximately valid for general experimental orientations. More precisely, the magnitudes of Hc1, Hc and Hc2 are consistent with the formulae given for bulk superconductors when the typical size of the superconducting specimen is greater than the coherence length ε, provided the penetration depth λ is substituted by a modified value λm. Consequently, the criterion for observing type-Ⅱ superconducting magnetic behaviors also becomes λm>ε, although the London equation is still governed by λ. In the second part of the paper, we shall also suggest an experiment, based on the fact of Hc1. of superconducting thin films in parallel magnetic field being much higher than that of bulk superconductors, to measure Hc1 precisely, especially for extreme type-Ⅱ superconductors,without influence of the penetration barrier.
Abstract
We shall discuss the magnetic behaviors associated with the boundary effects for type-Ⅱ superconductors in general orientations. Using previous results, we speculate that the relation among the lower critical field Hc1, the thermodynamic critical field Hc and the upper critical field Hc2, namely Hc2～Hc1Hc2, is still approximately valid for general experimental orientations. More precisely, the magnitudes of Hc1, Hc and Hc2 are consistent with the formulae given for bulk superconductors when the typical size of the superconducting specimen is greater than the coherence length ε, provided the penetration depth λ is substituted by a modified value λm. Consequently, the criterion for observing type-Ⅱ superconducting magnetic behaviors also becomes λm>ε, although the London equation is still governed by λ. In the second part of the paper, we shall also suggest an experiment, based on the fact of Hc1. of superconducting thin films in parallel magnetic field being much higher than that of bulk superconductors, to measure Hc1 precisely, especially for extreme type-Ⅱ superconductors,without influence of the penetration barrier.
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] V.L. Ginzburg and L.D. Landau, Zh. Eksperim. i. Theor. Fiz. 20 (1950) 1064.
[2] E. Guyon, F. Meunier and R.S. Thomson, Phys. Rev. 156 (1967) 452.
[3] D. Saint-James and P.G. de Gennes, Phys. Lett. 7 (1963) 306.
[4] Y. Nambu and S.F. Tuan, Phys. Rev. 133 (1964) Al.
[5] This result has been criticized, see Ref. [a], based on the BCS theory. But for an extreme type-Ⅱ superconductor, the Ginzburg-Landau theory is still applicable in our problem.
[6] K. Maki, Physics 1 (1964) 21.
[7] C. Caroli, M. Cyrot and P.G. de Gennes, Solid State Commun. 4 (1966) 17.
[8] J. Pearl, Low Temperature Physics, LT9, eds J. Daunt, et al., Plenum Press, New York (1965)p. 566.
[9] M. Tinkham, Phys. Rev. 129 (1962) 2431.
[10] C.P. Bean and J.D. Livingston, Phys. Rev. Lett. 12 (1964) 14; A.S. Joseph and W.J. Tomasch,Phys. Rev. Lett. 12 (1964) 219; R.W. de Blois and W. de Sorbo, Phys. Rev. Lett. 12 (1964)499.
[11] J.D. Livingston, Phys. Rev. 129 (1963) 1943.
[12] Y.B. XIE, Ph. D thesis USTC (1994).
[13] In this paper, the natural units h= c = 1 are employed.
[14] A.A. Abrikosov, J. Exp. Theor. Phys. (Russian) 32 (1957) 442.
[15] C.R. HU, Phys. Rev. B6 (1972) 1756. This paper corrected the numerical number appeared in Ref.
[14] .
[16] T.P. Orlando and K.A. Delin, Foundations of Applied Superconductivity. Addison-Wesley (1931)p. 387. In this book, Hc1 of a superconducting thin film in parallel magnetic field was solved,but their result contains an error and the numerical correction number was not displayed.
[17] G. Bobel and C.F. Ratto, Solid State Commun. 3 (1965) 177; G. Bobel, Nuovo Cimento 38(1965) 1740. Similarly, the constant 0.08 is corrected to be 0.50 based on Ref.
[15] .
[18] M. Tinkham, Introduction to Superconductivity, McGraw-Hill (1975) p. 148.
[19] D. Saint-James, G. Sarma and E.J. Thomas, Type Ⅱ Superconductivity, Pergamon Press Ltd.(1969).
[20] A detailed proof of this statement was given by Y.B. XIE (1995), submitted for publication.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
基金
Prof. T.D. Lee's NNSF, National Natural Science Foundation of China;Foundation of Ph. D Directing Programme of Chinese Universities;Grant LWTZ-1298 of the Chinese Academy of Science
{{custom_fund}}
PDF(266 KB)
