On a New Equation for Critical Current Density Directly in Terms of the BCS Interaction Parameter, Debye Temperature and the Fermi Energy of the Superconductor


Recasting the BCS theory in the larger framework of the Bethe-Salpeter equation, a new equation is derived for the temperature-dependent critical current density jc(T) of an elemental superconductor (SC) directly in terms of the basic parameters of the theory, namely the dimensionless coupling constant [N(0)V], the Debye temperature θD and, additionally, the Fermi energy EF—unlike earlier such equations based on diverse, indirect criteria. Our approach provides an ab initio theoretical justification for one of the latter, text book equations invoked at T = 0 which involves Fermi momentum; additionally, it relates jc with the relevant parameters of the problem at T ≠ 0. Noting that the numerical value of EF of a high-Tc SC is a necessary input for the construction of its Fermi surface—which sheds light on its gap-structure, we also briefly discuss extension of our approach for such SCs.

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G. Malik, "On a New Equation for Critical Current Density Directly in Terms of the BCS Interaction Parameter, Debye Temperature and the Fermi Energy of the Superconductor," World Journal of Condensed Matter Physics, Vol. 3 No. 2, 2013, pp. 103-110. doi: 10.4236/wjcmp.2013.32017.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. Randeria, “Crossover from BCS Theory to Bose-Einstein Condensation,” In: A. Griffin, D. W. Snoke and S. Stringari, Eds., Bose-Einstein Condensation, Cambridge University Press, Cambridge, 1995, p. 355. doi:10.1017/CBO9780511524240.017
[2] M Tinkham, “Introduction to Superconductivity,” McGraw Hill, New York, 1975.
[3] H. Ibach and H. Lüth, “Solid State Physics,” Springer, Berlin, 1996. doi:10.1007/978-3-642-88199-2
[4] C. P. Bean, “Magnetization of High-Field Superconductors,” Reviews of Modern Physics, Vol. 36, No. 1, 1964, pp. 31-39. doi:10.1103/RevModPhys.36.31
[5] Y. B. Kim, C. F. Hempstead and A. R. Strand, “Magnetization and Critical Supercurrents,” Physical Review, Vol. 129, No. 2, 1963, pp. 528-535. doi:10.1103/PhysRev.129.528
[6] A. S. Alexandrov, “Nonadiabatiic Superconductivity in MgB2 and Cuprates,” 2001. http://arxiv.org/abs/cond-mat/0104413
[7] A. P. Cracknell and K. C. Wong, “The Fermi Surface,” Clarendon Press, Oxford, 1973.
[8] J. C. Campuzano, G. Jennings, M. Faiz, L. Beaulaigue, B. W. Veal, J. Z. Liu, A. P. Paulikas, K. Vandervoort, H. Claus, R. S. List, A. J. Arko and R. J. Bartlett, “Fermi Surfaces of YBa2Cu3O6.9 as seen by Angle-Resolved Photoemission,” Physical Review Letters, Vol. 64, No. 19, 1990, pp. 2308-2311. doi:10.1103/PhysRevLett.64.2308
[9] C. G. Olsson, R. Liu, D. W. Lynch, R. S. List, A. J. Arko, B. W. Veal, P. Z. Jiang and A. P. Paulika, “High-Resolution Angle-Resolved Photoemission Study of the Fermi Surface and the Normal-State Electronic Structure of Bi2Sr2CaCu2O8,” Physical Review B, Vol. 42, No. 1, 1990, pp. 381-386. doi:10.1103/PhysRevB.42.381
[10] D.-H. Lee, “Iron-Based Superconductors: Nodal Rings,” Nature Physics, Vol. 8, 2012, pp. 364-365. doi:10.1038/nphys2301
[11] Y. Zhang, Z. R. Ye, Q. Q. Ge, F. Chen, J. Jiang, M. Xu, B. P. Xie and D. L. Feng, “Nodal Superconducting-Gap Structure in Ferropnictide Superconductor BaFe2(As0.7P0.3)2,” Nature Physics, Vol. 8, 2012, pp. 371-375. doi:10.1038/nphys2248
[12] M. P. Allan, A. W. Rost, A. P. Mackenzie, Y. Xie, J. C. Davis, K. Kihou, C. H. Lee, A. Iyo, H. Eisaki and T.-M. Chuang, “Anisotropic Energy Gaps of Iron-Based Superconductivity from Intraband Quasiparticle Interference in LiFeAs,” Science, Vol. 336, No. 6081, 2012, pp. 563-567. doi:10.1126/science.1218726
[13] G. P. Malik, “On the Equivalence of the Binding Energy of a Cooper Pair and the BCS Energy Gap: A Framework for Dealing with Composite Superconductors,” International Journal of Modern Physics B, Vol. 24, No. 9, 2010, pp. 1159-1172. doi:10.1142/S0217979210055408
[14] G. P. Malik, I. Chávez and M. de Llano, “Generalized BCS Equations and Iron-Pnictide Superconductors,” Journal of Modern Physics, Vol. 4, 2013, pp. 474-480.
[15] E. E. Salpeter, “Mass Corrections to the Fine Structure of Hydrogen-Like Atoms,” Physical Review, Vol. 87, No. 2, 1952, p. 328. doi:10.1103/PhysRev.87.328
[16] G. P. Malik and U. Malik, “High-Tc Superconductivity via Superpropagators,” Physica B, Vol. 336, No. 3-4, 2003, pp. 349-352. doi:10.1016/S0921-4526(03)00302-8
[17] G. P. Malik, “Generalized BCS Equations: Applications,” International Journal of Modern Physics B, Vol. 24, No. 19, 2010, pp. 3701-3712. doi:10.1142/S0217979210055858
[18] G. P. Malik and U. Malik, “A Study of the Thalliumand Bismuth-Based High-Temperature Superconductors in the Framework of the Generalized BCS Equations,” Journal of Superconductivity and Novel Magnetism, Vol. 24, No. 1-2, 2011, pp. 255-260. doi:10.1007/s10948-010-1009-0
[19] A. C. Rose-Innes and E. H. Rhoderic, “Introduction to Superconductivity,” Pergamon, Oxford, 1978.
[20] C. Kittel, “Introduction to Solid State Physics,” Wiley Eastern, New Delhi, 1974.
[21] G. P. Malik, “High-Tc Superconductivity via Superpropagators Revisited,” Physica C, Vol. 468, No. 13, 2008, pp. 949-954. doi:10.1016/j.physc.2008.03.002
[22] G. P. Malik, “On Landau Quantization of Cooper Pairs in a Heat Bath,” Physica B, Vol. 405, 2010, pp. 3475-3481. doi:10.1016/j.physb.2010.05.026

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