Spatial structures in a generalized Ginzburg-Landau free energy

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 10, 2005, Pages

  Farid, Abdel Khalek ^a   Yu, Yonggang ^a   Saxena, Avadh ^b   Kumar, Pradeep ^a  

^a University of Florida   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BISMUTH; OXIDE;

ANALYTICAL PARAMETERS; ARTICLE; CALCULATION; DENSITY; ELECTRIC CONDUCTIVITY; ELECTRIC CURRENT; ENERGY; PHASE TRANSITION; PREDICTION; SUPERCONDUCTOR; TEMPERATURE DEPENDENCE;

EID: 20344361934     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.104509     Document Type: Article

References (26)

1. L. D. Landau and E. M. Lifshitz, in Statistical Physics, V. 5 Course of Theoretical Physics Vol. 5, edited by E. M. Lifshitz and L. P. Pitaevskii, 3rd ed. (Butterworth Heinemann, Oxford, 1980), Chap. XIV.
2. D. C. Mattis, Statistical Physics Made Simple (World Scientific, Hackensack, NJ, 2003).
3. L. P. Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization (World Scientific, Singapore, 2000).
4. P. Ehrenfest, Proc. Amsterdam Acad. 36, 153 (1933).
5. Also available in, P. Ehrenfest: Collected Scientific Papers, edited by M. J. Klein (North Holland, Amsterdam, 1959), p. 628.
6. P. Kumar, D. Hall, and R. G. Goodrich, Phys. Rev. Lett. 82, 4532 (1999).
7. P. Kumar, Phys. Rev. B 68, 064505 (2003).
8. P. Kumar and A. Saxena, Philos. Mag. B 82, 1201 (2002).
9. The reasons behind as well as the implications of the following free energy have been discussed in Kumar (See Ref. 6). In brief, the goals are to (a) consider powers of the order parameter which are invariant with respect to the symmetry operations and (b) allow the thermodynamic free energy to have the desired temperature and field dependence. In Ref. 6, there are two expressions for the free energy, one with a weight function as below and the other with a Gaussian-like form similar to Eqs. (9) and (12). These expressions are related via a variable transformation. Because the latter contain fractional powers of the order parameter, we expect that the expressions given below are more likely to be directly related to a microscopic theory.
10. J. R. Schrieffer, Theory of Superconductivity (Perseus Books, Reading, MA, 1999).
11. M. Tinkham, Introduction to Superconductivity, 2nd ed. (McGraw-Hill, New York, 1996).
12. D. Hall, R. G. Goodrich, C. G. Grenier, P. Kumar, M. Chaparala, and M. Norton, Philos. Mag. B 80, 61 (2000).
13. M. F. Hundley, J. D. Thompson, and G. H. Kwei, Solid State Commun. 70, 1155 (1989).
14. There have been reports of small discontinuities, such as in B. F. Woodfield, D. A. White, R. A. Fisher, N. E. Phillips, and H. Y. Tang, Phys. Rev. Lett. 83, 4622 (1999). These authors cite the small discontinuity as a reason for the phase transtion in BKBO being of a standard second order. However, their possible consistency with a vanishing specific heat discontinuity is discussed in Ref. 6. That a higher order transition could look like a smeared discontinuity, but that the temperature dependence of the superfluid density (as measured by the London penetration length) would have a characteristic temperature dependence. Regardless of whether the interpretations of Ref. 5 or those of Woodfield et al. stand the test of time, the model free energies in Eqs. (2) and (3) are worth examining for their consequences, as in the results reported here.
15. A. Junod, A. Erb, and C. Renner, Physica C 317-318, 333 (1999).
16. F. Sharifi, A. Pargellis, R. C. Dynes, B. Miller, E. S. Hellman, J. Rosamilia, and E. H. Hartford, Jr., Phys. Rev. B 44, 12 521 (1991);
17. P. Szabo, P. Samuely, L. N. Bobrov, J. Marcus, C. Escribe-Filippini, and M. Affronte, Physica C 235, 1873 (1994).
18. D. R. Nelson, Defects and Geometry in Condensed Matter Physics (Cambridge University Press, Cambridge, 2002).
19. V. P. Mineev, Topologically Stable Defects and Solitons in Ordered Media, (Harwood Academic, Amsterdam, 1998).
20. 3He (Taylor and Francis, London, 1990).
21. Here we limit ourselves to those defects that are described by a GL type free energy in Eqs. (2) and (3).
22. J. S. Langer and V. Ambegaokar, Phys. Rev. 164, 498 (1967); also see, M. Tinkham, in Ref. 10, p. 288.
23. N. S. Manton, Nucl. Phys. B 150, 397 (1979).
24. D. E. McCumber and B. I. Halperin, Phys. Rev. B 1, 1054 (1970).
25. B. I. Ivlev and N. B. Kopnin, J. Low Temp. Phys. 44, 453 (1981).
26. A. Khare, A. Saxena, and P. Kumar (unpublished).