Time-dependent Ginzburg–Landau approach and its application to superconductivity

• Published in: Superconductor science & technology 2003-08, Vol.16 (8), p.936-940, Article 936
• Main Authors: Zagrodziński, J A, Nikiciuk, T, Abal'osheva, I S, Lewandowski, S J
• Format: Article
• Language: English
• ISSN: 0953-2048; 1361-6668
• DOI: 10.1088/0953-2048/16/8/319

We present a systematic approach to the time-dependent generalization of the Ginzburg-Landau Lagrangian for a lossless medium. We consider a Lagrangian, which contains four arbitrary scalar functions and admits two alternative terms determining the time dependence. Standard variational technique then yields Ginzburg-Landau equations, which coincide with the equations obtained from the corresponding Hamiltonian and determine the energy conservation law. The alternative time-dependent terms lead either to the first, or to the second order time derivatives in the equations. By introducing the gauge-invariant potentials and choosing a gauge, which differs slightly from the classical Lorentz one, we are able to simplify significantly the theory. The results are discussed and compared to some earlier propositions. When the problem involving first order time derivative is reduced to the static case, the results are found to be in perfect agreement with those reported recently by Kolacek et al (Kolacek, Lipavsky and Brandt 2001 Phys. Rev. Lett. 86 312), which may be considered as an indirect indication that this particular alternative form of the theory is better adapted to treat the physical problems.