Springer Online Journal Archives 1860-2000
Abstract The structure of an isolated vortex line, and the lower critical fieldH c 1, is calculated by means of the generalized Ginzburg-Landau (GL) theory for arbitrary values of the GL-parameterk(≧1/√2) and the mean free pathl at temperaturesT in the vicinity ofT c . The free energy functional including the corrections of order [1−(T/T c )] to the GL-functional is derived exactly. The corresponding Euler-Lagrange equations determining the zero-order (GL) contributions and the corrections of order [1−(T/T c )] to the order parameter,f(r), and the superfluid velocity,v(r), have been solved numerically. The shapes of the first-order corrections off(r), v(r), and the magnetic field,h(r) are found to depend markedly, for a given value ofκ, on a second parameter,α=0.882(ξ 0 /l) (whereξ 0 is theBCS-coherence-distance). The deviations from the GL-solutions become largest forh(r) at parameter valuesk≈ 1 andα ≈ 0(the deviation ofh(0) is about 6% atT=0.9T c forκ=1 andα=0). The ratioH c1/H c (where the thermodynamic criticalH c has the BCS-temperature-dependence) is found to increase slightly in the “clean” limit (α=0), and to decrease slightly in the “dirty” limit (α=∞) asT decreases (the variation ofH c 1/H c is always less than 3% for arbitrary values ofκ andα asT decreases fromT c to 0.9T c ).
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