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2004 | 2 | 1 | 220-240

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Critical fields of a superconducting cylinder



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The self-consistent solutions of the nonlinear Ginzburg-Landau equations, which describe the behavior of a superconducting mesoscopic cylinder in an axial magnetic field H (provided there are no vortices inside the cylinder), are studied. Different, vortex-free states (M-, e-, d-, p-), which exist in a superconducting cylinder, are described. The critical fields (H
1, H
2, H
p, H
i, H
r), at which the first or second order phase transitions between different states of the cylinder occur, are found as functions of the cylinder radius R and the GL-parameter
$$\kappa $$
. The boundary
$$\kappa _c (R)$$
, which divides the regions of the first and second order (s, n)-transitions in the icreasing field, is found. It is found that at R→∞ the critical value, is
$$\kappa _c = 0.93$$
. The hysteresis phenomena, which appear when the cylinder passes from the normal to superconducting state in the decreasing field, are described. The connection between the self-consistent results and the linearized theory is discussed. It is shown that in the limiting case
$$\kappa \to {1 \mathord{\left/ {\vphantom {1 {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }}$$
and R ≫ λ (λ is the London penetration length) the self-consistent solution (which correponds to the socalled metastable p-state) coincides with the analitic solution found from the degenerate Bogomolnyi equations. The reason for the existence of two critical GL-parameters
$$\kappa _0 = 0.707$$
$$\kappa _0 = 0.93$$
in, bulk superconductors is discussed.










Physical description


1 - 3 - 2004
1 - 3 - 2004


  • P.N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky pr., 53, 119991, Moscow, Russia


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