Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory |
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Authors: | Gely F Zharkov |
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Institution: | (1) P.N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky pr., 53, 119991 Moscow, Russia |
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Abstract: | Self-consistent solutions of the nonlinear Ginzburg-Landau (GL) equations are investigated numerically for a superconducting
(SC) cylinder, placed in an axial magnetic field, with a single vortex on the axis (m=1). Two modes, which show the original state of the cylinder, SC or normal (s
0 andn
0), are studied. The field increase (FI) and the field decrease (FD) regimes are studied. The critical fields destroying the
SC state withm=1 are found in both regimes. It is shown that in a cylinder of radiusR and GL-parameter ϰ, there exist a number of solutions depending only on the radial co-ordinater corresponding to different states such as M,e, d, p,i, n,
,n
*, and the state diagram on the plane of the variables (ϰ,R) is described. The critical fields corresponding to intrastate transitions and the onset of hysteresis are obtained. The
critical fieldH
0(R) dividing the paramagnetic and diamagnetic states of the cylinder withm=1 is determined. The limiting fields of supercooling or superheating of the normal state at which the restoration of the
SC state occurs are established. It is shown, that (in both casesm=1,0) there exist two critical parameters,
and
, which divide bulk SC into three groups (with
and
), in accordance with the behavior in a magnetic field. The parameters
and
mark the boundary for the existence of a supercooled normal
-state in FD-regime and a superheated SC M-state in FI-regime respectively. It is shown, that the value
, which was claimed in a number of papers as related to type-I superconductors, is illusory.
We regret to inform that Professor Gely Zharkov passed away on 9th July 2004. |
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Keywords: | GL-equations critical fields hysteresis |
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