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Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory

100%

Zharkov G.

Open Physics

2005

vol. 3

issue 1

77-103

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, $$\bar n$$ ,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, $$\kappa _0 = {1 \mathord{\left/ {\vphantom {1 {\sqrt 2 = 0.707}}} \right. \kern-\nulldelimiterspace} {\sqrt 2 = 0.707}}$$ and $$\kappa _0 = 0.93$$ , which divide bulk SC into three groups (with $$\kappa< \kappa _0 ,\kappa _0 \leqslant \kappa \leqslant \kappa _c $$ and $$\kappa > \kappa _c $$ ), in accordance with the behavior in a magnetic field. The parameters $$\kappa _0 $$ and $$\kappa _c $$ mark the boundary for the existence of a supercooled normal $$\bar n$$ -state in FD-regime and a superheated SC M-state in FI-regime respectively. It is shown, that the value $$\kappa _* = 0.417$$ , which was claimed in a number of papers as related to type-I superconductors, is illusory.

Critical fields of a superconducting cylinder

100%

Zharkov G.

Open Physics

2004

vol. 2

issue 1

220-240

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 $$\kappa _0 = 0.707$$ and $$\kappa _0 = 0.93$$ in, bulk superconductors is discussed.

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Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory

Critical fields of a superconducting cylinder