Superconductors

Gor’kov and Eliashberg found the time- dependent G-L equations using microscopic theory: These equations are solved numerically Model superconductors

Fluxons moving into a Superconductor Coated With a Normal Metal,  = 5 as the applied magnetic field increases H = 0.05 H c2 The material is in the Meissner state

H = 0.10 H c2 The material is in the Meissner state Magnetization Loop

H = 0.15 H c2 The material is in the mixed state

Magnetization Loop H = 0.20 H c2 The material is in the mixed state

Magnetization Loop H = 0.25 H c2 The material is in the mixed state

Magnetization Loop H = 0.30 H c2 Note the nucleation of fluxons at the superconductor- normal boundary

Magnetization Loop H = 0.35 H c2 Note the nucleation of fluxons at the superconductor- normal boundary

Magnetization Loop H = 0.40 H c2 Note the nucleation of fluxons at the superconductor- normal boundary

Magnetization Loop H = 0.45 H c2 Note the nucleation of fluxons at the superconductor- normal boundary

Magnetization Loop H = 0.50 H c2 Note the nucleation of fluxons at the superconductor- normal boundary

Magnetization Loop H = 0.55 H c2 In the reversible region, one can determine 

Magnetization Loop H = 0.60 H c2 In the reversible region, one can determine 

Magnetization Loop H = 0.65 H c2 In the reversible region, one can determine 

Magnetization Loop H = 0.70 H c2 In the reversible region, one can determine 

Magnetization Loop H = 0.75 H c2 In the reversible region, one can determine 

Magnetization Loop H = 0.80 H c2 The core of the fluxons overlap and the average value of the order parameter drops

Magnetization Loop H = 0.85 H c2 The core of the fluxons overlap and the average value of the order parameter drops

Magnetization Loop H = 0.90 H c2 The core of the fluxons overlap and the average value of the order parameter drops

Magnetization Loop H = 0.95 H c2 The core of the fluxons overlap and the average value of the order parameter drops

Magnetization Loop H = 1.00 H c2 Eventually the superconductivity is destroyed

Magnetization Loop H = 0.95 H c2 Superconductivity nucleates

Magnetization Loop H = 0.90 H c2 Superconductivity nucleates

Magnetization Loop H = 0.85 H c2 Superconductivity nucleates

Magnetization Loop H = 0.80 H c2 Note the Abrikosov flux-line-lattice with hexagonal symmetry

Magnetization Loop H = 0.75 H c2 Note the Abrikosov flux-line-lattice with hexagonal symmetry

Magnetization Loop H = 0.70 H c2 Note the Abrikosov flux-line-lattice with hexagonal symmetry

Magnetization Loop H = 0.65 H c2 Note the Abrikosov flux-line-lattice with hexagonal symmetry

Magnetization Loop H = 0.60 H c2 Note the Abrikosov flux-line-lattice with hexagonal symmetry

Magnetization Loop H = 0.55 H c2 Note the Abrikosov flux-line-lattice with hexagonal symmetry

Magnetization Loop H = 0.50 H c2 Note the Abrikosov flux-line-lattice with hexagonal symmetry

Magnetization Loop H = 0.45 H c2 The flux-line-lattice is defective

Magnetization Loop H = 0.40 H c2 The flux-line-lattice is defective

Magnetization Loop H = 0.35 H c2 The flux-line-lattice is defective

Magnetization Loop H = 0.30 H c2 The flux-line-lattice is defective

Magnetization Loop H = 0.25 H c2 The flux-line-lattice is defective

Magnetization Loop H = 0.20 H c2 The flux-line-lattice is defective

Magnetization Loop H = 0.15 H c2 The flux-line-lattice is defective

Magnetization Loop H = 0.10 H c2 The magnetisation is positive because of flux pinning

Magnetization Loop H = 0.05 H c2 The magnetisation is positive because of flux pinning

Magnetization Loop H = 0.00 H c2 A few fluxons remain as the inter-fluxon repulsion is lower than the surface pinning