1. Superconductors

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

3. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

23. Magnetization Loop H = 0.95 H c2 Superconductivity nucleates

24. Magnetization Loop H = 0.90 H c2 Superconductivity nucleates

25. Magnetization Loop H = 0.85 H c2 Superconductivity nucleates

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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