Superconductors Model superconductors Gorkov and Eliashberg found the
Superconductors
• Model superconductors • Gor’kov and Eliashberg found the timedependent G-L equations using microscopic theory: • These equations are solved numerically 9/16/2020 2
Fluxons moving into a Superconductor Coated With a Normal Metal, = 5 as the applied magnetic field increases • H = 0. 05 Hc 2 • The material is in the Meissner state 9/16/2020 3
Magnetization Loop • H = 0. 10 Hc 2 • The material is in the Meissner state 9/16/2020 4
Magnetization Loop • H = 0. 15 Hc 2 • The material is in the mixed state 9/16/2020 5
Magnetization Loop • H = 0. 20 Hc 2 • The material is in the mixed state 9/16/2020 6
Magnetization Loop • H = 0. 25 Hc 2 • The material is in the mixed state 9/16/2020 7
Magnetization Loop • H = 0. 30 Hc 2 • Note the nucleation of fluxons at the superconductor 9/16/2020 normal boundary 8
Magnetization Loop • H = 0. 35 Hc 2 • Note the nucleation of fluxons at the superconductor 9/16/2020 normal boundary 9
Magnetization Loop • H = 0. 40 Hc 2 • Note the nucleation of fluxons at the superconductor 9/16/2020 normal boundary 10
Magnetization Loop • H = 0. 45 Hc 2 • Note the nucleation of fluxons at the superconductor 9/16/2020 normal boundary 11
Magnetization Loop • H = 0. 50 Hc 2 • Note the nucleation of fluxons at the superconductor 9/16/2020 normal boundary 12
Magnetization Loop • H = 0. 55 Hc 2 • In the reversible region, one can determine 9/16/2020 13
Magnetization Loop • H = 0. 60 Hc 2 • In the reversible region, one can determine 9/16/2020 14
Magnetization Loop • H = 0. 65 Hc 2 • In the reversible region, one can determine 9/16/2020 15
Magnetization Loop • H = 0. 70 Hc 2 • In the reversible region, one can determine 9/16/2020 16
Magnetization Loop • H = 0. 75 Hc 2 • In the reversible region, one can determine 9/16/2020 17
Magnetization Loop • H = 0. 80 Hc 2 • The core of the fluxons overlap and the average value of the order 9/16/2020 parameter drops 18
Magnetization Loop • H = 0. 85 Hc 2 • The core of the fluxons overlap and the average value of the order 9/16/2020 parameter drops 19
Magnetization Loop • H = 0. 90 Hc 2 • The core of the fluxons overlap and the average value of the order 9/16/2020 parameter drops 20
Magnetization Loop • H = 0. 95 Hc 2 • The core of the fluxons overlap and the average value of the order 9/16/2020 parameter drops 21
Magnetization Loop • H = 1. 00 Hc 2 • Eventually the superconductivity is destroyed 9/16/2020 22
Magnetization Loop • H = 0. 95 Hc 2 • Superconductivity nucleates 9/16/2020 23
Magnetization Loop • H = 0. 90 Hc 2 • Superconductivity nucleates 9/16/2020 24
Magnetization Loop • H = 0. 85 Hc 2 • Superconductivity nucleates 9/16/2020 25
Magnetization Loop • H = 0. 80 Hc 2 • Note the Abrikosov flux-line-lattice with hexagonal 9/16/2020 symmetry 26
Magnetization Loop • H = 0. 75 Hc 2 • Note the Abrikosov flux-line-lattice with hexagonal 9/16/2020 symmetry 27
Magnetization Loop • H = 0. 70 Hc 2 • Note the Abrikosov flux-line-lattice with hexagonal 9/16/2020 symmetry 28
Magnetization Loop • H = 0. 65 Hc 2 • Note the Abrikosov flux-line-lattice with hexagonal 9/16/2020 symmetry 29
Magnetization Loop • H = 0. 60 Hc 2 • Note the Abrikosov flux-line-lattice with hexagonal 9/16/2020 symmetry 30
Magnetization Loop • H = 0. 55 Hc 2 • Note the Abrikosov flux-line-lattice with hexagonal 9/16/2020 symmetry 31
Magnetization Loop • H = 0. 50 Hc 2 • Note the Abrikosov flux-line-lattice with hexagonal 9/16/2020 symmetry 32
Magnetization Loop • H = 0. 45 Hc 2 • The flux-line-lattice is defective 9/16/2020 33
Magnetization Loop • H = 0. 40 Hc 2 • The flux-line-lattice is defective 9/16/2020 34
Magnetization Loop • H = 0. 35 Hc 2 • The flux-line-lattice is defective 9/16/2020 35
Magnetization Loop • H = 0. 30 Hc 2 • The flux-line-lattice is defective 9/16/2020 36
Magnetization Loop • H = 0. 25 Hc 2 • The flux-line-lattice is defective 9/16/2020 37
Magnetization Loop • H = 0. 20 Hc 2 • The flux-line-lattice is defective 9/16/2020 38
Magnetization Loop • H = 0. 15 Hc 2 • The flux-line-lattice is defective 9/16/2020 39
Magnetization Loop • H = 0. 10 Hc 2 • The magnetisation is positive because of flux pinning 9/16/2020 40
Magnetization Loop • H = 0. 05 Hc 2 • The magnetisation is positive because of flux pinning 9/16/2020 41
Magnetization Loop • H = 0. 00 Hc 2 • A few fluxons remain as the inter-fluxon repulsion is lower than the surface pinning 9/16/2020 42
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