Type II superconductors Superconductivity: outline of 10.10 Superconductor in magnetic field Thin superconductor in magnetic field Interface energy Type II superconductors Mixed phase Abrikosov vortices Pinning and Dissipation Applications Superconductor in magnetic field Superconductor in magnetic field SC N H H c H H c Superconductor in magnetic field H.ds NI H NI L non-sc: F a r 0 L F n r 1 L 1 0H sc: F b r 0 L F s r 1 r 0 L 1 0H At H H c F n F s 1 0H c we have F a F b r 0 L F n F s r 0 L 1 0H c 0 Has the normal state the lowest energy? Superconductor in magnetic field F n F s 1 0H c H NI L Upon n sc induction! F ext a b VI dt a b N d dt NI r 0 0 H c L r 0 0 H c F ext /L r 0 0 H c F n F s 1 0H c I dt N a b I 1
B x B x 0 exp z/ L Flux penetration B L B 0 j L j 0 B x z L B x 0 j y z L j y 0 j y j y 0 exp z/ L Thin superconductor in magnetic field B x z L B x 0 B x B x 0 exp z/ L B 1 B exp z/ L B B exp z/ L L m 0 n se London penetration depth L Thin superconductor in magnetic field B d B cosh d L B 0 B B 0 cosh ' L B z B 0 cosh z ' L d d cosh ' L rather flat is small H c can be larger B 1 B exp z/ L B B exp z/ L B B cosh z/ L Thin superconductor in magnetic field rather flat superconducting state does not have to pay 1 H cb c Effective H c is increased (Thin) superconductor in magnetic field S/N Interface energy Break up in lamina increases H c Does this always happen? Generally: no Because creating the interface costs energy B 1 exp z/ L n C exp z/ coh pay gain coh CP Let s calculate the energies
S/N Interface energy S/N Interface energy 1 0H c coh L coh L positive interface energy make as few as possible type I 500 µm In normal conductor E B and E con are zero Deep inside the SC they are equal: E B E con 1 0H c V (energy per volume) E E con E B 1 0H c 1 e z/ coh 1 e z/ L 0 Edz 1 0H c coh L (energy per surface area) coh L negative interface energy make as many as possible type II S/N Interface energy 1 0H c coh L coh L positive interface energy make as few as possible coh L negative interface energy make as many as possible CP E F 0 k F Type II superconductors L m 0 n se smaller mfp coh L type II alloys are type II, elements type I (not always true, e.g. Nb is type II) Type II superconductors Mixed phase Mixed phase Shubnikov phase Meissner effect Meissner phase 3
Mixed phase Superconductors expel magnetic field I 0 H ext Mixed phase Superconductors expel magnetic field I 0 H ext vortex h Φ 0 = e Abrikosov vortices B Abrikosov vortex λ Φ = h 0 e B ξ Mixed phase Hexagonal lattice Hexagonal lattice of vortices 40 nm 4
Abrikosov lattice (neutron scattering) Abrikosov Nobel prize 003 0.18 H c 0.70 H c Lifting a superconductor Gradient in vortex density At high fields: fieldlines penetrate the sc through vortices Vortices are pinned Gradient in density J.H. Johanson - University of Oslo Current in bulk of type II superconductor Bean model = sand heap Η Η 0 0 5
The vortex sand-heap Movie: flux penetration J.H. Johanson University of Oslo Experimental technique: the Faraday effect Superconducting ring 0 H ext 15 µm 3000 µm YBa Cu 3 O 7 T c = 91 K 100 nm thick J c =5 10 11 A/m Pulsed Laser Deposition time Fixed sweep rate, variable display speed Experiment on a superconducting ring Experiment on a superconducting ring: First penetration after ZFC M H ext H j 6
Experiment on a superconducting ring: Field reversal M Flux penetration in a disk with a square array of anti-dots H ext H j Disk with rectangular array of anti-dots B t E P/V j E pin the vortices! Dissipation B j F L Application: train Application: train 7
Superconducting magnet 7T Nb 3 Sn: > 3 T Superconducting magnet LLL 375 ton NbTi The news from 8 nov 006: Atlas detector Large Hadron Collider 4T field 1kA current 8pc 5x5m 6wk cooldown 1 GJ magnetic energy Magnetic Resonance MRI Magnet Imaging Magnet Superconductivity+Spin Magnetic Resonance Imaging Aorta Hart 8
Hart Brain 9