7. Superconductivity - University of Liverpool

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Type II superconductors. The existence of vortices is in fact not consistent with Meissner’s effect. We have learnt that when a metal becomes superconducting, it expels all magnetic field (except for some near its surface). A vortex in a superconductor is a circulating current. This must produce a magnetic field in the superconductor. This contradicts the Meissner’s effect. It turns out that the Meissner’s effect is only true for some metals - mainly pure metals. These are called Type I superconductors. For alloys and other materials, it is possible for magnetic field to penetrate the body of the superconductor to some extent. Superconductivity 35
Type II superconductors. This shows the magnetisation of Lead alloy with different amount of Indium: Below a certain critical field, the magnetisation (e.g. OB) is strong enough to cancel the applied field. For higher field, the magnetisation decreases (e.g. curve to the right of B). It is not enough to cancel the applied field, which then penetrates the superconductor. These are called type II superconductors. Superconductivity 36
Page 1 and 2: Statistical and Low Temperature Phy
Page 3 and 4: Resistance, magnetic field and heat
Page 5 and 6: Examples of superconductors. http:/
Page 7 and 8: Measuring magnetic field. This grap
Page 9 and 10: Heat capacity. Recall the heat capa
Page 11 and 12: If we select the normal conducting
Page 13 and 14: Explanation using macroscopic wavef
Page 15 and 16: Lenz’s law. According to Lenz’s
Page 17 and 18: Macroscopic wavefunction. We shall
Page 19 and 20: Ampere’s law. The right side of t
Page 21 and 22: ∫ ∆φ = m ∫L v.dl + q A.dl. L
Page 23 and 24: Meissner effect. According to Farad
Page 25 and 26: London’s penetration depth. Flux
Page 27 and 28: London penetration depth Assuming t
Page 29 and 30: Integrating the current along a cir
Page 31 and 32: Combining with the solenoid formula
Page 33 and 34: Vortices. In the lectures on superf
Page 35: Likewise, Essmann and Trauble sprin
Page 39 and 40: Flux measurement. Deaver and Fairba
Page 41 and 42: In the case of the superfluid, no m
Page 43 and 44: So if we choose the loop L away fro
Page 45 and 46: Cooper pairs Superconductivity 44
Page 47 and 48: The Isotope Effect. If electrons re
Page 49 and 50: How electrons “attract” When a
Page 51 and 52: Cooper pair in real space The wavef
Page 53 and 54: Energy gap. As an example of a pred
Page 55 and 56: BCS superfluid. The most obvious pr
Page 57 and 58: Cooper pair The average charge in a
Page 59 and 60: When a lattice vibrates the maximum
Page 61 and 62: This is also the length, or extent,
Page 63 and 64: It has an energy 2E F − ∆, wher
Page 65 and 66: Applications of superconductors Sup
Page 67 and 68: Maglev train. A train can be levita
Page 69 and 70: Particle accelerators Particle acce
Page 71 and 72: High Temperature Superconductors In
Page 73: Applications? Using these high temp

7. Superconductivity - University of Liverpool

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