7. Superconductivity - University of Liverpool

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It looks like we have just “explained” the Meissner effect. However, let us now look at what happens if the magnet is already there before cooling. We start with a normal metal with a magnetic field going through the body. Then we cool this down and the resistance falls to zero. According to Faraday’s law, since there is no change in magnetic flux, no current is induced. So the original field from the magnet remains in the body. In a real superconductor, we know from the Meissner effect that, even in this case, the magnetic field must be expelled. This shows that there is something different about a superconductor that the familiar laws of electromagnetism cannot explain. Superconductivity 15
Macroscopic wavefunction. We shall now see how a macroscopic wavefunction, ψ, can explain the Meissner effect. Recall the operator in quantum mechanics for momentum: −i dψ dx = p xψ where p is the momentum mv. In the presence of an electromagnetic field, this is changed to −i dψ = (mv + qA)ψ dx where A is the vector potential and q the charge of the particle. http://quantummechanics.ucsd.edu/ph130a/130_notes/node29.html Both equations are quantum mechanical postulates that have been shown to give correct results in physics. Superconductivity 16
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: Lenz’s law. According to Lenz’s
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 and 36: Likewise, Essmann and Trauble sprin
Page 37 and 38: Type II superconductors. This shows
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
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7. Superconductivity - University of Liverpool

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