Superconductivity fact file (part 2)

• Transition between normal and superconducting state is thermodynamically reversible.
• London's equation is j=-CA/4π(λ_L)² , where λ_L is constant with dimensions of length and A is the vector potential.
• London equation accounts for Meissner effect . In a pure SC state the only field allowed is exponentially damped as we go from an external surface  B(x)=B(0)exp(-x/λ_L)  where λ_Lis the London penetration depth and is the measure of penetration of magnetic field.
• An applied magnetic field will penetrate a thin film fairly uniformly if the thickness is much less than λ_L. Thus in a thin film Meissner effect is not complete.
• Coherence length ξ is the measure of the distance within which SC electronic concentration can not change drastically in spatially varying magnetic field.
• Coherence length is a measure of the range over which we should average A to obtain j.
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Superconductivity fact file (part 1)

• Bulk superconductor in a week magnetic field will act as a perfect diamagnet , with zero magnetic induction in the interior.
• Nonmagnetic impurities have no marked effect on the SC transition temperature.
• A sufficiently strong magnetic field will destroy SC. At critical temperature critical field is zero H_C(T_C)=0
• Values of H_C are always low for type I superconductors.
• For a given H_C the area under magnetization curve is same for type II SC as for type I SC.
• In all SC entropy decreases markedly on cooling below transition temperature.
• Superconducting state is the more ordered state.
• Contribution to the heat capacity in the SC state is an exponential form with an argument proportional to -1/T
• In SC the important interaction is electron-electron interaction which orders the electrons in K space with respect to the fermi gas of the electrons.
• The argument of the exponential factor in the electronic heat capacity of a SC is found to be -E_g/2kT
• The transition in zero magnetic field from the superconducting state to the normal state is the second order phase transition, not involving any latent heat but discontinuity in heat capacity.
• Energy gap decreases continuity to zero as the temperature is increased to transition temperature.
• For photons of energy less than energy gap , the resistivity of the superconductor vanishes at absolute zero.
• As the temperature is increased not only does the gap decreases , but the resistivity for photon with energy below the energy gap no longer vanishes except at zero frequency.