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Boris V. Vasiliev Supercondustivity Superfluidity

Superconductivity and Superfluidity Since at the critical point H c = 0, then from (4.30) this follows directly the Rutgers formula that determines the value of a specific heat jump at the transition point: C s − C n = T 4π ( ) 2 ∂Hc . (4.31) ∂T T c Figure 4.2 Low-temperature heat capacity of normal and superconducting aluminum[25]. The theory of the specific heat of superconductors is well-confirmed experimentally. For example, the low-temperature specific heat of aluminum in both the superconducting and normal states supports this in Figure 4.2. Only the electrons determine the heat 38 Science Publishing Group

Chapter 4 Basic Milestones in the Study of Superconductivity capacity of the normal aluminum at this temperature, and in accordance with the theory of Sommerfeld, it is linear in temperature. The specific heat of a superconductor at a low temperature is exponentially dependent on it. This indicates the existence of a two-tier system in the energy distribution of the superconducting particles. The measurements of the specific heat jump at T c is well described by the Rutgers equation (4.31). 4.3.3 Magnetic Flux Quantization in Superconductors The conclusion that magnetic flux in hollow superconducting cylinders should be quantized was firstly expressed F.London. However, the main interest in this problem is not in the phenomenon of quantization, but in the details: what should be the value of the flux quantum. F. London had not taken into account the effect of coupling of superconducting carriers when he computed the quantum of magnetic flux and, therefore, predicted for it twice the amount. The order parameter can be written as: Ψ(r) = √ n s e iθ(r) . (4.32) where n s is density of superconducting carriers, θ is the order parameter phase. As in the absence of a magnetic field, the density of particle flux is described by the equation: n s v = i 2m e (Ψ∇Ψ ∗ − Ψ ∗ ∇Ψ) . (4.33) Using (4.32), we get ∇θ = 2m e v s and can transform the Ginzburg-Landau equation (4.21) to the form: ∇θ = 2m e v s + 2e A. (4.34) c If we consider the freezing of magnetic flux in a thick superconducting ring with a wall which thickness is much larger than the London penetration depth λ L , in the depths of the body of the ring current density of j is zero. This means that the equation (4.34) reduces to the equation: ∇θ = 2e A. (4.35) c One can take the integrals on a path that passes in the interior of the ring, not going Science Publishing Group 39

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Part IV Conclusion

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References [1] W. Gilbert: De magne

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References [33] Bethe H., Sommerfel