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Additional info for The LMTO method
The critical current depends strongly on the applied magnetic field, since that spatially modulates the phase difference across the junction. In the presence of an external magnetic field H in a barrier the supercurrent density Js(x) varies spatially along the barrier according to Copyright © 1998 IOP Publishing Ltd 32 The evolution of SC theories where Λ = d + 2λ(T) is the so-called magnetic thickness of the barrier and d is the distance between junction electrodes. 106) leads to the following Fraunhofer pattern for the field dependence of the critical current Ic(H ) Here W is the junction length along the x direction and Φ = HWΛ is the magnetic flux trapped in the barrier region of a junction.
A practical interesting example is a thin-film loop placed near the top of the superconducting screen. 074. Therefore there is a strong reduction of the inductance due to the use of a superconducting screen. 21) allow one to consider a much broader class of problems concerning the high-frequency properties of superconductors. In fact the London theory gives a good phenomenological basis for predicting the properties of superconducting waveguides, cavity resonators etc. A more complicated approach was developed by Pippard (1953) by phenomenological account of the so-called nonlocal effects and then by Mattis and Bardeen (1958) and Abrikosov et al (1958) in the framework of the microscopic BCS theory.
53) is valid only near Tc where the order parameter ψ(r ) is small enough. The GL coefficients α and β are phenomenological parameters and all measurable physical quantities are expressed through them. Alternatively, α and β can be determined from a microscopic approach. Both these relations will be given below. The central problem of the GL approach is now to find functions Ψ(r ) and A(r ) which make the total free energy of the specimen a minimum, subject to appropriate boundary conditions. Copyright © 1998 IOP Publishing Ltd 18 The evolution of SC theories In the absence of the magnetic field and in the absence of spatial variations the order parameter is obtained from ∂(δFsn )/δns.