By using Londons' equations, the two-fluid model, and the classical skin effect for the normal component of the current, a sinusoidal wave solution is found for a superconducting transmission line. This solution gives a slow mode of propagation which is dependent on the ratios of the dielectric and superconducting film thicknesses to the penetration depth. At low temperatures and frequencies where the losses are low, the velocity is dispersionless even though there is a component of electric field in the direction of propagation. The solutions for velocity and attenuation vary continuously as one passes through the critical temperature into the normal state. The solutions are interpreted in terms of lumped circuit characteristics.
No abstract
Results of numerical calculations of the electrical resistivity of the following primary solidsolution alloys are presented: Cu(Zn), Cu(Ga), Cu(Ge), Ag(Pd), and Ni(Mo). Our theoretical model is one reported earlier by Butler and uses a charge-self-consistent Korringa-Kohn-Rostoker coherent-potential approximation. The calculations are valid for strong as well as weak scattering, and for the first time, vertex corrections are included. Excellent agreement is obtained with experiment for the resistivity. PACS numbers: 72.10.Fk, 71.15.JfWe report here rigorous and realistic ab initio calcurequire the existence of well-defined quasiparticles. lations of the dc residual resistivity of random substi-We believe that the model is valid in the regime where tutional alloys. The calculations do not use adjustable the Boltzmann equation breaks down because energy parameters and they start with only the atomic bands are not defined. The model includes vertex numbers, the alloy concentrations, and the lattice corrections, and it properly treats the momentum maparameters as input. 1 The model is based on the trix elements. In this paper we discuss our results for Korringa-Kohn-Rostoker coherent-potential approxicopper-rich alloys of zinc, gallium, and germanium, mation (KKR-CPA) 2 and the one-electron Kubo forfor silver alloys containing palladium, and for nickel mula. 3 It goes beyond any previous model for deteralloyed with molybdenum. mination of transport properties of random alloys inThe dc electrical conductivity tensor in the onethat it is not limited to weak scattering and does not electron approximation can be written in the Kubo for-' malism as 1where the current operators are * e 9 • * e 9 ei\ * m 9r M m 8r v For a spherical nonoverlapping muffin-tin potential, the imaginary part of the Green's function can be expressed as 4 ImG(r,r',€ + ir\) G{t,x\z)~^XT™Xz)Z?{t mt z)Zl,(x' n ,z)for the complex energy z The point r is in unit cell m while the point r' is in cell n with r = R m + r m , where R m is the vector to the center of cell m (We consider, for simplicity only, one atom per unit cell) Zp(r m ,z) is the wave function of angular momentum L (= /,/x) centered on cell m which is regular at the origin and which satisfies the one-electron Schrodinger equation with the spherical muffin-tin potential and complex energy z The T^ is the scattering-path operator which propagates the electron from site m to site n taking into account scatterings at all possible sites.For a binary alloy of atoms A and 5, the potential site n depends on whether it is occupied by an A or B atom. To represent a real random system, we take a configurational average considering all possible arrangements of the two species on the fixed lattice and for the given concentration. We assume that the arrangements are completely random with no shortrange chemical order. We then carry out the configurational average within the CPA. The scattering-path operator r^ for a given configuration is replaced by T cnm (jfaQ scattering-path operator for the CPA ef...
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