Kondo impurities in anisotropic superconductors. Eliashberg formulation

The Kondo effect in an anisotropic superconductor is studied within the framework of the Migdal-Eliashberg (ME) formulation of superconductivity. The renormalization of the ME equations arising from the scattering by the Kondo impurities is obtained on the basis of the Müller-Hartmann and Zittartz theory. Both the decrease of the transition temperature T_c and the specific heat jump at T_c are calculated.     

Transition temperature of anisotropic superconductors with kondo impurities

The Matsuura-Ichinose-Nagoako (MIN) model for Kondo impurities in a superconductor has been generalized to include the effect of gap anisotropy. Analytic results are obtained for the change in the transition temperature. It is shown that, in appropriate limits, one recovers the recent results of Schachinger and Carbotte and Okabe and Nagi. The resulting formulae yield corrections to those of MIN in the BCS isotropic model.     

μSR measurements of off-axis internal magnetic fields in anisotropic superconductors

A systematic procedure which enables the study of complicated internal field distributions is discussed. It is proposed that this may be useful for studying the fields due to the flux line lattice (FLL) of the high temperature superconductors. Moment distributions of the Fourier transform of the internal field components can be obtained. We have used the London theory as developed by Kogan and others to calculate the internal field distributions, explicitly including those field components which are transverse to the average internal field. We have used this to make estimates of the expected frequency dependence of these moment distributions.     

Zinc impurities in d-wave superconductors

We study the two-dimensional Hubbard model with nonmagnetic Zn impurities modeled by binary diagonal disorder using quantum Monte Carlo within the dynamical cluster approximation. With increasing Zn content we find a strong suppression of d-wave superconductivity and an enhancement of antiferromagnetic spin correlations. T(c) vanishes linearly with Zn impurity concentration. The spin susceptibility changes from pseudogap to Curie-Weiss-like behavior indicating the existence of free magnetic moments in the Zn doped system. We interpret these results within the resonating-valence-bond picture.     

Theory of magnetic impurities in superconductors

The jump of the specific heat at the transition temperature is calculated for a superconductor with magnetic impurities. The calculation includes the Kondo effect and is exact within the Nagaoka-approximation.     

Theory of magnetic impurities in superconductors

Ground state properties of a Kondo superconductor of low impurity concentration are calculated exactly within the Nagaoka approximation. The results for the location of the bound state motivate us to formulate the notion of intrinsic gaplessness. The order parameter, the ground state energy, and the thermodynamic critical field are computed. The relation to experiments and to the Hartree-Fock theory of magnetic impurities in a superconductor is discussed.Dedicated to Prof. G. van den Berg on the occasion of his retirement from a readership at the University of Leiden (March 1976).Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln.Supported by the Deutsche Forschungsgemeinschaft.     

Stimulation effect in anisotropic superconductors

The stimulation of superconductivity in anisotropic superconductors by electromagnetic and acoustic pumping as well as by the injection of a tunnel current at temperatures close to the superconducting transition temperature is studied. The features distinguishing the stimulation effect from the isotropic case are indicated. Zh. éksp. Teor. Fiz. 111, 2134–2146 (June 1997)     

Spin-wave excitations of paramagnetic impurities in superconductors

The existence of spin-wave excitations of paramagnetic impurities in a superconductor in an external magnetic field due to the long-range exchange interactions is predicted. The damping has been calculated and possible manifestations of this collective excitations in ESR experiments are analysed.     

Effect of impurities on the low-temperature behavior of the specific heat of anisotropic superconductors in a mixed state

In the presence of zeros of the order parameter in an anisotropic superconductor, the combined effect of a magnetic field and impurities leads to two different limiting magnetic-field dependences of the specific heat. These dependences are studied both for Born scatterers and in the unitary limit for several specific examples of anisotropic pairing. A estimate is given for the crossover field. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 606–611 (25 April 1997)     

Anisotropy effects in superconductors with magnetic impurities

The influence of Fermi surface anisotropy on the specific heat jumps,C, at the phase transition for superconductors containing magnetic and nonmagnetic impurities is discussed. In the framework of a simple two-band or two-zone model we find for small interband electron-phonon coupling constants characteristic maxima in theC(T _c )-curve.These departures from the correspondingC-curve of a single-band isotropic superconductor are mostly pronounced forweak andstrong interband Coulomb scattering of conduction electrons on nonmagnetic ions. There is only a small range of intermediate scattering rates for which the maxima are smeared out.Work performed within the research program of the Sonderforschungsbereich 125 — Aachen/Jülich/Köln