This review considers unusual effects in superconductor-ferromagnet structures, in particular, the triplet component of the condensate generated in those systems. This component is odd in frequency and even in momentum, which makes it insensitive to nonmagnetic impurities. If the exchange field is not homogeneous in the system, the triplet component is not destroyed even by a strong exchange field and can penetrate the ferromagnet over long distances. Some other effects considered here and caused by the proximity effect are enhancement of the Josephson current due to the presence of the ferromagnet, induction of a magnetic moment in superconductors resulting in a screening of the magnetic moment, and formation of periodic magnetic structures due to the influence of the superconductor. Finally, theoretical predictions are compared with existing experiments.

https://arxiv.org/pdf/cond-mat/0506047.pdf

Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures

We review recent developments in our understanding of how impurities influence the electronic states in the bulk of superconductors. Our focus is on the quasi-localized states in the vicinity of impurity sites in conventional and unconventional superconductors and our goal is to provide a unified framework for their description. The non-magnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional s-wave systems. We review the physics behind these states, including quantum phase transition between screened and unscreened impurity, and emphasize recent work on d-wave superconductors. The bound states are most spectacularly seen in scanning tunneling spectroscopy measurements on high-$T_c$ cuprates, which we describe in detail. We also discuss very recent progress on the states coupled to impurity sites which have their own dynamics, and impurity resonances in the presence of an order competing with superconductivity. Last part of the review is devoted to influence of local deviations of the impurity concentration from its average value on the density of states in s-wave superconductors. We review how these fluctuations affect the density of states and show that s-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.

Impurity-induced states in conventional and unconventional superconductors

Recently it has been shown that many traditional models used for a description of dilute magnetic alloys are completely integrable and may be solved exactly without any approximation. In this article we summarize the results which have been obtained in this way. The main part of the article is devoted to the consistent and detailed account of the Bethe-Ansatz technique for the s-d exchange (Kondo) model with arbitrary impurity spin, s-d model with anisotropic exchange, degenerate exchange model and for the canonical Anderson model. The thermodynamic properties of a magnetic impurity in a non-magnetic metal host obtained by the Bethe method are considered in detail. Mainly attention is paid to the analysis of singularities associated with the formation of a localized moment, Kondo effect and mixedvalence phenomenon, which can be treated analytically. In the introductory part of the article we discuss the applicability of the models which we study in the paper to the real alloys and consider some m...

Exact results in the theory of magnetic alloys

Magnetic ions embedded in a nonmagnetic host exhibit a number of unusual low-temperature properties known collectively as the Kondo effect. Conventional small-parameter expansions for the Kondo effect are plagued by infrared divergences, and the theory of dilute magnetic alloys has for many years centered on nonperturbative techniques. This paper reviews a novel perturbative approach to the magnetic alloy problem based on expansion in $\frac{1}{N}$, with $N$ the ionic angular momentum degeneracy. This approach is analogous to perturbative expansions in statistical mechanics and field theory based on an integer-valued parameter (such as the number of spin components or the number of colors). The large-$N$ expansion reproduces the essential features of the Kondo effect at $O(1)$ and appears to yield convergent (or asymptotic) expressions for ground-state properties. In contrast with previous nonperturbative approaches, the expansion provides information on dynamic, as well as static, properties. The evidence for convergence of the expansion is reviewed, and large-$N$ calculations are compared with exact results for static properties. A number of independent, but essentially equivalent, approaches to the large-$N$ expansion have been developed during the last five years. These techniques are reviewed pedagogically, and their relative strengths and weaknesses emphasized. A guide to notation in the recent literature is provided.

Review of techniques in the large-N expansion for dilute magnetic alloys

The local effects of isolated magnetic adatoms on the electronic properties of the surface of a superconductor were studied with a low-temperature scanning tunneling microscope. Tunneling spectra obtained near magnetic adsorbates reveal the presence of excitations within the superconductor's energy gap that can be detected over a few atomic diameters around the impurity at the surface. These excitations are locally asymmetric with respect to tunneling of electrons and holes. A model calculation based on the Bogoliubov-de Gennes equations can be used to understand the details of the local tunneling spectra.

http://science.sciencemag.org/content/sci/275/5307/1767.full.pdf

Probing the Local Effects of Magnetic Impurities on Superconductivity

/pdf/comments-on-superconductors-with-magnetic-impurities-42uj6bdtbi.pdf

Comments on Superconductors with Magnetic Impurities

/pdf/functional-integral-approach-to-the-bound-state-due-to-the-s-36rqx5x7yu.pdf

Functional Integral Approach to the Bound State Due to the s-d Exchange Interaction

Ferromagnetism of itinerant electrons with strong correlations

Recently the asymmetric Anderson modeP1 has been discussed by several authors in connection vvith the phenomena of valence fluctuation observed in rareearth metals and compounds. In particular, Krishna-murthy et al.'l calculated numerically the temperature dependence of the susceptibility and Haldane\") presented scaling-lavv arguments. In this paper, we discuss the general feature of the ground state of this Hamiltonian by a simple consideration which is based on the Anderson orthogonality catastrophe41 and the compensation theorem11 for the localized conduction electrons. This way of consideration has first been contrived by Anderson') for calculating the singlet ground-state energy for the symmetric Anderson model, and later used by Yosida and Yoshimori61 for general deriv

/pdf/a-remark-on-the-ground-state-of-the-asymmetric-anderson-2ds214gy84.pdf

A Remark on the Ground State of the Asymmetric Anderson Model

/pdf/ground-state-of-the-asymmetric-anderson-model-in-the-t-37djlaulhj.pdf

Akio Sakurai

Papers

Comments on Superconductors with Magnetic Impurities

Functional Integral Approach to the Bound State Due to the s-d Exchange Interaction

Ferromagnetism of itinerant electrons with strong correlations

A Remark on the Ground State of the Asymmetric Anderson Model

Ground State of the Asymmetric Anderson Model in the T-Matrix Approximation