We consider novel unusual effects in superconductor-ferromagnet (S/F) structures. In particular we analyze the triplet component (TC) of the condensate generated in those systems.This component is odd in frequency and even in the momentum, which makes it insensitive to non-magnetic 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, formation of periodic magnetic structures due to the influence of the superconductor, etc. We compare the theoretical predictions with existing experiments.

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The development of the supersymmetry technique has led to significant advances in the study of disordered metals and semiconductors. The technique has proved to be of great use in the analysis of modern mesoscopic quantum devices, but is also finding applications in a broad range of other topics, such as localization and quantum chaos. This book provides a comprehensive treatment of the ideas and uses of supersymmetry. The first four chapters of the book set out the basic results and some straightforward applications of the technique. Thereafter, a range of topics is covered in detail, including random matrix theory, persistent currents in mesoscopic rings, transport in mesoscopic devices, localization in quantum wires and films, and the quantum Hall effect. Each topic is covered in a self-contained manner, and the book will be of great interest to graduate students and researchers in condensed matter physics and quantum chaos.

We analyze the proximity effect in a superconductor/ferromagnet (S/F) structure with a local inhomogeneity of the magnetization in the ferromagnet near the S/F interface. We demonstrate that not only the singlet but also the triplet component of the superconducting condensate is induced in the ferromagnet due to the proximity effect. Although the singlet component of the condensate penetrates into the ferromagnet over a short length ξ h = D/h (h is the exchange field in the ferromagnet and D the diffusion coefficient), the triplet component, being of the order of the singlet one at the S/F interface, penetrates over a long length D/ǫ (ǫ is the energy). This long-range penetration leads to a significant increase of the ferromagnet conductance below the superconducting critical temperature Tc.In recent experiments on S/F structures a considerable increase of the conductance below the superconducting critical temperature T c was observed [1][2][3]. Although in a recent work [4] it was suggested that such an increase may be due to scattering at the S/F interface, a careful measurement of the conductance demonstrated that the entire change of the conductance was due to an increase of the conductivity of the ferromagnet [1,2].Such an increase would not be a great surprise if instead of the ferromagnet one had a normal metal N. It is well known (see for review [5,6]) that in S/N structures proximity effects can lead to a considerable increase of the conductance of the N wire provided its length does not exceed the phase breaking length L ϕ . However in a S/F structure, if the superconducting pairing is singlet, the proximity effect is negligible at distances exceeding a much shorter length ∼ ξ h . This reduction of the proximity effect due to the exchange field h of the ferromagnet is clear from the picture of Cooper pairs consisting of electrons with opposite spins. The proximity effect is not considerably affected by the exchange energy only if the latter is small h < T c . As concerns such strong ferromagnets as F e or Co used in the experiments [1,2], whose exchange energy h is by several orders of magnitude larger than T c , a singlet pairing is impossible due to the strong difference in the energy dispersions for the two spin bands. At the same time, an arbitrary exchange field cannot destroy a triplet superconducting pairing because the spins of the electrons forming Cooper pairs are already parallel. A possible role of the triplet component in transport properties of S/F structures has been noticed in Refs. [7,8], where the triplet component arose only as a result of mesoscopic fluctuations. However, in both cases the corrections to the conductance are much smaller than the observed ones.In this paper, we suggest a much more robust mechanism of formation of the triplet pairing in S/F structures, which is due to a local inhomogeneity of the magnetization M in the vicinity of the S/F interface. We show that the inhomogeneity generates a triplet component of the superconducting order parameter with an amplitude co...

Notes by S. Ribault Here ǫ is a function, for instance ǫ(p) = p 2 2m −ǫ F where ǫ F is the Fermi energy. And U r is a random potential. As we are looking for universal results, we may as well assume that U r has a Gaussian law

A granular metal is an array of metallic nano-particles imbedded into an insulating matrix. Tuning the intergranular coupling strength a granular system can be transformed into either a good metal or an insulator and, in case of superconducting particles, experience superconductor-insulator transition. The ease of adjusting electronic properties of granular metals makes them most suitable for fundamental studies of disordered solids and assures them a fundamental role for nanotechnological applications. This Review discusses recent important theoretical advances in the study of granular metals, emphasizing on the interplay of disorder, quantum effects, fluctuations and effects of confinement in formation of electronic transport and thermodynamic properties of granular materials.

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It is shown that the criticism presented in the Comment by Galanakis et al [1] on the paper by Efetov et al [2] is irrelevant to the bosonization approach.In spite of the far going conclusion that our bosonization scheme cannot help to overcome the negative sign problem, the Comment does not really address the suitability of the method for Monte Carlo (MC) calculations. We wrote in the paper that our mapping of the fermionic model onto a bosonic one was exact having in mind the continuous with respect to (imaginary) time limit. Any quantum MC scheme implies generically a discrete time with extremely strong variation of the HubbardStratonovich (HS) field φ on different slices. In this case, our bosonization scheme is not necessarily exact for a given HS field and we make an approximation. If everything remained exact also in this case, we would not be able to overcome the sign problem because the partition function Z [φ] for a given φ would be the same for both bosonic and fermionic representations and could be negative.In our opinion, the comment of Galanakis et al. is based on a misunderstanding of the definition of Z b . Indeed Z b should not be understood as coming from Eqn (9) but from Eqns(12-13). [We apologize for this confusion, which is the result of writing the paper several times in order to improve the presentation]. Having failed to understand this point, Galanakis et al. re-derive the same steps leading to Z f and jump on the far reaching conclusion that our technique does not solve the MC sign problem. However, the bosonization method starts later with Eqs. (12, 13), which means that Galanakis et al make their conclusions not about the bosonized model but still about the original fermionic one.They fail as well to understand that for finite time slices, our method is not exact but requires an approximation. The crucial approximation is made when writing Eq. (13). According to Eq. (11), the function A r,r ′ (τ ) is expressed in terms of the Green functions at slightly different times τ and τ + δ,where δ → +0. Therefore, deriving the equation for the function A r,r ′ and making no approximations one would have the fields φ r and φ r ′ at slightly different times τ and τ + δ. Nevertheless, we put δ = 0 in Eq. (13). In the continuous limit, (implying subsequent averaging over φ r (τ )), this approximation becomes exact. Therefore our field theory based on the introduction of superfields is exact.However, working with finite slices of time and putting δ = 0 changes the function Z b [φ] for a given configuration of φ. Taking Eq. (13) with the fields φ r (τ ) and φ r ′ (τ ) at coinciding times τ results in a symmetry of the solution A r,r ′ (τ ) under the replacement r ⇆ r ′ . We argue in the paragraph after Eq. (23) that any possible singularity in the integral over u in the exponent should be absent due to this symmetry. This means that the imaginary part in the exponent does not arise and the function Z b [φ] must be positive.In order to make everything well defined one needs a regularization, otherwis...