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Andreev reflection is a scattering process where electrical current is converted to supercurrent where there is an interface between a normal metal and a superconductor. Recently, much attention has been focused on Andreev reflection in nanohybrids of ferromagnet (F) and superconductor (S). This is for a variety of reasons. Andreev reflection in a F-S point contact provides a powerful tool for determining the spin polarization of conducting electrons. The coherence length of a superconductor can be estimated by measuring the tunnel magnetoresistance of a F-S-F double junction system. A novel scattering process called crossed Andreev reflection can be predicted for a superconductor with two ferromagnetic leads, where Andreev reflection occurs even if the ferromagnetic leads are half metallic. In this chapter the theory of Andreev reflection in nanohybrids of F and S is introduced, and recent progress in this field is reviewed.

This chapter discusses the main phenomena related to superconductivity. It explains the basics of the BCS theory and applies it in calculating the superconducting density of states and describing the Andreev reflection. It introduces Feynman's picture of the Josephson effect, allowing the derivation of the dc and ac Josephson relations. The microscopic theory of Andreev reflection is then connected to the description of Andreev bound states and the associated supercurrent through superconducting contacts. The chapter ends with a short description of the superconducting proximity effect that needs to be taken into account in mesoscopic superconducting systems.

This chapter opens the part of the book devoted to quantum vacuum in non-trivial gravitational background and to vacuum energy. There are several macroscopic phenomena, which can be directly related to the properties of the physical quantum vacuum. The Casimir effect is probably the most accessible effect of the quantum vacuum. The chapter discusses different types of Casimir effect in condensed matter in restricted geometry, including the mesoscopic Casimir effect and the dynamic Casimir effect resulting in the force acting on a moving interface between ³He-A and ³He-B, which serves as a perfect mirror for the ‘relativistic’ quasiparticles living in ³He-A. It also discusses the vacuum energy and the problem of cosmological constant. Giving the example of quantum liquids it is demonstrated that the perfect vacuum in equilibrium has zero energy, while the nonzero vacuum energy arises due to perturbation of the vacuum state by matter, by texture, which plays the role of curvature, by boundaries due to the Casimir effect, and by other factors. The magnitude of the cosmological constant is small, because the present universe is old and the quantum vacuum is very close to equilibrium. The chapter discusses why our universe is flat, why the energies of the true vacuum and false vacuum are both zero, and why the perfect vacuum (true or false) is not gravitating.

After reviewing the physical systems that may host exciton condensation, this chapter illustrates some recent proposals concerning the detection of coherent exciton flow. It focuses on the exciton analogues of two phenomena—Andreev reflection and the Josephson effect—which are hallmarks of superconducting behavior and stress the crucial differences between excitons and Cooper pairs. It shows that the excitonic insulator is the perfect insulator in terms of both charge and heat transport, with an unusually high resistance at the interface with a semimetal—the normal phase of the condensed state. Such behavior may be explained in terms of the coherence induced into the semimetal by the proximity of the exciton condensate. The exciton superflow may be directly probed in the case that excitons are optically pumped in a double-layer semiconductor heterostructure. The chapter proposes a correlated photon counting experiment for coupled electrostatic exciton traps.

This chapter explains how the exchange splitting between up- and down-spin bands in ferromagnets unexceptionally generates spin-polarized electronic states at the Fermi energy. The quantity of spin polarization P in ferromagnets is one of the important parameters for application in spintronics, since a ferromagnet having a higher P is able to generate larger various spin-dependent effects such as the magnetoresistance effect, spin transfer torque, spin accumulation, and so on. However, the spin polarizations of general 3d transition metals or alloys generally limit the size of spin-dependent effects. Thus,“‘half-metals” attract much interest as an ideal source of spin current and spin-dependent scattering because they possess perfectly spin-polarized conduction electrons due to the energy band gap in either the up- or down-spin channel at the Fermi level.