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This chapter provides a scheme of nonlocal electromagnetism and develops a scheme of superconductivity. In essence, nonlocality is meant as a description of constitutive properties through appropriate spatial gradients. This is allowed by generalizing the expressions of the energy and the entropy fluxes while keeping the possible dependence on the history. Superconductivity is developed by starting from an improvement of the London theory and the thermodynamic analysis is performed. The Ginzburg-Landau theory is improved through an evolution model.

This chapter demonstrates how the Ginzburg-Landau functional can be carried out from the microscopic theory of superconductivity. For this, the method of functional integration, alternative to the diagrammatic technique approach, is used. The partition function is presented as the functional integral of the exponent of effective action over all possible fluctuation realizations of the order parameter. The analysis corresponding to this free energy function permits the reproduction of both the results of the BCS theory (mean field approximation) and allows us to obtain microscopically the GL functional. This analysis is generalized for the case of a nontrivial order parameter symmetry.

This chapter argues that the widespread notion that the discipline of condensed matter physics is devoted to deriving the properties of complex many-body systems from that of their atomic-level components is a myth, and that the analogy of map-making is much more appropriate. After a brief discussion of the experimental techniques available in this area and of the properties of the simplest condensed-matter systems (gases, simple liquids, and crystalline solids), attention is focussed first on the problem of second- and first-order phase transitions, and secondly on issues arising in amorphous (glassy) materials and their possible relevance to biological systems. The chapter concludes by introducing the phenomena of superconductivity and superfluidity, and discussing the general problem of interfacing condensed-matter systems with their environments.

This chapter starts with a discussion of the symmetry conditions which have to be imposed on the wave function of a many-particle system, and the distinction between bosons and fermions. It then examines the consequences of these conditions for simple systems of non-interacting particles (Fermi-Dirac and Bose-Einstein statistics), and in particular, introduces the phenomenon of Bose-Einstein condensation (BEC) in a noninteracting Bose gas. The phenomenon of Cooper pairing of interacting fermions is introduced by a thought-experiment in which one starts from a BEC of tightly bound diatomic molecules made of fermion atoms and gradually weakens the binding. The chapter closes with a description of the various physical systems to be treated in the book, and an account of the phenomenology of superfluidity and superconductivity. An appendix treats the statistical mechanics of a rotating system.

Starting with an account of the chemical composition, crystalline structure, and phase diagram of the high-temperature (cuprate) superconductors, this chapter reviews the principal experimental properties of the optimally doped normal phase, the superconducting phase, and the so-called “pseudogap” region of the phase diagram, and some general comments made on the implications of the experimental data. The question is then raised: what do we know for sure about cuprate superconductivity in the absence of a specific microscopic model? And some answers are attempted. Next, various ideas which may be important in understanding these systems are reviewed. Finally, some novel consequences of the type of pairing realized in the cuprates are explored.

Four different systems, mostly of recent vintage, which are known or conjectured to manifest BEC/Cooper pairing are discussed. First, various non-cuprate “exotic” superconductors (alkali fullerides, organics, heavy fermions, ruthenates) are reviewed. Next, an account is given of the superfluid phases of liquid 3He in the pores of aerogel. A third section introduces the topic of the “supersolid” behavior recently reported in solid 4He, and comments on some theoretical issues raised by the experiments. The last section of the chapter considers the newly realized system of ultracold Fermi alkali gases, where one can study experimentally the apparently smooth crossover between the BEC of diatomic molecules and BCS superfluidity in a degenerate Fermi gas, thus unifying the concepts of BEC and Cooper pairing.

This chapter is devoted to the LHC accelerator complex. It first presents the history of the construction of the LHC and the challenges involved. It then describes the functioning of the LHC, following the path made by the beams of protons. The cutting-edge technologies developed for the LHC are explained using simple analogies. Applications outside particle physics of these technologies are also discussed. The different components of the LHC are described, with special emphasis on the superconducting dipole magnets, which are used to steer the proton beams inside the underground tunnel.

This chapter introduces the theory of superfluid ³He. It begins with a summary of the BCS theory of superconductivity, which is the basis for the development of the most complex theory of superfluid ³He. This is followed by the Ginzburg–Landau theory that is only valid for superfluids at temperatures near their transition temperature, Tc. A discussion of spin-triplet pairing leads to the identification of the B phase with the Balian–Werthamer state and the A phase with the Anderson–Morel state.

This chapter demonstrates the potentialities of the quasiclassical method for selected problems in the theory of stationary superconductivity. The Ginzburg–Landau equations are derived, the upper critical field of dirty superconductors at arbitrary temperatures is calculated, and the gapless regime in superconductors with magnetic impurities is discussed. Effects of impurities on the critical temperature and the density of states in d-wave superconductors are discussed. The energy spectra of excitations in vortex cores of s-wave and d-wave superconductors are calculated.

This chapter applies the quasiclassical approximation to nonstationary problems in the theory of superconductivity. The Eliashberg equations for the quasiclassical Keldysh Green functions are derived. Normalization of the Green functions in nonequilibrium situation is found. The Keldysh function is expressed in terms of a two-component generalized distribution function. The diffusive limit in nonstationary superconductivity is described. An example of stimulated superconductivity due to microwave irradiation is considered: the order parameter becomes enhanced as a result of a depletion of nonequilibrium distribution of excitations in the energy range of the superconducting gap.

A superconductor is a remarkable emergent state of matter in which electrons pair up and develop long range phase coherence resulting in zero resistance and perfect diamagnetism. How can a superconductor decohere? A thin superconducting film can be driven insulating in a remarkable number of ways: decreasing thickness, increasing disorder, changing the gate voltage, or applying a magnetic field. Such superconductor-insulator transitions (SIT) are quantum phase transitions of strongly correlated electrons occurring at very low temperatures. This chapter gives an overview of the field, with particular emphasis on recent developments. This chapter describes how the theoretical understanding of SITs has evolved over the years, and how the increasing quality of experimental data is beginning to reveal the importance of amplitude and phase fluctuations. Most importantly new paradigms have been developed to describe these phenomena. This chapter contains numerous references to the contributions by various authors in subsequent chapters

Transport and spin-resolved electron tunneling measurements on ultra-thin Al and Be films are used to extract the spin-mediated behavior on either side of the zero-field superconductor-insulator transition. The primary focus of these studies is the behavior of the Zeeman-mediated superconductor-insulator transition in Al films with sheet resistances well below the quantum resistance and the nature of the correlated insulator phase in very high resistance Be films. By applying magnetic fields in the plane of the films one can control the Zeeman splitting in these low spin-orbit scattering systems without introducing an orbital response. The data give clear evidence for incoherent pairing effects in both the Zeeman-limited normal state of low resistance Al films and in the correlated insulator phase of very high resistance Be films.

A motivation for the development of atomically resolved spectroscopic imaging STM (SI-STM) has been to study the broken symmetries in the electronic structure of cuprate high temperature superconductors. Both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates exhibit two distinct classes of electronic states when studied using SI-STM. The class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor. These signature are detected below a lower energy scale |E| = D₀ and only upon a momentum space (k-space) arc which terminates near the lines connecting k = ±(p/a₀, 0) to k = ±(0̣,p/a₀). This ‘nodal’ arc shrinks continuously with decreasing hole density. In both the dSC and PG phases, the only broken symmetries detected in the |E|≤D₀ states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale |E|~̣D₁ can be associated with the ‘antinodal’ states near k = ±(p/a₀,0) and k = ±(0̣,p/a₀). These states break the expected 90º-rotational (C₄) symmetry of electronic structure within CuO₂ unit cells, at least down to 180º-rotational (C₂) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C₄ symmetry breaking coexists at |E|~̣D₁ with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). Empirically, the characteristic wavevector Q of the latter is determined by the k-space points where Bogoliubov quasiparticle interference terminates and therefore evolves continuously with doping. The properties of these two classes of |E|~̣D₁ states are indistinguishable in the dSC and PG phases. To explain these two regimes of k-space that are distinguished by the symmetries of their electronic states and their energy scales |E|~D₁ and |E|≤D₀, and to understand their relationship to the electronic phase diagram and the mechanism of high-T_c superconductivity, represent key challenges for cuprate studies.