Materials (II)

This chapter describes the properties of a number of interesting superconducting materials. The study of phonon-mediated superconductors, such as A-15 materials and MgB2, flourished after the discovery of the high-Tc hydrides. At present, this family displays, under high pressure, record values of Tc close to room temperature. Other interesting systems, such as pnictides, heavy fermions, and ruthenates, with their peculiar interplay of superconductivity and magnetism, are also described. Fe-based superconductors, which were recently discovered, have relatively high Tc at ambient pressure. They display a two-gap energy spectrum. Pairing in intercalated nitrides is mainly provided by acoustic plasmons. Tungsten oxides represent a new family of oxides containing elements other than copper; they form filamentary structures. A special class is formed by topological superconductors; usually their properties are caused by odd-parity pairing. The presence of the states inside of the energy gap make these superconductors similar to topological insulators.

Properties: Spectroscopy

This chapter focuses on the spectroscopy of the superconducting state. Various manifestations of macroscopic quantisation are described, including flux quantisation, the Josephson effect, vortices, and the Little–Parks effect. The Ginzburg–Landau theory and its microscopic derivation are presented. An interesting new direction, the search for the lossless ground current state, undergoes an intensive development. If the electronic density of states contains several peaks, it manifests as a multigap structure. Impurity scattering and, especially, the pair-breaking effect can drastically affect the spectrum and lead to gapless superconductivity. Pairing can be induced by the proximity effect (S–N contact). The isotope effect is the signature of the pairing mechanism, but it can be affected by Coulomb terms, magnetic impurities, and polaron formation. The study of fluctuations forms a large area of research. Fluctuations affect the behaviour of heat capacity and nuclear magnetic resonance relaxation, lead to peculiar paraconductivity, and so on.

Introduction

This chapter outlines the story of superconductivity, which started at the beginning of the twentieth century, and describes major breakthroughs, such as the discovery of the Meissner effect and the isotope effect. Several important developments preceded the microscopic theory formulated by Bardeen, Cooper, and Schrieffer: the two-fluid model, London equations, and the Ginzburg–Landau theory. Formulation of the theory brought further progress, such as quasiparticle tunnelling and the Josephson effect, and the search for new mechanisms of superconductivity and novel materials such as high-Tc oxides and hydrides. The main excitations in normal solids, including phonons, polaronic states, plasmons, and magnons, are described. A rigorous description of the adiabatic method, the foundation of the theory of solids, is provided, and the electron–phonon interaction, renormalisation phenomena, and the dynamic polaronic effect are introduced. The Heisenberg model, the key ingredient of the theory of magnetism, is also described.

Experimental Methods

In this chapter, several of the most important experimental techniques are described. These have been used to probe the most fundamental properties of the superconducting state: the energy gap and the pairing interaction. These methods have played a crucial role in validating the mechanism of superconductivity in conventional superconductors and are key to a fundamental understanding of superconductivity in more recently discovered novel superconductors like cuprates, Fe-based superconductors, and so on. The techniques that are described are all spectroscopic: tunnelling of quasiparticles through an insulating barrier or through a point contact ,Josephson tunnelling, the interaction of photons with a superconducting film or surface, the attenuation of ultrasonic waves,, the relaxation and/or resonance of muons interacting with a superconducting compound, and resonant inelastic X-ray scattering (RIXS). High-pressure techniques and the preparation of thin films and junctions are described. In addition, a state-of-the-art experimental procedure that enables the observation of the Little mechanism is discussed.

Materials (III)

This chapter focuses on organic and nanoscale superconducting systems. The tetramethyl-tetraselenafulvalene (TMTSF) and ethylenedithiotetrathiafulvalene (ET) organic families, along with the fullerides, are described. Special attention is paid to graphene-like structures, which are examples of two-dimensional systems. As for nanoscale systems, small-scale nanoscale structures are introduced and the pairing in aromatic molecules, like coronene, is discussed. The presence of the energy shell in some nanoclusters makes the pairing of electrons with opposite projections of orbital momenta perfectly realistic. This phenomenon has been observed experimentally for some aluminium clusters with a Tc on the order of 120 K. The nano-based tunnelling networks can transfer a macroscopic dissipationless current. Interface superconductivity is discussed, with a special focus on the FeSe/SrTiO3 system. The dream of room temperature superconductivity, envisioned shortly after the discovery of the phenomenon, has become perfectly realistic. This final chapter on materials describes various paths towards to this goal.

Manganites

This chapter focuses on manganites. There is a large similarity between the two families of mixed-valence compounds, the cuprates and the manganites. However, manganites display colossal magnetoresistance. The most fundamental property of manganites is the strong correlation between their transport properties and their magnetic properties. This correlation is caused by the double-exchange mechanism. The Hund interaction and the Jahn–Teller effect are the key ingredients of the microscopic theory. The transition to the ferromagnetic and metallic state is of a percolative nature. The superconducting–antiferromagnetic–superconducting Josephson junction is described. One can observe giant oscillations of the Josephson current as a function of a weak external magnetic field. The main properties, including the electron–hole asymmetry can be described in the framework of a generalised two-band picture. A peculiar isotope effect can be observed.

Superconducting States in Nature

This chapter discusses superconducting states in nature. The absence of resistance is the most remarkable manifestation of the superconducting state. But pair correlation is a general phenomenon that can be manifested in various systems, such as atomic nuclei, where the pairing is manifested in spectra, especially via the odd–even effect (the presence of unpaired nucleons makes it possible for nuclei to absorb a lower frequency of radiation than nuclei with an even number of nucleons can) and in the amplitudes of their momenta of inertia, which are smaller than in a rigid model. Another system, the neutron star, has an entirely different spatial scale. However, its low heat capacity leads to its rapid cooling, and the existence of a vortex structure affects the star’s rotation period. Finally, biologically active systems contain delocalised electrons, and the formation of electron pairs affects charge transfer, which is similar to Josephson tunnelling.

Materials I: High-Tc Copper Oxides

This chapter focuses on the cuprates, which are uniquely interesting superconducting compounds due to their high Tc, peculiar properties, and potential for applications. The history of the discovery of this very unusual class of superconductors is described, together with the properties and key theoretical concepts that can be used to understand their superconducting and normal behaviours. This chapter contains a description of some very key aspects of these materials: their very unusual phase diagram, where doping takes the compounds from antiferromagnetic insulators to high-temperature superconductors and finally to metallic conductivity; their very anomalous upper critical field Hc2; the symmetry of their order parameter; and the unusual isotope effect on Tc and penetration depth. There are two main approaches to the issue of the origin of high Tc in the cuprates: the phonon mechanism, with the strong impact of the polaronic effect, and a mechanism based on strong correlation effects.

Mechanisms

This chapter introduces the general concepts of pair correlation, and superconductivity as a strong non-adiabatic phenomenon. Phonon, electronic, and magnetic mechanisms play the major roles; each of them can serve as the origin of the superconducting state. Speaking of the phonon mechanism, it is essential that an explicit expression for Tc depend on the intensity of the electron–phonon interaction. In principle, the electron–phonon mechanism can provide high values of Tc, up to room temperature. Pioneering work by Little, who introduced the electronic mechanism, is described. The mechanism has been analysed for one-dimensional, two-dimensional, and three-dimensional systems. The plasmon mechanism can play a role for layered materials. The superconducting state can be provided by magnetic degrees of freedom. The band limit with spin fluctuations and the regime of strong electron correlations are described. The Hubbard Hamiltonian and the t − J model are the ingredients of the approach.

Inhomogeneous Superconductivity and the ‘Pseudogap’ State of Novel Superconductors

This chapter discusses the high-Tc oxides, which display many unusual properties above Tc, especially for the underdoped compounds. One can observe some features typical for the superconducting state, such as the energy gap, anomalous diamagnetism, and the isotope effect; they coexist with finite resistance. These features are caused by an intrinsic inhomogeneity of the compound. Various energy scales (Tc, Tc*, T*) can be introduced. The system contains a set of superconducting ‘islands’ embedded in a normal metallic matrix. The inhomogeneity is caused by the statistical nature of doping and the pair-breaking effect. The formation of a macroscopic superconducting phase (at T = Tc) corresponds to the transition, which is of a percolative nature. The resistive and Meissner transitions are split. The granular superconductors are inhomogeneous and their properties are similar to those of doped systems. The ordered doping should lead to an increase in the value of the critical temperature.