Theoretical studies on some superconductors.

Abstract

Superconductivity can be considered to be one of the most attractive branches of solid-state physics. This is especially true now, with the sensational discoveries of high transition-temperature superconductors. On the technological side, the role of superconductivity is well known. Research in superconductivity has resulted in the construction of powerful magnets used in high-energy physics, fusion research, and nuclear magnetic resonance tomography; in the manufacture of quantum interferometers finding use in biomagnetism and as detectors for gravitational waves; in the construction of digital computer elements; and in many other applications. On the theoretical side, superconductivity has spawned and nurtured theories that are beautiful and illustrative examples of the techniques of many-body physics and quantum field theory. Though superconductivity was originally found in metals, it has since been found in a variety of alloys and compounds—a fact which makes the search for high-temperature superconductors more meaningful. It has also been found in compounds that exhibit long-range magnetic order. This phenomenon of coexistence of superconductivity and magnetism has been under study for the past two decades. In this thesis we shall be concerned with the coexistence problem, in particular the coexistence of antiferromagnetism and superconductivity, as well as with the problem of high-temperature superconductivity. The introductory first chapter starts, after a brief enumeration of the basic properties of superconductors, with a description of the BCS and Ginzburg-Landau theories. This is followed by a selective and qualitative survey of the literature concerned with magnetic superconductors. In the final section, in the context of the problem of high-temperature superconductivity, the limitations of the phonon mechanism are discussed along with a couple of alternative mechanisms that had been proposed well before the recent startling discoveries of the oxide superconductors. The second chapter deals with a microscopic mechanism that can possibly bring about a coexistence of antiferromagnetism and superconductivity. The mechanism involves a simultaneous creation or destruction of a Cooper pair and destruction or creation of two electrons at two neighboring localized f-sites, with the f-electron system having perfect antiferromagnetic order. This interaction, in second order, is shown to produce an enhancement of the superconducting pairing. The upper critical field is calculated for the case of SmRh?B? and is shown to agree satisfactorily with the experimental data. A Green’s function calculation has been performed to explicitly show the interdependence of the superconducting and magnetic order parameters. In the third chapter the problem of the coexistence of superconductivity and antiferromagnetism is dealt with from a phenomenological point of view. A physically clear derivation of the free-energy functional, in the context of magnetic superconductors, is given. It is shown that the electrodynamic effects can only suppress the magnetic transition temperature and the upper critical field. The superconducting order parameter is also reduced due to the electrodynamic effects when the magnetization is nonzero. On the other hand, the terms that directly couple the magnetization and the superconducting order parameter can act either way. In particular, when the coefficients of these direct coupling terms are negative, an enhancement of the magnetic transition temperature and the upper critical field results. The enhancement of the upper critical field in the case of SmRh?B? has been demonstrated. It is shown that the superconducting order parameter is also enhanced when the coefficients are negative, thus encouraging the coexistence. It has been suggested that the microscopic mechanism responsible for the negative values of the coefficients of the direct coupling terms is the one dealt with in the previous chapter. In the last chapter the problem of high-temperature superconductivity is considered. A review of the recent developments is given. Two possible mechanisms have been suggested. One involves the virtual exchange of electronic excitations. The other involves the interaction of conduction electrons with the distortion field modes that are suggested to arise in the system due to structural instabilities which exist in the incipient state. Although no detailed calculations have been attempted, it is shown that both the mechanisms can produce transition temperatures that are in the range of those of the new oxide superconductors.