Superconductivity

Given the Debye temperature of an elemental superconductor (SC) and its T c , BCS theory enables one to predict the value of its gap Δ 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the g... Read more

Given the Debye temperature of an elemental superconductor (SC) and its T c , BCS theory enables one to predict the value of its gap Δ 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the generalized BCS equations (GBCSEs) which, given any two parameters of the set {T c , Δ 10 , Δ 20 > Δ 10 }, enable one to predict the third. Also given herein are new equations for the critical magnetic field and critical current density of an elemental and a non-elemental SC — equations that are derived directly from those that govern pairing in them. The monograph includes topics that are usually not covered in any one text on superconductivity, e.g., BCS-BEC crossover physics, the long-standing puzzle posed by SrTiO 3 , and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the T c s, Δs and other properties (e.g., number densities of charge carriers) of high-T c SCs via GBCSEs incorporating chemical potential may lead to tangible clues about raising their T c s. The final chapter in this monograph deals with solar emission lines and quarkonium spectra because of a feature common between them and superconductivity: existence of a bound state in a medium at finite temperature. This is a problem on which the author has worked for more than 25 years. The treatment in the text is elementary — even those who have only a cursory familiarity with Feynman diagrams should be able to follow it without much difficulty. Contents: The Bethe–Salpeter Equation (BSE); Customization of Bethe–Salpeter Equation (BSE) to Superconductivity; Re-derivation of Some Well-Known Results of BCS Theory via BSE-Based Approach; Generalized BCS Equations for Superconductors Characterized by High-T c s and Multiple Gaps; Multi-Gap Superconductivity: Generalized BCS Equations (GBCSEs) as an Alternative to the Approach Due to Suhl, Matthias, and Walker (SMW); Thermal Conductivity of MgB 2; Dynamical Equations for Temperature-Dependent Critical Magnetic Fields; Dynamical-based Equations for Critical Currents Densities; BCS-BEC Crossover Physics without Appeal to Scattering Length Theory; On the Puzzle Posed by Superconducting SrTiO 3; Some Exceptional Superconductors: La 2 CuO 4 (LCO) and Heavy-fermion Superconductors (HFSCs); Solar Emission Lines and Quarkonium Mass Spectra. Readership: Graduate students and researchers in condensed matter physics and low-temperature physics. Keywords:Bethe-Salpeter Equation;Matsubara Prescription;Superpropagator;Propagator Representing Exchanges of More Than One Species of Phonons Responsible for the Formation of Cooper Pairs;Generalized BCS Equations;Mean-Field Approximation;One-, Two-Phonon Exchange Mechanism for Pairing;High-Tc Superconductors;Thermal Conductivity of MgB2;Dynamical Equations for Critical Magnetic Field and Critical Current Density of both Elemental and Composite Superconductors;BCS-BEC Crossover Physics without Appeal to Scattering Length Theory;The Puzzle Posed by SrTiO3;Study of La2CuO4 via Equations Incorporating Chemical Potential;Heavy-Fermion Superconductors Less