### Superconductivity: A New Approach Based On The Bethe-salpeter Equation In The Mean-field Approximation

##### A New Approach Based on the Bethe–Salpeter Equation in the Mean-Field Approximation

#### G P Malik

#### $82.00

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### Description

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.

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