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

Given the Debye temperature of an elemental superconductor (SC) and its T_c, BCS theory enables one to predict the value of its gap Δ₀ 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, Δ₁₀, Δ₂₀ > Δ₁₀}, 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 SrTiO₃, and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the T_cs, 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_cs. 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.