Proposed Universal Relationships Describing Electron Phonon Mediated Superconductivity and Accommodation of the Cuprates and Pnictides

TL;DR

This paper develops universal, self-consistent equations linking key parameters of superconductivity, demonstrating their applicability across conventional, cuprate, and pnictide superconductors, based solely on electron-phonon interactions.

Contribution

It introduces a universal set of equations relating critical superconducting parameters, applicable to various superconductor classes, derived exclusively from electron-phonon mediated data.

Findings

Critical temperature relates exponentially to Debye energy and electron-phonon coupling.

Coherent condensation temperature equals the energy gap and is constant across superconductors.

Electron-phonon coupling constant relates exponentially to zero point energy.

Abstract

A universal and self-consistent set of equations is developed utilizing the principle empirical parameters of Superconductivity which are the coherent condensation temperature, the Debye temperature, the coherent condensation energy gap at critical temperature equals zero degrees Kelvin and the electron phonon coupling constant. Empirical data from both crystalline elements and amorphous compounds is shown to produce the same self consistent relationships which are critical temperature equals Debye energy/2 exp(-2/electron phonon coupling constant), coherent condensation temperature equals the Debye energy exp (-2/electron phonon coupling constant) and the ratio of coherent condensation temperature/critical temperature equals 2.0 i.e. coherent condensation temperature equals coherent energy gap and is found to be constant for all superconductors. We also find that electron phonon coupling constant is related exponentially related to the zero point energy where the zero point energy equals the Debye energy/2 and is the zero point energy of a quantum mechanical oscillator. These relationships are derived exclusively from electron phonon mediated superconductor data and are also shown to encompass cuprate superconductors with ease. [Abridged]