Creation of Electron Spinless Pairs in the Superconductivity

TL;DR

This paper corrects the Froolich Hamiltonian for superconductivity, demonstrating the formation of spinless electron pairs via an attractive interaction, and challenges the Cooper approximation's validity in gap formation.

Contribution

It provides a corrected Froolich Hamiltonian and establishes a new condition for metals to become superconductors, highlighting the formation of spinless electron pairs.

Findings

Corrected Froolich Hamiltonian with proper interaction terms

Identified flaw in the Cooper approximation regarding energy gap formation

Derived a new condition for metals to exhibit superconductivity

Abstract

First, it is demonstrated that the Froolich Hamiltonian of system in the superconductivity, proposed by the model of a phonon gas and an electron gas mixture, contains a subtle error. In this respect, we present a correct form of the Froolich Hamiltonian of system where the term of the interaction between the phonon modes and the density modes of the electron modes is described by the term of scattering, introduced by the Froolich in a phonon gas electron gas mixture. The later is removed by a canonical transformation of the Froolich Hamiltonian by an appearance of the attractive interaction mediated via the electron modes, which leads to a bound state on a spinless electron pairs. In this letter, we show that the Cooper approximation as the constancy of the density states within around of the Fermi level has a flaw because the effective attractive forces cannot create the Cooper pairs into energetic gap at the Fermi level. In this letter, we find a condition for density metal which determines metal as superconductor.