Mechanisms for the superconducting state from a one-particle derivation of the BCS gap equations

TL;DR

This paper derives the BCS superconducting gap equations from a one-particle model, linking superconductivity to electronic energy gains surpassing vibrational or magnetic energies, and highlighting the role of the Fermi surface.

Contribution

It presents a novel one-particle derivation of the BCS gap equations, providing a less exotic interpretation of the superconducting mechanism and emphasizing the importance of band structure and Fermi surface.

Findings

Superconductivity occurs when electronic energy gains exceed vibrational/magnetic energies.

The superconducting gap is determined by vibration/oscillation amplitudes.

The Fermi surface influences the q-dependence of superconductivity.

Abstract

The BCS results for the superconducting gap $\Delta$ and $T_C$ are obtained from a one-particle model. Superconductivity appears when the electronic energy gains of the band structure surpass the energy needed for atomic vibrations or magnetic moment oscillations. The vibration/oscillation amplitudes determine the superconducting gap, and the Fermi surface is important for the q-dependence. This permits for complementary interpretations of the parameters for superconductivity and modeling of density-of-state effects. It also makes the superconducting mechanism less exotic.