# The role of phase fluctuations in model of superconductivity with the external pair potential

## TL;DR

This paper examines how phase fluctuations affect the stability of superconductivity in a model with an external pair potential, highlighting that electron interactions are essential and external potential alone cannot sustain superconductivity.

## Contribution

It demonstrates that phase fluctuations destabilize superconductivity in the model, emphasizing the importance of electron-electron interactions over external potentials.

## Key findings

- Superconductivity is driven by electron-electron interactions, not the external pair potential.
- Phase fluctuations can destroy superconducting order through quantum turbulence.
- The transition to the normal state follows a bosonic scenario in this model.

## Abstract

We investigate the stability of the solutions of the BCS model with the external pair potential formulated in a work K.V. Grigorishin arXiv:1605.07080. It has been shown that the cause of superconductivity in this model is the electron-electron interaction only and the potential cannot impose superconductivity since the superconducting ordering will be destroyed by phase fluctuations in a form of quantum turbulence (vortexes, vortex rings, vortex tangles etc.). The external pair potential renormalizes the order parameter in initial superconducting matter and the bosonic scenario of transition to normal state in a clear 3D superconductor occurs unlike BCS theory where the fermionic scenario takes place.