Landau Theory for States with local translation symmetry and the Phenomenological Potential with minimal electron-phonon interactions

TL;DR

This paper develops a Landau theory framework for inhomogeneous states with local translation symmetry, incorporating electron-phonon interactions and phonon potentials, aligning with BCS theory without charge doubling.

Contribution

It introduces a phenomenological Ginzburg-Landau potential that explicitly includes electromagnetic and electron-phonon interactions, avoiding charge doubling and aligning with BCS theory.

Findings

The model accurately describes current density without charge doubling.

It provides a phenomenological approach to sound based on phonon potential.

The theory is consistent with BCS superconductivity.

Abstract

In the paper, the inhomogeneous states with local translational symmetry are under investigation in the framework of the Landau theory. The phonon potential is defined as a compensating field of local representation of the subgroup of translations. The constructed phenomenological Ginzburg-Landau potential takes into account both electromagnetic and electron-phonon interactions explicitly. The suggested phenomenological model does not require doubling of charge to get the correct expression of current density in the Londons equations and is in agreement with the BCS model. A phenomenological description of sound based on the phonon potential is also proposed.