Minimal Interaction in the Local Landau Theory and Construction of the Phenomenological Ginzburg-Landau Potential in Terms of Electron-Phonon Interaction

TL;DR

This paper develops a local Landau theory framework to describe inhomogeneous states with local translational symmetry, linking it to electron-phonon interactions and constructing a Ginzburg-Landau potential relevant for high-temperature superconductors.

Contribution

It introduces a symmetry-based method for describing inhomogeneous states and constructs a Ginzburg-Landau potential incorporating electron-phonon interactions.

Findings

Correctly defines transformational properties of physical fields in local Landau theory.

Proposes a mechanism for constructing Ginzburg-Landau potential for HTS states.

Identifies minimal interaction as responsible for electron-phonon coupling in BCS model.

Abstract

In the present paper, the method for describing inhomogeneous states with local translational symmetry is proposed, based on the symmetry-dependent interaction between the order parameter (OP) and compensating field in the phenomenological Landau theory. It is shown that dimensionality of the compensating field in the extended derivative is associated with representation of the OP and does not coincide with the dimensionality of the derivative itself. This results in the correct definition of transformational properties of physical fields in the local Landau theory and in the equations of continuum theory of dislocations in the system of equations of state. The mechanism is proposed to construct the Ginzburg-Landau potential for states with local translational symmetry that correspond to HTS states. It is shown that minimal interaction between the superconducting OP and tensor compensating field is responsible for electron-phonon interaction in the BCS model.