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

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