Unbalanced superconductivity induced by the constant electron-phonon coupling on a square lattice

TL;DR

This paper investigates unbalanced superconductivity on a square lattice with constant electron-phonon coupling, revealing how unbalance affects thermodynamic properties beyond BCS theory using Eliashberg formalism.

Contribution

It introduces analysis of unbalanced superconductivity with k-dependent dispersion on a square lattice within the Eliashberg framework, highlighting effects beyond BCS theory.

Findings

Balanced superconductivity is suppressed due to high effective mass.

Unbalanced superconductivity shows distinct thermodynamic behavior.

Strong-coupling effects are significant in the unbalanced state.

Abstract

In the present paper, we analyze the properties of the unbalanced superconducting state on a square lattice with the constant value of the electron-phonon coupling function. We conduct our analysis in the framework of the Eliashberg formalism, explicitly considering {\bf k}-dependence of the electron and phonon dispersion relations. It is found that the balanced superconducting state does not induce itself in the system due to the high value of the electron effective mass. However, in the unbalanced case the thermodynamic properties of the superconducting condensate can be distinctly different from the predictions of the Bardeen-Cooper-Schieffer theory; when the coupling constant value in the diagonal channel of the self-energy is diminished comparing to the non-diagonal channel. This is due to the reduced dimensionality of the tested system and the strong-coupling effects included in the Eliashberg formalism.