Persistence of translational symmetry in the BCS model with radial pair interaction

TL;DR

This paper proves that in a 2D BCS model with radial pairing, translational symmetry remains unbroken below the critical temperature, and extends some results to 3D for zero angular momentum.

Contribution

It demonstrates the persistence of translational symmetry in the BCS model with radial interaction, extending results to three dimensions for zero angular momentum.

Findings

Translational symmetry is not broken below the critical temperature in the 2D BCS model.

Results extend to 3D for the case of zero angular momentum.

Symmetry preservation holds within a certain temperature interval below critical.

Abstract

We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the critical temperature. In the case of vanishing angular momentum our results carry over to the three-dimensional case.