Revisiting Anderson-Higgs mechanism: application of Lieb-Schultz-Mattis theorem

TL;DR

This paper explores the application of the Lieb-Schultz-Mattis theorem to a 3D electron model with superconductivity, revealing potential conflicts with experimental observations and implications for theoretical models.

Contribution

It applies the Lieb-Schultz-Mattis theorem to analyze superconductivity models, highlighting possible symmetry breaking and constraints on theoretical descriptions.

Findings

Fully gapped s-wave superconductivity may break translation symmetry.

Inconsistencies between supersolid states and experiments are identified.

Constraints on theoretical models of superconductivity are proposed.

Abstract

We consider an electron model of superconductivity on a three-dimensional lattice where there are on-site attractive Hubbard interaction and long-range repulsive Coulomb interaction. It is claimed that fully gapped $s$-wave superconductivity within this model, if present, exhibits spontaneous translation symmetry breaking possibly related to a charge order. Our discussions are based on an application of the Lieb-Schultz-Mattis theorem under some physical assumptions. The inconsistency between the proposed supersolid and experiments can impose some constraints on a reasonable choice of a theoretical model.