Two No-Go Theorems on Superconductivity

TL;DR

This paper presents two theorems showing that superconductivity may involve surface persistent currents stabilized by boundary fields and that the traditional symmetry-breaking explanation is not necessary, emphasizing the role of massive photons.

Contribution

It introduces no-go theorems demonstrating that surface persistent currents can exist without bulk symmetry breaking, challenging conventional views on superconductivity.

Findings

Surface persistent currents can be stabilized by boundary magnetic fields.

Superconductivity may be characterized by massive photons rather than U(1) symmetry breaking.

Symmetry breaking of the U(1) phase is absent for almost all gauge fields at finite temperature.

Abstract

We study lattice superconductors such as attractive Hubbard models. As is well known, Bloch's theorem asserts absence of persistent current in ground states and equilibrium states for general fermion systems. While the statement of the theorem is true, we can show that the theorem cannot exclude possibility of a surface persistent current. Such a current can be stabilized by boundary magnetic fields which do not penetrate into the bulk region of a superconductor, provided emergence of massive photons, i.e., Meissner effect. Therefore, we can expect that a surface persistent current is realized for a ground/equilibrium state in the sense of stability against local perturbations. We also apply Elitzur's theorem to superconductors at finite temperatures. As a result, we prove absence of symmetry breaking of the global $U(1)$ phase of electrons for almost all gauge fields. These observations suggest that the nature of superconductivity is the emergence of massive photons rather than the symmetry breaking of the $U(1)$ phase of electrons.