Gauge Invariance and Spontaneous Symmetry Breaking in Two-Gap Superconductors

TL;DR

This paper investigates gauge invariance in two-gap superconductors, revealing that explicit symmetry breaking occurs due to multiple phases and Josephson coupling, and proposing a new kinetic coupling term to restore gauge symmetry via spontaneous symmetry breaking.

Contribution

It introduces a novel kinetic coupling between vector fields that restores gauge invariance in two-gap superconductors through spontaneous symmetry breaking.

Findings

Explicit gauge symmetry breaking by multiple phases and Josephson coupling.

Restoration of gauge invariance achieved by adding a kinetic coupling term.

Electrodynamics described in terms of supercurrents within the superconductor.

Abstract

The gauge symmetry of the Ginzburg-Landau theory for two-gap superconductors is analyzed in this letter. We argue that the existence of two different phases, associated with the two independent scalar Higgs fields, explicitly breaks the gauge symmetry of the Ginzburg-Landau hamiltonian, unless a new additional vector field is included. Furthermore, the interference term, or Josephson coupling, holding a direct dependence with the phase difference, also explicitly breaks down the gauge symmetry. We show that a solution for the problem is achieved by adding an additional kinetic coupling term between the two vector fields, which generates the desired terms through a spontaneous symmetry breaking mechanism. Finally, the electrodynamics of the system is also presented in terms of the supercurrents inside the superconducting region.