Tensor extension of the Abelian-Higgs model for a superconductor
We extend the Abelian-Higgs model of superconductivity to incorporate higher-spin particles. Microscopically, these higher-spin states can be modeled as multi-electron clusters, such as spin-1 Copper pairs or quartets, existing alongside the standard Cooper pairs predicted by BCS theory. To account for these composites, we introduce vector and higher-rank tensor non-gauge fields into the Lagrangian, which serve as sources for higher-rank tensor gauge fields. In this work, we extend the particle spectrum by one rank (including the necessary auxiliary fields) and examine the resulting modifications to the fundamental phenomenological parameters of superconductivity, specifically the penetration depth and the correlation length.
hep-th↗