Tensor extension of the Abelian-Higgs model for a superconductor

TL;DR

This paper extends the Abelian-Higgs model of superconductivity by incorporating higher-spin particles modeled as multi-electron clusters, introducing tensor fields to explore their impact on key superconducting parameters.

Contribution

It introduces a tensor extension to the Abelian-Higgs model, accounting for higher-spin states like multi-electron clusters and analyzing their effects on superconducting properties.

Findings

Modified penetration depth and correlation length due to higher-spin states

Inclusion of tensor fields alters the fundamental parameters of superconductivity

Extended particle spectrum with auxiliary fields enhances the model's descriptive power

Abstract

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.