Lorentz-violating QED inspired superconductivity

TL;DR

This paper explores how Lorentz-violating modifications to the Ginzburg-Landau model affect superconductivity, revealing new phases and phenomena that could explain unusual superconducting states like those in UTe₂.

Contribution

It introduces a Lorentz-violating CPT-odd term into the Ginzburg-Landau model and analyzes its impact on superconducting phenomenology and vortex behavior.

Findings

Small Lorentz-violating term preserves Meissner state

Large terms induce in-plane currents and anomalous vortices

Model suggests possible new superconducting phases

Abstract

We studied a Lorentz-violating inspired Ginzburg-Landau model for superconductivity where we considered a CPT-odd contribution given by $(k_{AF})^{\mu}$, also known as the Carroll-Field-Jackiw term. In the static limit of the equations, we could find a pair of modified Ginzburg-Landau equations. Furthermore, these equations were reduced to the London equation for the magnetic field when assumed that the characteristic length of the order parameter is much smaller than the characteristic length of the magnetic field, i.e. the London penetration length. Our numerical solutions showed a simple Meissner state when this new term is small compared to $\lambda_L$ and a phase transition into phases with strong in-plane currents and anomalous vortices for large contributions. This model becomes useful in exemplifying the changes in the phenomenology of superconductors when the setup of the system shows an important breakdown of Lorentz invariance. Based on these results, we discuss how such models might be the hallmark of unusual superconducting states where there is a direction where the system shows stratification, as in anapole superconductors UTe$_2$.