Lorentz-symmetry Violation and Electrically Charged Vortices in the Planar Regime

TL;DR

This paper explores Lorentz violation effects in a reduced planar Abelian-Higgs model, revealing charged vortex solutions with unique electromagnetic properties and implications for the Aharonov-Casher effect in layered superconductors.

Contribution

It introduces a novel Lorentz-violating planar model derived from 3+1 dimensions and analyzes its vortex solutions and electromagnetic phenomena.

Findings

Charged vortex solutions with screened electric fields.

Recovery of Nielsen-Olesen vortices asymptotically.

Implications for the Aharonov-Casher effect in layered superconductors.

Abstract

We start from a Lorentz non-invariant Abelian-Higgs model in 1+3 dimensions, and carry out its dimensional reduction to $D=1+2$. The planar model resulting thereof is composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background, $v^{\mu}$) that realizes Lorentz violation for the reduced model. Vortex-type solutions of the planar model are investigated,revealing charged vortex configurations that recover the usual Nielsen-Olesen configuration in the asymptotic regime. The Aharonov-Casher Effect in layered superconductors, that shows interference of neutral particles with a magnetic moment moving around a line charge, is also studied. Our charged vortex solutions exhibit a screened electric field that induces the same phase shift as the one caused by the charged wire.