Self-dual $CP(2)$ vortex-like solitons in the presence of magnetic impurities

TL;DR

This paper explores vortex-like solitons in gauged-$CP(2)$ models with magnetic impurities, demonstrating self-dual structures, quantized flux, and impurity effects on solutions in Maxwell and Chern-Simons scenarios.

Contribution

It introduces self-dual vortex solutions in gauged-$CP(2)$ models with impurities, extending the BPS formalism and analyzing impurity effects on vortex configurations.

Findings

Existence of vortex solutions with magnetic impurities in both Maxwell and Chern-Simons-$CP(2)$ models.

Impurities influence BPS potentials and equations, affecting vortex behavior.

Solutions exhibit nonmonotonic magnetic and electric field profiles due to impurities.

Abstract

We investigate the existence of vortex configurations in two gauged-$CP(2)$ models extended via the inclusion of magnetic impurities. In particular, we consider both the Maxwell-$CP(2)$ and the Chern-Simons-$CP(2)$ enlarged scenarios, separately. We choose a $CP(2)$-field configuration with a null topological charge not only in the simplest (free) case, but also when coupled to an Abelian gauge field. The implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism shows that the effective models for such a configuration possess a self-dual structure which looks like those inherent to the gauged sigma models. Therefore, when the $CP(2)$ field is coupled to the Maxwell term, the corresponding total energy possesses both a well-defined Bogomol'nyi bound and a quantized magnetic flux. Further, when the $CP(2)$ scenario is gauged with the Chern-Simons action, the total electric charge is verified to be proportional to the quantized magnetic flux. In addition, the analysis verifies that the magnetic impurity contributes to the BPS potentials and appears in both the models' BPS equations. Next, we introduce a Gaussian type impurity and solve the self-dual equations via a finite-difference scheme. The resulting solutions present a nonmonotonic behavior that flips both the magnetic and electric fields. Finally, we discuss the topologically trivial solutions in the limit for which the impurity becomes a Dirac $\delta $-function.