We investigate the presence of vortex solutions in potentials without vacuum state. The study is conducted considering Maxwell and Chern-Simons dynamics. Also, we use a first order formalism that helps us to find the solutions and their respective electromagnetic fields and energy densities. As a bonus, we get to calculate the energy without knowing the explicit solutions. Even though the solutions present a large "tail" which goes far away from the origin, the magnetic flux remains a well defined topological invariant.
@article{arxiv.1807.05431,
title = {Vortices in vacuumless systems},
author = {M. A. Marques},
journal= {arXiv preprint arXiv:1807.05431},
year = {2019}
}