Vortices in vacuumless systems

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.