  In this work, using two scalar fields ($\phi$, $\psi$) coupled to 4+1
dimensional gravity, we construct novel topological brane solutions through an
explicit $U(1)$ symmetry breaking term. The potential of this model is
constructed so that two distinct degenerate vacua in the $\phi$ field exist, in
analogy to the $\phi^{4}$ potential. Therefore, brane solutions appear due to
the vacuum structure of the $\phi$ field. However, the topology and vacuum
structure in the $\psi$ direction depends on the symmetry breaking parameter
$\beta^{2}$, which leads to different types of branes. As a result, one can
interpret the present model as a combination of a $\phi^{4}$ brane with an
auxiliary field, which leads to deviations from the $\phi^{4}$ system with the
brane achieving a richer internal structure. Furthermore, we analyse in detail
the behaviour of the superpotentials, the warp factors, the Ricci and
Kretschmann scalars and the Einstein tensor components. In addition to this, we
explore the stability of the brane in terms of the free parameters of the
model. The analysis presented here complements previous work and is
sufficiently novel to be interesting.
