  In this work we study asymmetric thick braneworld scenarios, generated after
adding a constant to the superpotential associated to the scalar field. We
study in particular models with odd and even polynomial superpotentials, and we
show that asymmetric brane can be generated irrespective of the potential being
symmetric or asymmetric. We study in addition the nonpolynomial
sine-Gordon-like model, also constructed with the inclusion of a constant in
the standard superpotential, and we investigate gravitational stability of the
asymmetric brane. The results suggest robustness of the new braneworld
scenarios and add further possibilities for the construction of asymmetric
branes.
