  The Aharonov-Bohm-Casher problem is examined for a charged particle
describing a circular path in presence of a Lorentz-violating background
nonminimally coupled to a spinor and a gauge field. It were evaluated the
particle eigenenergies, showing that the LV background is able to lift the
original degenerescence in the absence of magnetic field and even for a neutral
particle. The Aharonov-Casher phase is used to impose an upper bound on the
background magnitude. A similar analysis is accomplished in a space endowed
with a topological defect, revealing that both the disclination parameter and
the LV background are able to modify the particle eigenenergies. We also
analyze the particular case where the particle interacts harmonically with the
topological defect and the LV background, with similar results.
