  Recently, a scheme to analyse topological phases in Quantum Mechanics by
means of the non-relativistic limit of fermions non-minimally coupled to a
Lorentz-breaking background has been proposed. In this letter, we show that the
fixed background, responsible for the Lorentz-symmetry violation, may induce
opposite Aharonov-Casher phases for a particle and its corresponding
antiparticle. We then argue that such a difference may be used to investigate
the asymmetry for particle/anti-particle as well as to propose bounds on the
associated Lorentz-symmetry violating parameters.
