A Comment on the Topological Phase for Anti-Particles in a Lorentz-violating environment

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.