On the influence of a Rashba-type coupling induced by Lorentz-violating effects on a Landau system for a neutral particle

• Landau system from crossed electric and magnetic fields and fixed time-like vector.
• Analogues of the Rashba coupling, the Zeeman term and the Darwin term.
• Lorentz symmetry breaking effects on a two-dimensional quantum ring.
• Upper bound for the Lorentz symmetry breaking parameters.

We study a possible scenario of the Lorentz symmetry violation background that allows us to build an analogue of the Landau system for a nonrelativistic Dirac neutral particle interacting with a field configuration of crossed electric and magnetic fields. We also discuss the arising of analogues of the Rashba coupling, the Zeeman term and the Darwin term from the Lorentz symmetry breaking effects, and the influence of these terms on the analogue of the Landau system confined to a two-dimensional quantum ring. Finally, we show that this analogy with the Landau system confined to a two-dimensional quantum ring allows us to establish an upper bound for the Lorentz symmetry breaking parameters.