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The Impact of Lorentz Violation on the Klein Tunneling Effect

We discuss the impact of a tiny Lorentz-violating $b^μ$ term on the one dimensional motion of a Dirac particle scattering on a rectangular barrier. We assume the experiment is performed in a particular inertial frame, where the components of $b^μ$ are assumed constants. The results show that Lorentz-violation modification to the transmission rate depends on the observer Lorentz nature of $b^μ$. For a spacelike or lightlike $b^μ$ the induced resonant frequency shift depends on the polarization, while for timelike $b^μ$ there is essentially no modification.