The Impact of Lorentz Violation on the Klein Tunneling Effect

We discuss the impact of a tiny Lorentz-violating $b^\mu$ 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 $b^\mu$ are assumed constants. The results show that Lorentz-violation modification to the transmission rate depends on the observer Lorentz nature of $b^\mu$. For a spacelike or lightlike $b^\mu$ the induced resonant frequency shift depends on the polarization, while for timelike $b^\mu$ there is essentially no modification.