Klein tunneling in the α−T3 model

We investigate Klein tunneling for the $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ model, which interpolates between graphene and the dice lattice via parameter $\ensuremath{\alpha}$. We study transmission across two types of electrostatic interfaces: sharp potential steps and sharp potential barriers. We find both interfaces to be perfectly transparent for normal incidence for the full range of the parameter $\ensuremath{\alpha}$ for both interfaces. For other angles of incidence, we find that transmission is enhanced with increasing $\ensuremath{\alpha}$. For the dice lattice, we find perfect, all-angle transmission across a potential step for incoming electrons with energy equal to half of the height of the potential step. This is analogous to the ``super'', all-angle transmission reported for the dice lattice for Klein tunneling across a potential barrier.