Quantum Tunneling in the $$\alpha -T_3$$ Model with an Effective Mass Term

Abstract

We investigate the quantum tunneling properties through a square potential barrier in the $$\alpha -T_3$$ model with an effective mass term. The additional mass term can be induced by the effective magnetic field or the site energy difference on different sublattices, in which the flat band is located at the center or edge of the band gap band, respectively. The linear dispersion in the $$\alpha -T_3$$ model is modified in the presence of the mass term, leading to the destroying of the Klein tunneling for the normal incidence. It is demonstrated that the additional mass term in general suppresses the transmission. When the flat band is located at the band edge, the super-Klein tunneling and the resonant tunneling are considerably suppressed with the increase in the energy gap. For the dice lattice that $$\alpha =1$$, the super-Klein tunneling is preserved when the flat band is located at the center of the band gap.