Klein tunneling and Fabry-Perot resonances in the α - T 3 bilayer with aligned stacking

Abstract

This paper investigates the quantum tunneling effect on the α − T 3 bilayer with aligned stacking. An effective model is constructed to describe the properties around the triple band crossings for stacking with a vertical alignment of sites in the bilayer system. Focusing on these band crossings, it is found that while the energy spectrum remains gapless throughout, it is characterized by flat energy bands. Subsequently, the transmission coefficient, T, for Dirac quasi-electrons across a rectangular potential barrier is calculated, alongside the relationship between the transmission rate and the coupling parameter α. It is observed that super-tunnel phenomena occur at certain values of the quasiparticle energy, where the transmission is perfect regardless of the angle of incidence on the barrier, with α = 1. Furthermore, it is found that for a wide range of parameter values, the transmittance evolves monotonically and exponentially with increasing alpha. The paper also highlights the occurrence of the Klein paradox in the system, where quasiparticles approaching the barrier with zero-angle incidence exhibit ideal quantum transparency.