Tunneling effect of fermions in silicene through potential barrier

The influence of a rectangular potential barrier on the quantum transport of fermions in silicene is explored. Specifically, analytical solutions are presented to derive transmission and reflection probabilities together with conductance. It is shown that the transmission is highly sensitive to both the barrier height and incident energy. As a result, the occurrence of Klein and resonant tunnelings is observed, with a significant dependence on the barrier width. Notably, it is found that perfect transmission extends beyond normal incidence, occurring at various oblique angles. Moreover, the transmission pattern exhibits a more fragmented structure with increasing barrier width, reminiscent of Fabry-P\'erot resonances. In contrast, the conductance displays a non-monotonic dependence on incident energy and features rapid oscillations with a rising barrier height. However, at a constant barrier height, there is a minimal disparity among conductance profiles for high incident energy values. When incident energy equals the barrier height, the conductance experiences a local minimum. For a thin barrier, a substantial reduction in conductance is observed, unlike the oscillatory behavior seen with a thicker barrier. These findings underscore the progress in silicene research and offer a fresh perspective on the relativistic applications of tunneling in this material.