Effect of periodic potential on transmission in phosphorene

Abstract

We study the transmission gaps of carriers in phosphorene through a superlattice of $n$ identical periodic units, each one formed by a barrier and a well. Using Bloch’s theorem in combination with the transfer matrix method, we first derive the solutions of the energy spectrum and then determine the transmission. The influence of incident energy, barrier height, potential region widths, number of periods, and transverse wave vector on the transmission behavior is analyzed. We find that for a single barrier ($n=1$), there is no transmission peak. However, as the number of periods increases ($n>1$), transmission resonances begin to appear. Interestingly, pseudo-gaps that appear in the early stages of periodicity evolve into well-defined transmission gaps as $n$ increases. The number, width, and position of these gaps can be finely tuned by adjusting the structural parameters. At normal incidence, we observe a well-defined forbidden gap, indicating no Klein tunneling effect.