Disorder effects on the ballistic transport of gated phosphorene superlattices

Abstract

In this paper, we carry out a theoretical study of the electronic ballistic transport in gated phosphorene superlattices. Our work is focused on the effects by the random introduction of structural disorder in the electrostatic potential barriers. Specifically, we consider various degrees of disorder in the width and height of the barriers. To explain the transport of the charge carriers (electrons and holes) in the armchair direction of phosphorene, we employ a low-energy two-band Hamiltonian derived from the tight-binding model. The transmission and conductance are calculated by the transfer matrix technique and the Landauer-B\"uttiker formalism, respectively. We have found that both types of disorder affect the transmission and conductance in different ways, and we also found distinct effects on the charge carriers. In general, the disorder significantly reduces the transmission as well as the peak zones associated with the tunneling effect. Particularly, for disorder in the width, the transmission miniband structure is greatly degraded, while for disorder in the height, the miniband structure is preserved. The variation in the width of the barriers interferes directly with the Fabry-P\'erot resonances of the propagating waves, while the variation in the height mainly reduces the magnitude of the transmission due to the dominance of evanescent waves. Consequently, the conductance loses its oscillatory characteristic and experiences flattening under the influence of disorder of the width, in contrast with the disorder of the height in which the oscillation prevails. Finally, we found that both types of disorder induce a redistribution of electron states. Specifically, the allowed energy bands are increased, and the occupation number as well as the accumulation of states are greatly reduced, which is in accordance with the effects of disorder observed in the transport properties.