Dirac cones in gated multilayer black phosphorus

Abstract

Black Phosphorus, one of the allotropes of the element Phosphorus, has gained a lot of attention since its rediscovery from the perspective of a two-dimensional material in 2014. Due to its interesting properties, such as high carrier mobility and thickness-dependent energy gap, multilayer BP is considered a material with great potential for applications in nano and optoelectronics. In particular, the wide range of values that its thickness-dependent gap can assume, ranging from ~2:0 eV (single-layer) to ~0:3 eV (bulk), has significant importance since it covers a broad range of the electromagnetic spectrum, not reached by other two-dimensional semiconductors. Additionally, the gap can also be tuned by other means, such as the application of an external perpendicular electric field. It has been shown that such mechanism induces a topological phase transition in the system, turning phosphorene from a semiconductor into a semi-metal and eventually into a Dirac semi-metal, at which stage the presence of Dirac cones can be observed in the energy spectrum of phosphorene. In this Monograph, we explore the electronic properties of gated multilayer phosphorene within the context of a tight-binding model, using an unscreened electric field approximation, giving emphasis to the appearance of the Dirac spectra, a transition that occurs when the gate density ng associated with the external electric field is greater than some critical value nc. Afterwards, a similar calculation is performed for phosphorene nanoribbons with zigzag and armchair edges. Finally, we suggest a scheme to determine the thickness and edge orientation of phosphorene nanoribbons.