Propriedades eletrônicas do fosforeno

Abstract

The search for new materials with useful electronic properties has led to an increasing interest on the investigation of a class of layered solids that can be produced as single or few layers. These new two-dimensional (2D) materials, which were first brought to attention by the production of graphene in 2004 , have been shown to display properties that are not found in their bulk form. Among these substances, there has been considerable interest on the study of black phosphorus, an allotrope of phosphorus. In contrast with graphene, black phosphorus is a semiconductor, and its high electronic mobility makes it a possible candidate for device applications. One important aspect of the electronic structure of black phosphorus, for instance, is the dependence of the gap on the number of layers. Experiments have shown that this property varies from ≈ 2.0 eV (for the monolayer) to ≈ 0.3 eV (for the bulk ), covering a frequency range not previously observed in other 2D materials. Recently, a series of calculations have obtained the band structure of black phosphorus, both from a first principles approaches, k · p methods, as well as tight-binding and continuum models. The results have shown that black phosphorus presents a large anisotropic effective masses and, in addition, that the gap itself can be modified by the application of an external bias. Most of these works have not considered the effects of edge termination and only considered single or bilayer black phosphorus, due to the increasing computational demands as the number of layers is increased. In this work, we propose boundary conditions based on sublattice symmetries for black phosphorus nanoribbons with zigzag and armchair edges using the continuum approach and show that our results for the energy spectra exhibit good agreement with those obtained by using the five-parameter tight-binding model. As a consequence, we demonstrate that the bands gaps for nanoribbons with di#erent terminations have different scaling laws. We also extend the previous proposed tight-binding and continuum approaches to consider black phosphorus #lms with arbitrary numbers of layers. We show that a system of N coupled black phosphorus layers can be approximately mapped into a system of N uncoupled single layers. Expressions for the low-energy electron and hole bands, as well as their effective masses are derived. This in turn permits a straightforward calculation of the Landau level spectrum of the system, as will be also discussed here. The combination of the methods developed here allows the study of general black phosphourus nanostructures, such as nanorings, quantum dot, hall bar and etc, in a way that is computationally cheap if compared to other approaches.