Condições de contorno para nanofitas de fosforeno com bordas enviesadas

Abstract

Phosphorene, a monolayer of black phosphorus, exhibits a honeycomb-like structure in top view and a puckered structure in other directions. This is due to sp3 hybridization, in which each phosphorus atom establishes three covalent bonds with neighboring atoms in the monolayer. As a result, phosphorene-based nanostructures can present different edge terminations, called normal and skewed, of the zigzag and armchair type. In the effective theoretical description of the phosphorene monolayer, the literature provides tight-binding models that account for two, five, or ten hopping interactions. Initially, this research employed these models to describe the band structure of the infinite system, exploring the role of each energetic connection between sites in the three theoretical models. It was found that adjustments in the interaction strengths, in-plane and out-of-plane, can drastically change the electronic dispersions of the system’s energy bands. Subsequently, using the three tight-binding models, phosphorene nanoribbons with different widths and distinct edge termination types were studied: normal zigzag, normal armchair, skewed zigzag, and skewed armchair. Results on the dispersion relations and wave functions of edge states were discussed. It was verified, for the case of nanoribbons with normal zigzag and skewed armchair edges, that adjustments in the interaction contributions allow quasi-flat edge states to become perfectly flat. As a perspective, it is intended to employ the continuum approximation, derived from the Taylor series expansion around the Γ point of the tight-binding model, to describe the electronic properties of different phosphorene nanoribbons. To this end, suitable boundary conditions will be proposed to describe the electronic properties of phosphorene nanoribbons with skewed and normal edges. The analytical results can then be compared with those provided by the tight-binding models. Finally, we seek to demonstrate the dependence of the bandgap on the width of the nanoribbons.