Éxcitons em multicamadas rotacionadas de fosforeno

Abstract

Phosphorene – a monolayer of black phosphorus – is one of the constituents of the large family of two-dimensional (2D) materials with semiconducting characteristics, exhibiting physical properties that depend on crystallographic orientations due to its puckered crystalline structure with sp3-type hybridization, which leads to highly anisotropic band structures. Its energy gap is tunable with the number of layers, ranging from ≈ 2 eV (monolayer) to ≈ 0.3 eV (bulk). Due to reduced dimensionality and dielectric screening, phosphorene multilayers exhibit pronounced excitonic effects with strong Coulomb interactions between electrons and holes, leading to high binding energies and long lifetimes. These unique properties of phosphorene multilayers make them potential candidates for applications in optoelectronic devices operating in the mid-infrared to near-infrared range. Another degree of freedom to tune the electronic properties of a multilayer system of 2D materials is through the relative rotation between layers. Thus, motivated by the strong excitonic effects and pronounced anisotropic properties of phosphorene, in this work, we explore the formation of intralayer and interlayer excitons in a system of rotated phosphorene multilayers separated by dielectrics with different thicknesses and dielectric constants, positioning each phosphorene layer at a certain relative angle concerning adjacent layers. Our theoretical approach combines the effective mass approximation to treat in-plane degrees of freedom with the tight-binding model to handle interlayer couplings, which we assume here to be exponentially dependent on the interlayer distance. We obtain the electron-hole pair interaction potential in a semi-analytical form, generalizing the Rytova-Keldysh solution of the Poisson equation through the transfer matrix method for structures composed of phosphorene layers separated by dielectrics, with the system deposited on specific substrate and superstrate, assuming the long-range Coulomb interaction regime. Results of the electron-hole interaction potential, binding energies, and exciton energies for different system configurations are discussed, analyzing the effects of the dielectric spacer thickness and dielectric constants, the number of phosphorene layers, and the rotation angle.