Theoretical Exploration of Structural and Excitonic Properties in Black Phosphorus: From First-Principles to a Semi-Empirical Approach
Diego Guedes‐Sobrinho, Celso R. C. Rêgo, Gabriel Reynald Da Silva, Henrique R. Da Silva, Wolfgang Wenzel, Maurício J. Piotrowski, Alexandre C. Dias
Abstract
Black phosphorus serves as an exemplary stacked bidimensional semiconductor, exhibiting anisotropic features in electronic and optical properties that demand special attention in theoretical investigations. Herein, we employed a series of computational protocols, starting with first-principles approaches (particularly density functional theory─DFT), combined with the solution of the Bethe–Salpeter equation within the tight-binding method to explore the structural stability and optoelectronic properties (bandgap, exciton binding energies, and optical absorption) of black phosphorus (P n ) across layers ranging from n = 1 to 6 and bulk. In our DFT investigations, we observed that empirical and semiempirical van der Waals models, contributing a dispersion energy component, revealed a myriad of differences and similarities in properties, such as interlayer nonbonded interactions. Notably, the many-body dispersion correction exhibited superior performance in connecting layered systems with the bulk. The magnitude of dispersion energies correlated with the stability during the aggregation process P ( n –1) + P 1 → P n . Additionally, the bandgap, properly corrected through relativistic quasi-particle calculations, narrowed due to enhanced interlayer wave function overlap, a result of the dispersion energies promoting the shortening of interlayer distances. Subsequently, we utilized the band structure relativistically corrected as a starting point to obtain the Hamiltonian, achieved through the generation of maximally localized Wannier functions. This facilitated a screening of the electron–hole (e–h) pairwise interaction Coulomb potential, specifically the exciton binding energy. We identified an indirect impact of the dispersion energies on excitonic properties, which were effectively described by the Rytova–Keldysh model for the e–h Coulomb potential, aligning well with photoluminescence experiments.