# Tight Binding Parametrization of Few-layer Black Phosphorus from First-Principles Calculations

## TL;DR

This paper develops a tight-binding model fitted to first-principles calculations to accurately describe the electronic band structures of single-layer, bilayer, and bulk black phosphorus, facilitating studies of complex systems.

## Contribution

The paper introduces a parametrized tight-binding model with 9 or 17 parameters that effectively reproduces ab-initio band structures of black phosphorus across different layers.

## Key findings

- Model accurately fits ab-initio band structures over a wide energy range
- Including overlap parameters improves conduction band fit
- Parameters are consistent across different layer configurations

## Abstract

We employ a tight-binding parametrization based on the Slater Koster model in order to fit the band structures of single-layer, bilayer and bulk black phosphorus obtained from first-principles calculations. We find that our model, which includes 9 or 17 parameters depending on whether overlap is included or not, reproduces quite well the ab-initio band structures over a wide energy range, especially the occupied bands. We also find that the inclusion of overlap parameters improves the quality of the fit for the conduction bands. On the other hand, hopping and on-site energies are consistent throughout the different systems, which is an indication that our model is suitable for calculations on multilayer black phosphorus and more complex situations in which first-principles calculations become prohibitive, such as disordered systems and heterostructures with a large lattice mismatch. We also discuss the limitations of the model and how the fit procedure can be improved for a more accurate description of bands in the vicinity of the Fermi energy.