# Improvements in the $GW$ and Bethe-Salpeter-equation calculations on phosphorene

## TL;DR

This paper improves $GW$ and Bethe-Salpeter-equation calculations for phosphorene, emphasizing convergence and providing results that align well with experimental data for electronic and optical properties.

## Contribution

It presents a detailed convergence study and refined calculations of phosphorene's electronic and optical properties using $GW$ and BSE methods, with results consistent with experiments.

## Key findings

- QP band gap of 2.06 eV in agreement with experiments
- Optical gap of 1.22 eV from BSE calculations
- Excitonic binding energy of 0.84 eV

## Abstract

Phosphorene is a bidimensional material that has properties useful for semiconductor devices. In this work we studied the electronic and optical properties of this material using the $GW$ approximation and the Bethe-Salpeter equation (BSE) methods. We stress the importance of a careful convergence study of the most relevant parameters, and we show how they affect the result of the calculations. A comparison with previous results is given. The QP band gap obtained was 2.06 eV and it is in good agreement with experimental results. BSE calculations were performed on top of $G_0W_0$ to include excitonic effects. The absorption spectrum was analysed and an optical gap of 1.22 eV was obtained. The calculated excitonic binding energy is 0.84 eV, also in good agreement with experimental results.