Many-body quantum Monte Carlo study of 2D materials: cohesion and band gap in single-layer phosphorene

TL;DR

This study uses quantum Monte Carlo methods to accurately determine the electronic band gap and cohesion of 2D phosphorene, providing benchmarks for GW calculations and experimental data, and highlighting the importance of many-body effects.

Contribution

It demonstrates the effectiveness of QMC in predicting 2D material properties, offering more reliable band gap estimates than existing GW methods.

Findings

QMC predicts the quasiparticle band gap of phosphorene to be about 2.4 eV.

The optical gap is estimated at 1.75 eV, consistent with recent experiments.

Phosphorene's cohesion is only slightly less than bulk black phosphorus.

Abstract

Quantum Monte Carlo (QMC) is applied to obtain the fundamental (quasiparticle) electronic band gap, $\Delta_f$, of a semiconducting two-dimensional (2D) phosphorene whose optical and electronic properties fill the void between graphene and 2D transition metal dichalcogenides. Similarly to other 2D materials, the electronic structure of phosphorene is strongly influenced by reduced screening, making it challenging to obtain reliable predictions by single-particle density functional methods. Advanced GW techniques, which include many-body effects as perturbative corrections, are hardly consistent with each other, predicting the band gap of phosphorene with a spread of almost 1 eV, from 1.6 to 2.4 eV. Our QMC results, from infinite periodic superlattices as well as from finite clusters, predict $\Delta_f$ to be about 2.4 eV, indicating that available GW results are systematically underestimating the gap. Using the recently uncovered universal scaling between the exciton binding energy and $\Delta_f$, we predict the optical gap of 1.75 eV that can be directly related to measurements even on encapsulated samples due to its robustness against dielectric environment. The QMC gaps are indeed consistent with recent experiments based on optical absorption and photoluminescence excitation spectroscopy. We also predict the cohesion of phosphorene to be only slightly smaller than that of the bulk crystal. Our investigations not only benchmark GW methods and experiments, but also open the field of 2D electronic structure to computationally intensive but highly predictive QMC methods which include many-body effects such as electronic correlations and van der Waals interactions explicitly.