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

Quantum Monte Carlo (QMC) is applied to obtain the fundamental (quasiparticle) electronic band gap, Δ_f, of a semiconducting 2D phosphorene. 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 or many-body GW methods. Using the recently uncovered universal scaling between the exciton binding energy and Δ_f, we predict the optical gap of about 1.7 eV that can be directly related to experiments. The QMC gaps agree with recent optical absorption and photoluminescence measurements. 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.