Many-Body Quantum Monte Carlo Study of 2D Materials: Cohesion and Band Gap in Single-Layer Phosphorene

Abstract

Quantum Monte Carlo (QMC) is applied to obtain the fundamental (quasiparticle) electronic band gap, ∆ 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 ∆ 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 ∆ 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.

Raman Activity of Multilayer Phosphorene under Strain

“…In addition to vibrational properties discussed here, scatter between different experimental sets is also observed in electronic properties, which causes a scatter of ≈1 eV in the measured optical band gap of single-layer phosphorene. 9 Hence, benchmark results free of such experimental complexities, such as ours, are required.…”

Diffusion quantum Monte Carlo andGWstudy of the electronic properties of monolayer and bulk hexagonal boron nitride

“…QMC methods have only recently been applied to calculate the energy gaps of 2D materials 40,41 . A major challenge is the need to extrapolate the QMC band gaps to the thermodynamic limit of large system size, because the computational expense of the method necessitates the use of relatively small simulation supercells subject to periodic boundary conditions 40 .…”

A first-principles Quantum Monte Carlo study of two-dimensional (2D) GaSe

“…Although more computationally demanding than DFT, QMC has been shown to produce more accurate results for ground and excited state energies in condensed matter systems than DFT and GW. In addition to low dimensional studies involving nanoclusters 64 and nanoparticles, 65 there have been few studies involving the study of monolayer [58][59][60]66,67 and bilayer [55][56][57] materials. Specifically, the cohesive energies and bandgaps have been accurately determined at the DMC level for monolayer phosphorene 66 and monolayer GeSe.…”