Energetic Stability of Free-standing and Metal-Supported Borophenes: Quantum Monte Carlo and Density Functional Theory Calculations

Abstract

Quantum Monte Carlo (QMC) and density-functional theory (DFT) calculations were carried out to study cohesion energetics of two-dimensional (2D) sheets of boron atoms called borophenes. Our QMC calculations confirmed the polymorphism among free-standing borophenes that was reported in previous DFT studies. Although Perdew–Burke–Ernzerhof (PBE) calculations significantly overestimate the cohesive energies of 2D boron sheets, DFT-PBE relative energetics with respect to each other among various free-standing borophenes are found to be in quantitative agreement with the corresponding QMC results. This suggests that one can make reliable predictions for relative stability of different boron sheets through DFT-PBE calculations. Our analysis of PBE formation energies of borophenes on metal surfaces shows that the polymorphic range is extended for borophenes on the Ag(111) and the Au(111) surfaces beyond that of free-standing borophenes, reflecting recent experimental synthesis of β12 and χ3 boron sheets on the Ag(111) surface. We have also found that a hexagonal borophene can be stabilized through charge transfer from a metal surface and is energetically favored on the Al(111) surface over other borophene structures. Finally, it is found that the bilayer formation could be energetically favored over its monolayer form for the borophene–Au system, especially for borophenes with hexagonal hole densities η lower than 1/9. This leads to our prediction that in addition to its monolayer form, a bilayer η = 1/12 borophene can be synthesized on the Au(111) surface, opening a new possibility for borophene-based electronic devices.

Bilayer borophene: The effects of substrate and stacking

“…We call this structure "the relaxed model", which is in agreement with several previous works. [14][15][16] However many stronger theoretical and experimental works suggest a closer interlayer distance (∼ 2 Å), and a covalent interlayer interaction for bilayer borophene. [17][18][19] Here, two important questions arise: Why the interlayer interaction should be covalent?…”

“…For instance, theoretical studies have suggested the interlayer distance of bilayer borophene in the range of 2.5 to 3 Å, suggesting a van der Waals (vdW) interaction between the layers. [14][15][16] However, the synthesized bilayer borophenes show a much closer interlayer distance, around 2 Å, implying relatively strong covalent bonds. 17,18 However, some theoretical studies considered some constraints to design the bilayer borophenes with similar interlayer distance to the experiment.…”

A two-dimensional tunable double Weyl fermion in BL-α borophene

“…One contender in the 2D materials that has attracted tremendous attention is borophene, [23][24][25][26][27][28][29][30][31][32][33][34] a single layer of boron. Because of the electron deficiency, borophene cannot have a normal hexagonal structure like graphene, but a boron atom is introduced at the center of the hexagonal structure, resulting in a triangle structure.…”

Structural Stability of Graphene-Supported Pt Layers: Diffusion Monte Carlo and Density Functional Theory Calculations

“…To this end, this study utilizes density functional theory (DFT) , calculations benchmarked to diffusion Monte Carlo (DMC) calculations to examine the structural stability and binding nature of various Pt layers on a graphene substrate. DMC, which fully incorporates electron–electron correlations, has been used to provide quantitatively accurate descriptions of cohesion energetics − and interlayer bindings − for different 2D vdW systems. The accuracy from DMC benchmarking is important here because the mixture of chemical, metallic, and vdW binding is particularly challenging to describe within the DFT framework alone.…”