The effects of substrate and stacking in bilayer borophene

Bilayer borophene has recently attracted much interest due to its outstanding mechanical and electronic properties. The interlayer interactions of these bilayers are reported differently in theoretical and experimental studies. Herein, we design and investigate bilayer β12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _{12}$$\end{document} borophene, by first-principles calculations. Our results show that the interlayer distance of the relaxed AA-stacked bilayer is about 2.5 Å, suggesting a van der Waals interlayer interaction. However, this is not supported by previous experiments, therefore by constraining the interlayer distance, we propose a preferred model which is close to experimental records. This preferred model has one covalent interlayer bond in every unit cell (single-pillar). Further, we argue that the preferred model is nothing but the relaxed model under a 2% compression. Additionally, we designed three substrate-supported bilayers on the Ag, Al, and Au substrates, which lead to double-pillar structures. Afterward, we investigate the AB stacking, which forms covalent bonds in the relaxed form, without the need for compression or substrate. Moreover, phonon dispersion shows that, unlike the AA stacking, the AB stacking is stable in freestanding form. Subsequently, we calculate the mechanical properties of the AA and AB stackings. The ultimate strengths of the AA and the AB stackings are 29.72 N/m at 12% strain and 23.18 N/m at 8% strain, respectively. Moreover, the calculated Young’s moduli are 419 N/m and 356 N/m for the AA and the AB stackings, respectively. These results show the superiority of bilayer borophene over bilayer MoS2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MoS}_2$$\end{document} in terms of stiffness and compliance. Our results can pave the way of future studies on bilayer borophene structures.