Simulations of twisted bilayer orthorhombic black phosphorus

We identified, by means of coincidence site lattice theory, an evaluative stacking phase with a wavelike Moir\'e pattern, denoted as $2\mathrm{O}\text{\ensuremath{-}}\mathrm{t}\ensuremath{\alpha}\mathrm{P}$, from all potentially twisted bilayer orthorhombic black phosphorus. Such a twisted stacking comes with a low formation energy of $\ensuremath{-}162.8\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$, very close to existing AB stacking, according to first-principles calculations. Particularly, classic molecular dynamic simulations verified that the stacking can be directly obtained in an in situ cleavage. The stability of $2\mathrm{O}\text{\ensuremath{-}}\mathrm{t}\ensuremath{\alpha}\mathrm{P}$ stacking can be directly attributed to the corrugated configuration of black phosphorus leading to the van der Waals constraining forces, where the top layer can get stuck to the bottom when one layer rotates in plane relative to the other by $\ensuremath{\sim}70.{5}^{\ensuremath{\circ}}$. Tribological analysis further revealed that the interlayer friction of $2\mathrm{O}\text{\ensuremath{-}}\mathrm{t}\ensuremath{\alpha}\mathrm{P}$ stacking reaches up to 1.3 nN, playing a key role in the origin of $2\mathrm{O}\text{\ensuremath{-}}\mathrm{t}\ensuremath{\alpha}\mathrm{P}$.