Stacking Domains and Dislocation Networks in Marginally Twisted Bilayers of Transition Metal Dichalcogenides
V. V. Enaldiev, Viktor Zólyomi, Celal Yelgel, S. J. Magorrian, Vladimir I. Fal’ko
Abstract
We apply a multiscale modeling approach to study lattice reconstruction in marginally twisted bilayers of transition metal dichalcogenides (TMD). For this, we develop density functional theory parametrized interpolation formulae for interlayer adhesion energies of ${\mathrm{MoSe}}_{2}$, ${\mathrm{WSe}}_{2}$, ${\mathrm{MoS}}_{2}$, and ${\mathrm{WS}}_{2}$, combine those with elasticity theory, and analyze the bilayer lattice relaxation into mesoscale domain structures. Paying particular attention to the inversion asymmetry of TMD monolayers, we show that $3R$ and $2H$ stacking domains, separated by a network of dislocations develop for twist angles ${\ensuremath{\theta}}^{\ensuremath{\circ}}<{\ensuremath{\theta}}_{\mathrm{P}}^{\ensuremath{\circ}}\ensuremath{\sim}2.5\ifmmode^\circ\else\textdegree\fi{}$ and ${\ensuremath{\theta}}^{\ensuremath{\circ}}<{\ensuremath{\theta}}_{\mathrm{AP}}^{\ensuremath{\circ}}\ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}$ for, respectively, bilayers with parallel (P) and antiparallel (AP) orientation of the monolayer unit cells and suggest how the domain structures would manifest itself in local probe scanning of marginally twisted P and AP bilayers.