Graphene on h-BN: to align or not to align?

Abstract: The contact strength, adhesion and friction, between graphene and an incommensurate crystalline substrate such as {\it h}-BN depends on their relative alignment angle $\theta$. The well established Novaco-McTague (NM) theory predicts for a monolayer graphene on a hard bulk {\it h}-BN crystal face a small spontaneous misalignment, here $\theta_{NM}$\,$\simeq$\,0.45 degrees which if realized would be relevant to a host of electronic properties besides the mechanical ones. Because experimental equilibrium is hard to achieve, we inquire theoretically about alignment or misalignment by simulations based on dependable state-of-the-art interatomic force fields. Surprisingly at first, we find compelling evidence for $\theta = 0$, i.e., full energy-driven alignment in the equilibrium state of graphene on {\it h}-BN. Two factors drive this deviation from NM theory. First, graphene is not flat, developing on {\it h}-BN a long-wavelength out-of-plane corrugation. Second, {\it h}-BN is not hard, releasing its contact stress by planar contractions/expansions that accompany the interface moir\'e structure. Repeated simulations by artificially forcing graphene to keep flat, and {\it h}-BN to keep rigid, indeed yield an equilibrium misalignment similar to $\theta_{NM}$ as expected. Subsequent sliding simulations show that friction of graphene on {\it h}-BN, small and essentially independent of misalignments in the artificial frozen state, strongly increases in the more realistic corrugated, strain-modulated, aligned state.