Robust structural superlubricity of twisted graphene bilayer and domain walls between commensurate moir\'e pattern domains from first-principles calculations

Abstract

Twisted graphene layers exhibit extremely low friction for relative sliding. Nevertheless, previous studies suggest that the area contribution to friction for commensurate moir\'e systems is finite and might restrict macroscopic superlubricity for large layer overlaps. In this paper, we investigate the potential energy surface (PES) for relative displacement of the layers forming moir\'e patterns (2,1) and (3,1) by accurate density functional theory calculations using the vdW-DF3 functional. The amplitudes of PES corrugations on the order of 0.4 and 0.03 $\mu$eV per atom of one layer, respectively, are obtained. The account of structural relaxation doubles this value for the (2,1) pattern, while causing only minimal changes for the (3,1) pattern. We show that different from aligned graphene layers, for moir\'e patterns, PES minima and maxima can switch their positions upon changing the interlayer distance. The PES shape is closely described by the first spatial Fourier harmonics both with and without account of structural relaxation. A barrier for relative rotation of the layers to an incommensurate state that can make superlubricity robust is estimated based on the approximated PES. We also derive a set of measurable physical properties related to interlayer interaction including shear mode frequency, shear modulus and static friction force. Furthermore, we predict that it should be possible to observe domain walls separating commensurate domains, each comprising a large number of moir\'e pattern unit cells, and provide estimates of their characteristics.