Rotational Disorder in Twisted Bilayer Graphene

Conventional means of stacking two-dimensional (2D) crystals inevitably leads to imperfections. To examine the ramifications of these imperfections, rotational disorder and strain are quantified in twisted bilayer graphene (TBG) using a combination of Raman spectroscopic and low-energy electron diffraction imaging. The twist angle between TBG layers varies on the order of 2 degrees within large (50-100 mu m) single-crystalline grains, resulting in changes of the emergent Raman response by over an order of magnitude. Rotational disorder does not evolve continuously across the large grains but rather comes about by variations in the local twist angles between differing contiguous subgrains, similar to 1 mu m in size, that themselves exhibit virtually no twist angle variation (Delta Theta similar to 0.1 degrees). Owing to weak out-of-plane van der Waals bonding between azimuthally rotated graphene layers, these subgrains evolve in conjunction with the 0.3% strain variation observed both within and between the atomic layers. Importantly, the emergent Raman response is altered, but not removed, by these extrinsic perturbations. Inter layer interactions are therefore resilient to strain and rotational disorder, a fact that gives promise to the prospect of designer 2D solid heterostructures created via transfer processes.