Unconventional Nonlocal Relaxation Dynamics in a Twisted Graphene Moire Superlattice

The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest energy configuration. Such relaxation phenomena can lead to unexpected and novel material properties. Here, we study twisted double trilayer graphene (TDTG) using nano-optical and tunneling spectroscopy tools. We reveal a surprising optical and electronic contrast, as well as a stacking energy imbalance emerging between the moir\'e domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during fabrication. We analyze the energetics of this transition and demonstrate that it is the result of a non-local relaxation process, in which an energy gain in one domain of the moire lattice is paid for by a relaxation that occurs in the other.