Unconventional non-local relaxation dynamics in a twisted trilayer graphene moiré 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 moiré domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during assembly, resulting in domains of ABABAB and BCBACA stacking. 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 moiré lattice is paid for by a relaxation that occurs in the other.

Experimental Observation of ABCB Stacked Tetralayer Graphene.

In tetralayer graphene, three inequivalent layer stackings should exist; however, only rhombohedral (ABCA) and Bernal (ABAB) stacking have so far been observed. The three stacking sequences differ in their electronic structure, with the elusive third stacking (ABCB) being unique as it is predicted to exhibit an intrinsic bandgap as well as locally flat bands around the K points. Here, we use scattering-type scanning near-field optical microscopy and confocal Raman microscopy to identify and characterize domains of ABCB stacked tetralayer graphene. We differentiate between the three stacking sequences by addressing characteristic interband contributions in the optical conductivity between 0.28 and 0.56 eV with amplitude and phase-resolved near-field nanospectroscopy. By normalizing adjacent flakes to each other, we achieve good agreement between theory and experiment, allowing for the unambiguous assignment of ABCB domains in tetralayer graphene. These results establish near-field spectroscopy at the interband transitions as a semiquantitative tool, enabling the recognition of ABCB domains in tetralayer graphene flakes and, therefore, providing a basis to study correlation physics of this exciting phase.