Imaging real-space chiral rotation of flat-band states in helical trilayer graphene

Flat bands have been experimentally realized in a wide variety of graphene-based moiré systems with designed stacking configurations. While these moiré systems feature similar flat-band structures, they differ markedly in key characteristics, such as band flattening, band isolation, and band topology, which give rise to their distinct strongly correlated phases. Here, we present a systematic real-space investigation comparing flat-band states across four representative graphene moiré systems, revealing a characteristic chiral rotation of flat-band states within helical trilayer graphene. Using scanning tunneling microscopy and spectroscopy, we directly observe that ultra-small twist-angle helical trilayer graphene unveils distinct threefold-anisotropic electronic states localized at certain moiré sites within the flat-band regime, distinguishing it from the other moiré systems investigated in this study. Spatial mapping of the threefold-anisotropic pattern reveals a chiral rotation that varies as a function of energy. Theoretical simulations based on the Bistritzer-MacDonald model reproduce the distinct orientations of the threefold-anisotropic patterns across different low-energy minibands and reveal a systematic correspondence between the direction of local density-of-states rotation and the structural chirality of helical trilayer graphene. Our results demonstrate that real-space electronic textures-previously overlooked-can partially reveal the intrinsic disparities among different flat bands, highlighting that systematic exploration of flat bands across moiré systems is critical for deciphering the origins of distinct correlated phases.