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.