Stacking-orientation and twist-angle control on integer and fractional Chern insulators in moir\'e rhombohedral graphene

Rhombohedral-stacked multilayer graphene aligned with hexagonal boron nitride has emerged as an excellent platform for investigating exotic quantum phenomena arising from the interplay between electron correlations and nontrivial topology. However, the microscopic mechanism governing the emergence of both the integer and fractional Chern insulator states in this system remains an open question. In this work, we systematically investigate the electrical transport properties of RMG/hBN moir\'e devices with controlled alignment orientations and twist angles. We demonstrate that alignment orientation strongly modulates correlated phenomena in the moir\'e-proximal regime, while having negligible influence on the formation of integer and fractional Chern insulators in the moir\'e-distant regime. Instead, the moir\'e periodicity, tuned by the twist angle, serves as the key parameter controlling the stability of these correlated topological states in the moir\'e-distant regime. Furthermore, in the moir\'e-proximal regime of one specific alignment, we observe anomalous Hall effect and a variety of competing phases near {\nu} = 1, including integer Chern insulator states, extended Chern insulator states, and trivial insulators, whose stability is highly sensitive to both the applied displacement electric field and magnetic field. Our results underscore the critical role of stacking-alignment and twist-angle engineering in exploring novel quantum states based on rhombohedral-stacked multilayer graphene moir\'e systems.