Fractional high-Chern insulator in twisted rhombohedral graphene

Key Points:

• Extended Data Fig. 1 presents optical micrographs and Raman spectra characterizing bilayer and rhombohedral tetralayer graphene regions in devices D1-D5, along with images post-nanofabrication showing measurement setups.
• Extended Data Fig. 2 shows Hartree-Fock calculations revealing spin/valley-polarized active bands with Chern numbers ranging from 3 to 4, indicating spontaneous breaking of time-reversal and spin SU(2) symmetries in the moiré Brillouin zone.
• Extended Data Figs. 3-6 detail electrical transport measurements of displacement field modulated Chern insulators near filling factors ν = 1 and ν = 3, demonstrating hysteresis, magnetic field dependence, and temperature evolution of Hall resistance, consistent with complex phase diagrams and cascades of high Chern number states.
• Extended Data Fig. 7 conceptually illustrates cascades of Chern insulators near ν = 3 as an anomalous Hall crystal with broken translation symmetry and quantized Berry curvature atop a robust |C|=4 Chern insulator background.
• Extended Data Figs. 8-9 analyze the temperature dependence and thermal activation gaps of fractional Chern insulator (FCI) states at ν = 2/3, proposing possible mechanisms for the formation of a C = 7/3 FCI through band folding and fractionalization in multiband Chern structures.