Fig. 1: Fractional Chern insulator (FCI) and quantum anomalous Hall crystal (QAHC) in ideal C = 1 and C = 2 bands.
From: Quantum anomalous Hall crystals in moiré bands with higher Chern number
a Many-body energy spectrum, b average Berry curvature, c structure factor, and d pair-correlation function demonstrating the FCI phase at \(\nu=\frac{2}{3}\) filling of the ideal C = 1 band in a system with Ns = 27 sites and generating vectors R1 = (6, 3), R2 = (1, 5). e–h are the respective results for the ideal C = 2 band demonstrating an integer QAHC phase. In the latter case, the generating vectors are R1 = (6, 3), R2 = (3, 6). The Berry curvature Ω(k) is normalized by the number of flux points NΦ = 302, i.e., Ω(k)NΦ/2π is shown here so that the Chern number can be read off directly. The black dots in (d) and (h) denote moiré lattice sites, and the black lines in (h) mark the unit cells of the Hall crystal.
