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Recent experiments on rhombohedral pentalayer graphene flakes with asubstrate induced moir\'e potential have identified both Chern insulators andfractional Quantum Hall states in the absence of an applied magnetic field.Surprisingly, these states are observed in strong displacement fields where theeffects of the moir\'e lattice are weak, and seem to be readily accessedwithout fine-tuning. To address these experimental puzzles we study aninteracting model of electrons in this geometry, first within theself-consistent Hartree-Fock (SCHF) approximation. We find an isolated Chernband with Chern number $|C|=1$, that moreover is relatively flat and shows goodquantum geometry. Exact diagonalization and density matrix renormalizationgroup methods at fractional filling establish the presence of fractionalquantum anomalous Hall (FQAH) states. The $|C|=1$ band in SCHF is remarkablyrobust to varying microscopic parameters, and is also found in the $N_L=4$ and$N_L=6$ layer systems. Remarkably, it appears stable even to switching off themoir\'e potential, pointing to spontaneous breaking of translation symmetry. Weterm this topological crystalline state the ``anomalous Hall crystal" (AHC),and argue that it constitutes a general mechanism for creating stable Chernbands in rhombohedral graphene. Our work elucidates the physics behind therecent rhombohedral pentalayer graphene observations, predicts the appearanceof the same phase in other systems, and opens the door to studying theinterplay between electronic topology and spontaneous translation symmetrybreaking.

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I:  Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero  Magnetic Field