| Popis: |
Breakthrough experiments have recently realized fractional Chern insulators (FCIs) in moir\'e materials. However, all states observed are Abelian, the possible existence of more exotic non-Abelian FCIs remains controversial both experimentally and theoretically. Here, we investigate the competition between charge density wave order, gapless composite fermion liquids and non-Abelian Moore-Read states at half-filling of a moir\'e band. Although groundstate (quasi-)degeneracies and spectral flow is not sufficient for distinguishing between charge order and Moore-Read states, we find evidence using entanglement spectroscopy that both these states of matter can be realized with realistic Coulomb interactions. In a double twisted bilayer graphene model transitions between these phases by tuning the coupling strength between the layers: at weak coupling there is a composite Fermi liquid phase and at strong coupling a low entanglement state signaling CDW order emerges. Remarkably, however, there is compelling evidence for a non-Abelian Moore-Read FCI phase at intermediate coupling. |
