Recently fractional quantum anomalous hall effects (FQAH) attract lots of attentions due to their experimental realizations in the moiré systems. The standard theoretical framework assumes an isolated flat Chern band in the single particle level. But in this paper we challenges this paradigm for the FQAH in the five layer rhombohedral stacked graphene aligned with hexagon boron nitride(hBN). We show that the external moiré superlattice potential is simply a perturbation in a model with continuous translation symmetry. Through Hartree fock calculation, we find that interaction opens a sizable superlattice gap, resulting an isolated narrow C=1 Chern band. From exact diagonalizations we identify FQAH phases at various fillings. But they exist also in the calculations with a zero external moiré potential. We suggest that the QAH phase at filling ν=1 in this system should be viewed as an interaction driven QAH-Wigner crystal, which is then pinned by a small external moiré potential. In the second part we propose a new setup with Coulomb generated moiré superlattice. For example, we separate n-layer graphene and twisted bilayer graphene (TBG) with a thin hBN and imprint the superlattice of the TBG to the n-layer graphene. Now the superlattice potential is controlled by the thickness d of the hBN and the superlattice period is controlled by the twist angle of the TBG. Overall in both setups the C=1 QAH-Wigner crystal is more robust with a superlattice constant slightly less than 10 nm in 4-layer, 5-layer, 6-layer and 7-layer graphene systems. Our work suggests a new direction to explore the interplay of topology and FQAH with spontaneous Wigner crystal formation in the vanishing moiré potential limit in hBN aligned and Coulomb imprinted n-layer graphene superlattice systems.
Condensed Matter Theory Seminar - Yahui Zhang - “Fractional quantum anomalous Hall effects in rhombohedral multilayer graphene in the moiréless limit and in Coulomb imprinted superlattice”
Thursday, February 15, 2024 - 1:00pm to 2:00pm
Sloane Physics Laboratory SPL, Room 51
217 Prospect StreetNew Haven, CT 06511
Yahui Zhang - Johns Hopkins University