Quantum Phase Transitions and Fractional Quantized Anomalous Hall Insulators in Rhombohedral Graphene

RESUMO

Fractional quantum anomalous Hall effect (FQAHE) has been discovered in twisted MoTe$_2$ and rhombohedral graphene/hBN moiré superlattices. Such van der Waals heterostructures feature a tuning knob of gate displacement field $D$, which is absent from the conventional fractional quantum Hall systems in two-dimensional electron gases. $D$ plays a critical role in engineering FQAHE and other emergent quantum states and provides an exciting new opportunity to explore their quantum phase transitions. However, the microscopic details of such transitions and temperature-dependent transport have remained mostly elusive. Here we report systematic resistance measurements in rhombohedral pentalayer graphene/hBN moiré superlattices. We found that the displacement field-driven phase transitions between Composite Fermi liquid, Fermi liquid, Fractional Chern insulators, and insulating states are described by semi-circle relations of the longitudinal and transverse resistivities (or conductivities), largely unexplored in the fractional quantum Hall systems. This agrees with a spatially separated two-phase picture for the phase transitions and further indicates a new insulator phase--fractional quantized anomalous Hall insulator. By comparing the temperature-dependence of longitudinal resistance with the thermal activation model, we estimated the transport gap sizes in three fractional Chern insulator states. Our work shed light on the quantum and temperature evolutions of fractional Chern insulator states--providing necessary background for anyon-braiding and gate-defined junctions in rhombohedral graphene.