Thermal crossover from a Chern insulator to a fractional Chern insulator in pentalayer graphene

By theoretically analyzing the recent temperature dependent transport data in pentalayer graphene [Lu et al., arXiv:2408.10203], we establish that the experimentally observed transition from low-temperature quantum anomalous Hall effect to higher-temperature fractional quantum anomalous Hall effect is a crossover phenomenon arising from the competition between interaction and disorder energy scales, with the likely zero temperature ground state of the system being either a localized insulator or a Chern insulator with a quantized anomalous Hall effect. In particular, the intriguing suppression of FQAHE in favor of QAHE with decreasing temperature is explained as arising from the low-temperature localization of the carriers where disorder overcomes the interaction effects. We provide a detailed analysis of the data in support of the crossover scenario.