Entropy-enhanced fractional quantum anomalous Hall effect

Strongly interacting electrons in a topologically nontrivial band may form exotic phases of matter. An especially intriguing example of which is the fractional quantum anomalous Hall phase, recently discovered in twisted transition metal dichalcogenides and in moir\'e graphene multilayers. However, it has been shown to be destabilized in certain filling factors at sub-100 mK temperatures in pentalayer graphene, in favor of a novel integer quantum anomalous Hall phase [Z. Lu, Extended quantum anomalous Hall states in graphene/hBN moir\'e superlattices, arXiv:2408.10203]. We propose that the culprit stabilizing the fractional phase at higher temperatures is its rich edge state structure. Possessing a multiplicity of chiral modes on its edge, the fractional phase has lower free energy at higher temperatures due to the excess edge mode entropy. We make distinct predictions under this scenario, including the system-size dependency of the fractional phase entropic enhancement, and how the phase boundaries change as a function of temperature.