Entropy-Enhanced Fractional Quantum Anomalous Hall Effect

TL;DR

This paper proposes that the stability of the fractional quantum anomalous Hall phase at higher temperatures is due to its complex edge state structure, which increases entropy and influences phase stability.

Contribution

It introduces the idea that edge state entropy stabilizes the fractional phase at elevated temperatures, providing testable predictions about phase boundaries and system size effects.

Findings

Edge state multiplicity increases entropy at higher temperatures.

Phase boundaries shift with temperature changes.

System size affects entropic stabilization of the fractional phase.

Abstract

Strongly interacting electrons in a topologically non trivial 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 et al., 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 modes 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.