Estimate the localization activation gap due to disorder in PLG samples

Derive the activation gap associated with disorder-induced localization (equivalently, pinning of an anomalous Hall crystal) in experimental rhombohedral pentalayer graphene moiré superlattice devices, by quantifying the amount of sample disorder and its screening, to enable predictive modeling of low-temperature insulating behavior and its role in the thermal crossover.

Background

Beyond the general lack of knowledge of the bare disorder, the authors state that the amount of disorder in actual PLG devices is unknown, which prevents estimating the activation gap for disorder-induced localization or pinning of a putative Hall crystal. This activation gap would set the energy scale for the insulating behavior that competes with interaction-driven fractional states.

Determining this gap is essential to quantitatively understand whether and how thermal activation of localized carriers can give rise to an intermediate-temperature FQAHE on top of a disordered background, and why strong insulating behavior dominates for fillings below 2/5.