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Quantify bare disorder in pentalayer graphene moiré superlattices

Determine the bare disorder strength in rhombohedral pentalayer graphene moiré superlattice devices that exhibit quantum anomalous Hall and fractional quantum anomalous Hall effects, so that quantitative calculations of the disorder energy scale E_dis, the interaction energy scale E_int, and the thermal crossover temperature between extended QAHE and FQAHE can be performed.

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Background

The paper argues that the observed thermal crossover from a high-temperature fractional quantum anomalous Hall phase to a low-temperature extended quantum anomalous Hall phase in pentalayer graphene arises from competition between interaction and disorder energy scales. For quantitative theory, the authors stress that both the disorder (E_dis) and interaction (E_int) scales must be known.

They explicitly state that the bare disorder in the experimental PLG system is unknown, which prevents reliable calculation of these energy scales and the crossover temperature. Establishing the disorder strength would enable a more predictive framework for understanding the temperature-driven crossover and the stability of QAHE/FQAHE phases under different displacement fields and fillings.

References

We emphasize that any actual calculation of the energy scales $E_{dis}$ and $E_{int}$ (and therefore, of the crossover temperature scale for the EQAHE to FQAHE crossover) is essentially impossible at this point since the bare disorder itself is unknown in PLG and even calculating the energy scales for the pristine system (i.e. $E_{int}$ and $\Delta$) is a challenge and is highly controversial since the results depend crucially on the approximation scheme as emphasized in Ref.~\onlinecite{FanZhang2024} from a microscopic perspective and in Ref.~\onlinecite{XiePenta2024} from a phenomenological perspective.

— Thermal crossover from a Chern insulator to a fractional Chern insulator in pentalayer graphene (2408.10931 - Sarma et al., 20 Aug 2024) in Main text, paragraph beginning “We emphasize that any actual calculation…” (discussion of energy scales and crossover; after Fig. 11; pre-acknowledgments)