AI 中文总结
研究菱方石墨烯中分数反常霍尔晶体，用变分波函数和蒙特卡罗方法评估能量，发现其在能量上有竞争力且稳定性有规律，预测了相关稳定性窗口演变，支持了连续和相互作用优先路径。
AI 中文摘要
分数反常霍尔晶体（FAHCs）在连续介质中复制了分数量子霍尔效应的拓扑序，无需任何外部磁场。它们像维格纳晶体一样自发打破连续平移对称性，但每个晶胞含有固定分数数量的电子。此前这些状态限于理论推测或工程模型，本文在现实材料环境中确定其为能量上有竞争力的候选态。研究了具有变分波函数的菱方五重层石墨烯（R5G），恢复现实色散和屏蔽库仑相互作用后用蒙特卡罗方法评估能量。发现FAHCs在能量上与整数反常霍尔晶体和费米液体有竞争力，其稳定性遵循简单原则。预测了整数和分数量子反常霍尔稳定性窗口随扭转角和位移场的演变，并与近期实验比较，支持了菱方石墨烯中分数反常霍尔态的连续和相互作用优先路径。
英文摘要
Fractional anomalous Hall crystals (FAHCs) replicate the topological order of the fractional quantum Hall effect in the continuum without requiring any external magnetic field. They spontaneously break continuous translation symmetry like a Wigner crystal, but are distinguished by each unit cell holding a fixed fractional number of electrons. Until now, these states have been confined to theoretical speculation or engineered models, leaving open the question of whether they can plausibly emerge in actual physical systems. Here, we establish them as energetically competitive candidate states in a realistic material setting. We study rhombohedral pentalayer graphene (R5G) with variational wavefunctions that are exact zero modes of a recently proposed ideal model of R5G. We evaluate their energies using Monte Carlo, after reinstating realistic dispersion and screened Coulomb interactions. We find FAHCs to be energetically competitive with integer anomalous Hall crystals and Fermi liquids, and their stability follows a simple principle. Each crystal maps onto a parent quantum Hall liquid that fixes its interaction energy, while the kinetic energy favors crystal periods that match the finite-momentum minimum of R5G's Mexican-hat dispersion. A weak periodic potential can then selectively lower and pin the commensurate fractional crystals. This picture predicts how the integer and fractional quantum anomalous Hall stability windows evolve with twist angle and displacement field, which we compare to recent experiments. These results support a continuum-and-interactions-first route to fractional anomalous Hall states in rhombohedral graphene.
Comments16 + 39 pages, 8 + 8 figures
