发表机构
Princeton Center for Theoretical Science, Princeton University; Department of Physics, Princeton University; Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ctd.qmat, Julius-Maximilians-Universität Würzburg; Donostia International Physics Center; IKERBASQUE, Basque Foundation for Science; Center for Computational Quantum Physics, Flatiron Institute; Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité（普林斯顿大学理论科学中心; 普林斯顿大学物理系; 维尔茨堡大学理论与天体物理研究所及维尔茨堡-德累斯顿卓越集群ctd.qmat; 圣塞巴斯蒂安国际物理中心; 伊卡巴斯科，巴斯克科学基金会; 平顿研究院计算量子物理中心; 巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎第七大学，索邦巴黎城）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对扭转双层MoTe₂的伊辛铁磁体系，提出对称模式近似（SyMA）描述低能磁振子谱，经数值计算验证其准确性，还证明了陈数等量子几何量可稳定陈能带磁性。
AI 中文摘要
莫尔材料拥有整数量子霍尔态和分数量子霍尔态（FCIs），其中时间反演对称性被平带铁磁性自发破缺。在扭转双层MoTe₂中，与量子霍尔体系不同，相反自旋携带相反的陈数，实现具有带隙磁振子激发的伊辛铁磁性。阐明这些集体模式的性质及磁振子带隙的起源，是理解这类材料中陈磁体稳定性的关键。为此，我们开发了一种广义单模近似，将其命名为对称模式近似（SyMA），用于描述低能磁振子谱。我们发现该近似在整数填充时与数值计算结果高度吻合，在包括FCIs在内的分数量子填充时也具有定性准确性。为解释SyMA的准确性，我们提出两类哈伯德模型（包括Haldane模型和连续理想能带），其集体模式可解析求解，且SyMA对这些模型要么精确成立，要么是准确近似。对于其中一类SyMA精确成立的模型，我们基于陈数、贝里曲率和量子度量，证明了零动量磁振子带隙的双向边界，揭示均匀量子几何足以稳定陈能带中的磁性。
英文摘要
Moiré materials host integer and fractional Chern insulators (FCIs) where time-reversal is broken spontaneously by flat band ferromagnetism. In twisted MoTe2, unlike in quantum Hall, opposite spins carry opposite Chern numbers and realize Ising ferromagnetism with gapped magnon excitations. Clarifying the nature of these collective modes and the origin of the magnon gap is key to understanding the stability of the Chern magnets in these materials. To do so, we develop a generalized single-mode approximation, which we call the symmetric mode ansatz (SyMA), to describe the low-energy magnon spectrum. We find it to be in exceptional agreement with numerical calculations at integer filling, and qualitatively accurate across fractional fillings including FCIs. To explain the accuracy of the SyMA, we present two families of Hubbard models (including the Haldane model and continuum ideal bands) whose collective modes are analytically solvable and for which the SyMA is either exact or an accurate approximation. For a class of these models where SyMA is exact, we prove two-sided bounds on the zero-momentum magnon gap in terms of the Chern number, Berry curvature, and quantum metric, revealing that uniform quantum geometry is sufficient for stabilizing magnetism in Chern bands.
