Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1746067696, G2152757567, G2158694287, Emergent Phenomena in Quantum Systems Theory Center, SFB 1170: Topologische und korrelierte Elektronik in Ober und Grenzflächen ("ToCoTronics"), Predicting Zero-Magnetic-Field Fractional Topological States in Twisted Graphene Systems, G5947738484, G5974671110, G6536552022, EXC 2147: Komplexität und Topologie in Quantenmaterialien (CT.QMAT), Princeton Center for Complex Materials
OpenAlex ID: W7221151340