Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912978074337280 |
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| author | Chen, Lei Ghorashi, Sayed Ali Akbar Cano, Jennifer Crépel, Valentin |
| author_facet | Chen, Lei Ghorashi, Sayed Ali Akbar Cano, Jennifer Crépel, Valentin |
| contents | Robust flavor-polarized phases are a striking hallmark of many flat-band moiré materials. In this work, we trace the origin of this spontaneous polarization to a lesser-known quantum-geometric quantity: the quantum-geometric dipole. Analogous to how the quantum metric governs the spatial spread of wavepackets, we show that the quantum-geometric dipole sets the characteristic size of particle-hole excitations, e.g. magnons in a ferromagnet, which in turn boosts their gap and stiffness. Indeed, the larger the particle-hole separation, the weaker the mutual attraction, and the stronger the excitation energy. In topological bands, this energy enhancement admits a lower bound within the local-mode approximation, highlighting the crucial role of topology in flat-band ferromagnetism. We illustrate these effects in microscopic models, emphasizing their generality and relevance to moiré materials. Our results establish the quantum-geometric dipole as a predictive geometric indicator for ferromagnetism in flat bands, a crucial prerequisite for topological order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_22417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands Chen, Lei Ghorashi, Sayed Ali Akbar Cano, Jennifer Crépel, Valentin Mesoscale and Nanoscale Physics Materials Science Strongly Correlated Electrons Robust flavor-polarized phases are a striking hallmark of many flat-band moiré materials. In this work, we trace the origin of this spontaneous polarization to a lesser-known quantum-geometric quantity: the quantum-geometric dipole. Analogous to how the quantum metric governs the spatial spread of wavepackets, we show that the quantum-geometric dipole sets the characteristic size of particle-hole excitations, e.g. magnons in a ferromagnet, which in turn boosts their gap and stiffness. Indeed, the larger the particle-hole separation, the weaker the mutual attraction, and the stronger the excitation energy. In topological bands, this energy enhancement admits a lower bound within the local-mode approximation, highlighting the crucial role of topology in flat-band ferromagnetism. We illustrate these effects in microscopic models, emphasizing their generality and relevance to moiré materials. Our results establish the quantum-geometric dipole as a predictive geometric indicator for ferromagnetism in flat bands, a crucial prerequisite for topological order. |
| title | Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands |
| topic | Mesoscale and Nanoscale Physics Materials Science Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2506.22417 |