Berry curvature from plane-wave mixing: A three-band model with emergent symmetries
Abstract
Two-dimensional materials can host topological phases stabilized either by an intrinsic moiré potential or topological crystallization. Crucial to the topology of these phases is the interplay between the (self-consistently generated) potential and the spinor structure, which imbues the band-projected potential with momentum-dependence. Truncating this potential at linear-order in momentum, we obtain a three-band model that captures the low-energy band structure and Berry curvature of such topological bands. We analytically find that the Berry curvature strongly depends on momentum-dependence of the potential. Furthermore, we identify that the model can be tuned to have emergent symmetries, including U(1) and anti-unitary symmetries. Emergent-symmetry breaking perturbations drive the system to regimes hosting topological flat bands, quadratic band touchings, and multiple Dirac cones. We recover many of these features when studying an un-truncated model of a λ-jellium spinor inside of a periodic potential. Our results reveal a rich interplay of spinor structure and a potential in determining the topology of the ground state.
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BibTeX
@misc{vadali2026berry,
title = {{Berry curvature from plane-wave mixing: A three-band model with emergent symmetries}},
author = {Avi Vadali and Tomohiro Soejima},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17209},
eprint = {2610.17209},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17209},
}
RIS
TY - UNPB
TI - Berry curvature from plane-wave mixing: A three-band model with emergent symmetries
AU - Avi Vadali
AU - Tomohiro Soejima
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17209
UR - https://arxiv.org/abs/2610.17209
AB - Two-dimensional materials can host topological phases stabilized either by an intrinsic moiré potential or topological crystallization. Crucial to the topology of these phases is the interplay between the (self-consistently generated) potential and the spinor structure, which imbues the band-projected potential with momentum-dependence. Truncating this potential at linear-order in momentum, we obtain a three-band model that captures the low-energy band structure and Berry curvature of such topological bands. We analytically find that the Berry curvature strongly depends on momentum-dependence of the potential. Furthermore, we identify that the model can be tuned to have emergent symmetries, including U(1) and anti-unitary symmetries. Emergent-symmetry breaking perturbations drive the system to regimes hosting topological flat bands, quadratic band touchings, and multiple Dirac cones. We recover many of these features when studying an un-truncated model of a λ-jellium spinor inside of a periodic potential. Our results reveal a rich interplay of spinor structure and a potential in determining the topology of the ground state.
ER -