Large-Chern-number flat bands, anomalous Dirac cones, and unconventional superfluidity in square-lattice systems with SU(N) non-Abelian gauge fields
Abstract
We study topological band structures and superfluid phases in two-dimensional square-lattice systems with homogeneous SU(N) non-Abelian gauge fields. Starting from an SU(4) gauge-field model related to the Hofstadter model with flux α=1/4, we show that the lowest and highest bands are isolated Chern bands that carry Chern numbers C=−4 and give rise to four chiral edge modes in a strip geometry. Remarkably, although the two middle bands touch and form $16$ gapless Dirac cones, their combined Chern number is C=8. We then generalize the construction to SU(N) systems and reveal an even--odd structure of the band topology: when N is odd, all bands are isolated and carry nonzero Chern numbers; when N is even, the two middle bands touch at N2 Dirac points, while all other bands remain isolated and topologically nontrivial. We find that the uppermost and lowermost bands become increasingly flat and their Berry curvature becomes more uniform as N increases, providing a promising platform for realizing fractional Chern insulating phases. We further examine the spin-3/2 SU(4) model with on-site attractive Hubbard interactions, exploring its superfluid phases at partial filling. We find that the non-Abelian gauge field breaks the hidden SO(5) degeneracy of the quintet pairing and selects distinct nematic superfluid states. For fillings in the middle-band regime, the resulting spectrum can host topologically protected Bogoliubov Fermi surfaces. Our results provide a starting point for exploring both topological band physics and unconventional superfluidity in synthetic SU(N) cold-atom systems.
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BibTeX
@misc{zhong2026largechernnumber,
title = {{Large-Chern-number flat bands, anomalous Dirac cones, and unconventional superfluidity in square-lattice systems with SU(N) non-Abelian gauge fields}},
author = {Wentao Zhong and Zhongbo Yan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08223},
eprint = {2609.08223},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08223},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Large-Chern-number flat bands, anomalous Dirac cones, and unconventional superfluidity in square-lattice systems with SU(N) non-Abelian gauge fields
AU - Wentao Zhong
AU - Zhongbo Yan
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08223
UR - https://arxiv.org/abs/2609.08223
AB - We study topological band structures and superfluid phases in two-dimensional square-lattice systems with homogeneous SU(N) non-Abelian gauge fields. Starting from an SU(4) gauge-field model related to the Hofstadter model with flux α=1/4, we show that the lowest and highest bands are isolated Chern bands that carry Chern numbers C=−4 and give rise to four chiral edge modes in a strip geometry. Remarkably, although the two middle bands touch and form $16$ gapless Dirac cones, their combined Chern number is C=8. We then generalize the construction to SU(N) systems and reveal an even--odd structure of the band topology: when N is odd, all bands are isolated and carry nonzero Chern numbers; when N is even, the two middle bands touch at N^2 Dirac points, while all other bands remain isolated and topologically nontrivial. We find that the uppermost and lowermost bands become increasingly flat and their Berry curvature becomes more uniform as N increases, providing a promising platform for realizing fractional Chern insulating phases. We further examine the spin-3/2 SU(4) model with on-site attractive Hubbard interactions, exploring its superfluid phases at partial filling. We find that the non-Abelian gauge field breaks the hidden SO(5) degeneracy of the quintet pairing and selects distinct nematic superfluid states. For fillings in the middle-band regime, the resulting spectrum can host topologically protected Bogoliubov Fermi surfaces. Our results provide a starting point for exploring both topological band physics and unconventional superfluidity in synthetic SU(N) cold-atom systems.
ER -