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 $N^{2}$ 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.