Algebraic flat bands and even central-band Chern numbers in a seven-orbital hopping model
Abstract
Turning a flat-band parent into an isolated Chern band requires supervise of destructive interference, hopping phases, and the cell translations of the bonds. We study this connection in a seven-orbital 2 times 2 supercell honeycomb-vacancy lattice, combining analytic reductions with Bloch spectra, lattice Chern invariants, and quantum geometry. The parent lattice has three exact flat branches, a smooth periodic zero mode, and a compact localized state. A uniform gap bound shows that faint intracell-loop hopping preserves two topologically trivial insulating gaps. The intracell hopping graph also admits a staggered chiral coloring: reversing site amplitudes according to this coloring links opposite energies at momenta separated by half a reciprocal period. This constraint restricts the isolated central band to even Chern numbers and forbids a zero-energy insulating filling at every loop phase. Purely imaginary loop hopping admits a real gauge, whereas other phases allow paired band contacts connecting central bands with C3=2 and C3=4. On a specified strong-loop cut, third-order masses open the direct gaps; these gaps shrink faster than the bandwidth as the coupling grows. Changing the bond connectivity to an oriented honeycomb next-nearest-neighbor extension generates a narrower Chern band with nonuniform quantum geometry. These results distinguish individual-band topology from occupied-group topology and reveal how bond connectivity and cell translations determine which topological bands can emerge from an exactly flat parent.
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BibTeX
@misc{xu2026algebraic,
title = {{Algebraic flat bands and even central-band Chern numbers in a seven-orbital hopping model}},
author = {Weizhuo Xu and Jiachen Qian and Shuaihua Zhang and Yanling Wu and Jun Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36738},
eprint = {2610.36738},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36738},
}
RIS
TY - UNPB
TI - Algebraic flat bands and even central-band Chern numbers in a seven-orbital hopping model
AU - Weizhuo Xu
AU - Jiachen Qian
AU - Shuaihua Zhang
AU - Yanling Wu
AU - Jun Li
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36738
UR - https://arxiv.org/abs/2610.36738
AB - Turning a flat-band parent into an isolated Chern band requires supervise of destructive interference, hopping phases, and the cell translations of the bonds. We study this connection in a seven-orbital 2 times 2 supercell honeycomb-vacancy lattice, combining analytic reductions with Bloch spectra, lattice Chern invariants, and quantum geometry. The parent lattice has three exact flat branches, a smooth periodic zero mode, and a compact localized state. A uniform gap bound shows that faint intracell-loop hopping preserves two topologically trivial insulating gaps. The intracell hopping graph also admits a staggered chiral coloring: reversing site amplitudes according to this coloring links opposite energies at momenta separated by half a reciprocal period. This constraint restricts the isolated central band to even Chern numbers and forbids a zero-energy insulating filling at every loop phase. Purely imaginary loop hopping admits a real gauge, whereas other phases allow paired band contacts connecting central bands with C3=2 and C3=4. On a specified strong-loop cut, third-order masses open the direct gaps; these gaps shrink faster than the bandwidth as the coupling grows. Changing the bond connectivity to an oriented honeycomb next-nearest-neighbor extension generates a narrower Chern band with nonuniform quantum geometry. These results distinguish individual-band topology from occupied-group topology and reveal how bond connectivity and cell translations determine which topological bands can emerge from an exactly flat parent.
ER -