PreprintCC BY 4.0arXiv
Designing Hamiltonians with Exactly Flat Higher-Vortexable Bands
Abstract
The zero modes of the Aharonov-Casher Hamiltonian form an exactly flat, vortexable Chern band in any nonuniform magnetic field, analogous to the lowest Landau level. We ask which local Hamiltonians host exactly flat higher-vortexable bands. For a scalar Hamiltonian, an exactly flat first-vortexable band requires a mass proportional to the local field; the Dirac analogue has the same structure. For periodic Bernal bilayer graphene with nonzero mean flux, the exact zero-mode pair is genuinely first-vortexable if and only if the interlayer hopping has nonzero mean; zero-mean hopping instead gives a decomposable pair. Multiorbital models yield exact higher-vortexable chains to arbitrary order, while remaining first order in momentum.
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BibTeX
@misc{spasicmlacak2026designing,
title = {{Designing Hamiltonians with Exactly Flat Higher-Vortexable Bands}},
author = {Daniel Spasic-Mlacak and Nigel R. Cooper},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20380},
eprint = {2610.20380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20380},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Designing Hamiltonians with Exactly Flat Higher-Vortexable Bands
AU - Daniel Spasic-Mlacak
AU - Nigel R. Cooper
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20380
UR - https://arxiv.org/abs/2610.20380
AB - The zero modes of the Aharonov-Casher Hamiltonian form an exactly flat, vortexable Chern band in any nonuniform magnetic field, analogous to the lowest Landau level. We ask which local Hamiltonians host exactly flat higher-vortexable bands. For a scalar Hamiltonian, an exactly flat first-vortexable band requires a mass proportional to the local field; the Dirac analogue has the same structure. For periodic Bernal bilayer graphene with nonzero mean flux, the exact zero-mode pair is genuinely first-vortexable if and only if the interlayer hopping has nonzero mean; zero-mean hopping instead gives a decomposable pair. Multiorbital models yield exact higher-vortexable chains to arbitrary order, while remaining first order in momentum.
ER -