Maximal Chern Numbers from Finite-Range Hopping
Abstract
Finite-range hopping constrains both the number of Dirac points and the masses that gap them. We determine the maximal absolute Chern numbers of an isotropic finite-range extension of the Qi--Wu--Zhang model on a square lattice through thirteenth-neighbor hopping. Algebraic zero counting and mass-weighted sum rules yield global bounds, and we construct explicit Hamiltonians that saturate them. We find |C|max=36,40,51 for eleventh-, twelfth-, and thirteenth-neighbor hopping. Equal numbers of Dirac points can produce different maxima because finite-range mass harmonics distinguish opposite vortex charges differently. Twice the squared hopping radius bounds every maximum through twelfth-neighbor hopping and is saturated at the eleventh and twelfth, but the thirteenth-neighbor maximum exceeds it. Thus finite-range hopping constrains the maximal Chern number in two complementary ways: through the number of Dirac vortices it can generate and through the mass-sign patterns it can assign to them. This geometric viewpoint provides a design principle for high-Chern bands and a route to analogous bounds in moiré and other lattice systems.
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BibTeX
@misc{cortes2026maximal,
title = {{Maximal Chern Numbers from Finite-Range Hopping}},
author = {Christopher Arriagada Cortés and Vladimir Juričić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31437},
eprint = {2609.31437},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31437},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Maximal Chern Numbers from Finite-Range Hopping
AU - Christopher Arriagada Cortés
AU - Vladimir Juričić
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31437
UR - https://arxiv.org/abs/2609.31437
AB - Finite-range hopping constrains both the number of Dirac points and the masses that gap them. We determine the maximal absolute Chern numbers of an isotropic finite-range extension of the Qi--Wu--Zhang model on a square lattice through thirteenth-neighbor hopping. Algebraic zero counting and mass-weighted sum rules yield global bounds, and we construct explicit Hamiltonians that saturate them. We find |C|_max=36,40,51 for eleventh-, twelfth-, and thirteenth-neighbor hopping. Equal numbers of Dirac points can produce different maxima because finite-range mass harmonics distinguish opposite vortex charges differently. Twice the squared hopping radius bounds every maximum through twelfth-neighbor hopping and is saturated at the eleventh and twelfth, but the thirteenth-neighbor maximum exceeds it. Thus finite-range hopping constrains the maximal Chern number in two complementary ways: through the number of Dirac vortices it can generate and through the mass-sign patterns it can assign to them. This geometric viewpoint provides a design principle for high-Chern bands and a route to analogous bounds in moiré and other lattice systems.
ER -