Landau quantization of C3 high-fold fermions in honeycomb lattices
Abstract
We present the theory of the Landau levels of C3 high-fold fermions in honeycomb lattices. These fermions arise as a generalization of the tight-binding model in a honeycomb lattice with one orbital per site, known to describe graphene, to a family of models with several orbitals per site transforming according to representations of C3, relevant for triangulene two-dimensional crystals. The models are defined by the number of orbitals na and nb at the a and b sites of the unit cell. They feature energy bands that combine flat bands and Dirac cones, that are isomorphic to those of graphene, the Lieb, pxy honeycomb, and the Kagome tight-binding models. Combining tight-binding and k· p methods, here we compute the Landau levels of the (1,1), (1,2), (2,2) and (3,3) models, we compare them to those of the reference models, and we explore the similarities and differences with the Landau levels in graphene. Our findings reveal that the nature of C3 high-fold fermions combine Dirac-type Landau quantization, originating from the linear crossings and associated relativistic band dispersion, with anomalous Landau quantization rooted in the quantum geometry of the singular flat bands.
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BibTeX
@misc{madail2026landau,
title = {{Landau quantization of $C_3$ high-fold fermions in honeycomb lattices}},
author = {Luisa Madail and Joaquín Fernández-Rossier},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20595},
eprint = {2610.20595},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20595},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Landau quantization of C_3 high-fold fermions in honeycomb lattices
AU - Luisa Madail
AU - Joaquín Fernández-Rossier
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20595
UR - https://arxiv.org/abs/2610.20595
AB - We present the theory of the Landau levels of C_3 high-fold fermions in honeycomb lattices. These fermions arise as a generalization of the tight-binding model in a honeycomb lattice with one orbital per site, known to describe graphene, to a family of models with several orbitals per site transforming according to representations of C_3, relevant for triangulene two-dimensional crystals. The models are defined by the number of orbitals n_a and n_b at the a and b sites of the unit cell. They feature energy bands that combine flat bands and Dirac cones, that are isomorphic to those of graphene, the Lieb, p_xy honeycomb, and the Kagome tight-binding models. Combining tight-binding and k· p methods, here we compute the Landau levels of the (1,1), (1,2), (2,2) and (3,3) models, we compare them to those of the reference models, and we explore the similarities and differences with the Landau levels in graphene. Our findings reveal that the nature of C_3 high-fold fermions combine Dirac-type Landau quantization, originating from the linear crossings and associated relativistic band dispersion, with anomalous Landau quantization rooted in the quantum geometry of the singular flat bands.
ER -