Electronic properties and topological aspects of graphene nanohelicoids
Abstract
We introduce graphene nanohelicoids, geometric analogs of graphene nanoribbons, in which the honeycomb lattice is embedded on a helicoidal surface. Starting from the three-dimensional helical structure, we construct effective one-dimensional lattice models with band structures characterized by a momentum-shifted particle-hole relation Ev(k)=−Ec(k+π) that reflects an antichiral symmetry arising from the nonsymmorphic symmetry. A systematic investigation of graphene nanohelicoids using the tight-binding approximation reveals a number of trends upon varying width and edge orientation, for instance, alternating transitions between semiconducting and metallic regimes. As the structure width varies, the band gap periodically closes and reopens, accompanied by an alternating Zak phase that switches between trivial and nontrivial. Using an analytic tight-binding model with a continuous deformation of the graphene nanohelicoids, we explain the origin of width- and termination-dependent band inversion and alternating Zak phase, and derive the relationship between the termination-resolved index and the sublattice symmetry operator in one-dimensional nonsymmorphic systems.
Versions
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BibTeX
@misc{liu2026electronic,
title = {{Electronic properties and topological aspects of graphene nanohelicoids}},
author = {Xiaoqian Liu and Arsen Herasymchuk and Yaroslav Zhumagulov and Oleg V. Yazyev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.13294},
eprint = {2607.13294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.13294},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Electronic properties and topological aspects of graphene nanohelicoids
AU - Xiaoqian Liu
AU - Arsen Herasymchuk
AU - Yaroslav Zhumagulov
AU - Oleg V. Yazyev
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2607.13294
UR - https://arxiv.org/abs/2607.13294
AB - We introduce graphene nanohelicoids, geometric analogs of graphene nanoribbons, in which the honeycomb lattice is embedded on a helicoidal surface. Starting from the three-dimensional helical structure, we construct effective one-dimensional lattice models with band structures characterized by a momentum-shifted particle-hole relation E_v(k)=−E_c(k+π) that reflects an antichiral symmetry arising from the nonsymmorphic symmetry. A systematic investigation of graphene nanohelicoids using the tight-binding approximation reveals a number of trends upon varying width and edge orientation, for instance, alternating transitions between semiconducting and metallic regimes. As the structure width varies, the band gap periodically closes and reopens, accompanied by an alternating Zak phase that switches between trivial and nontrivial. Using an analytic tight-binding model with a continuous deformation of the graphene nanohelicoids, we explain the origin of width- and termination-dependent band inversion and alternating Zak phase, and derive the relationship between the termination-resolved index and the sublattice symmetry operator in one-dimensional nonsymmorphic systems.
ER -