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Electronic properties and topological aspects of graphene nanohelicoids

Xiaoqian Liu1,*,†, Arsen Herasymchuk2,*,‡, Yaroslav Zhumagulov1, and Oleg V. Yazyev1,§

  • *These authors contributed equally to this work.
  • †Contact author: xiaoqian.liu@epfl.ch
  • ‡Contact author: arsen.herasymchuk@uzh.ch
  • §Contact author: oleg.yazyev@epfl.ch
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Phys. Rev. Research 8, 043069 – Published 19 October, 2026

DOI: https://doi.org/10.1103/yfl3-2p2c

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.

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Phys. Rev. Research 8, 043069– Published 19 October, 2026
  • Received 22 July 2026
  • Accepted 29 September 2026
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