Physics

Electronic properties and topological aspects of graphene nanohelicoids

Xiaoqian Liu, Arsen Herasymchuk, Yaroslav Zhumagulov, Oleg V. Yazyev

Featured July 21, 2026

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Simply

Twisting flat graphene ribbons into nanohelicoids creates a new kind of material where the electronic properties, like whether it conducts electricity or not, switch on and off depending on how wide the twist is, due to a special 'anti-chiral' symmetry.

In depth

The study introduces graphene nanohelicoids (GNHs), a novel class of graphene structures where the honeycomb lattice is embedded on a helicoidal surface. They construct effective one-dimensional lattice models for GNHs and demonstrate that these systems exhibit an anti-chiral symmetry, leading to a momentum-shifted particle-hole relation in their band structure. Crucially, the paper reveals that the electronic band gap and a topological invariant, the Zak phase, alternate between gapped/gapless and trivial/nontrivial states, respectively, as the helicoid's width is varied.

Key Takeaways

1
The paper introduces graphene nanohelicoids (GNHs), a new class of graphene structures with a helicoidal geometry, analogous to graphene nanoribbons but incorporating screw symmetry.
2
GNHs exhibit an anti-chiral symmetry in their effective one-dimensional band structure, characterized by a momentum-shifted particle-hole relation $E_{v} (k) = - E_{c} (k + π)$ .
3
The electronic band gap and Zak phase in GNHs show a periodic alternation between semiconducting/metallic and trivial/nontrivial states, respectively, as the helicoid's width is varied.

Conceptual Flow

HIGH LEVEL

Methodology: From Flat to Twisted Graphene

Instead of flat graphene strips, the researchers twisted them into tiny spirals, then used math to understand how electrons move in these new shapes.

Flat Graphene Sheet

Cut and Twist

Tiny Graphene Spiral

Results: Width Controls Electronic Behavior

They found that simply changing the spiral's width makes it switch between acting like a wire or an insulator, and also changes a hidden 'topological' property.

Spiral Width Changes

Switches Properties

Conducts / Insulates

Trivial / Topological