Abstract

We introduce graphene nanohelicoids, geometric analogues 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 anti-chiral 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. We derive an analytic tight-binding model and introduce a continuous deformation of the graphene nanohelicoids that explains the origin of width-dependent band inversion and alternating Zak phase.

Abstract

We introduce graphene nanohelicoids, geometric analogues 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 anti-chiral 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. We derive an analytic tight-binding model and introduce a continuous deformation of the graphene nanohelicoids that explains the origin of width-dependent band inversion and alternating Zak phase.

Abstract

We introduce graphene nanohelicoids, geometric analogues 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 anti-chiral 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. We derive an analytic tight-binding model and introduce a continuous deformation of the graphene nanohelicoids that explains the origin of width-dependent band inversion and alternating Zak phase.

Abstract

We introduce graphene nanohelicoids, geometric analogues 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 anti-chiral 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. We derive an analytic tight-binding model and introduce a continuous deformation of the graphene nanohelicoids that explains the origin of width-dependent band inversion and alternating Zak phase.