Peculiar width dependence of the electronic properties of carbon nanoribbons

Nanoribbons (nanographite ribbons) are carbon systems analogous to carbon nanotubes. We characterize a wide class of nanoribbons by a set of two integers $⟨p,q⟩$, and then define the width $w$ in terms of $p$ and $q$. Electronic properties are explored for this class of nanoribbons. Zigzag (armchair) nanoribbons have similar electronic properties to armchair (zigzag) nanotubes. The band gap structure of nanoribbons exhibits a valley structure with streamlike sequences of metallic or almost metallic nanoribbons. These sequences correspond to equiwidth curves indexed by $w$. We reveal a peculiar dependence of the electronic property of nanoribbons on the width $w$.