Structure-imposed electronic topology in cove-edged graphene nanoribbons

TL;DR

This paper classifies the electronic states of cove-edged zigzag graphene nanoribbons based on their atomistic structure, providing a scheme to predict their electronic properties and an empirical formula for their band gaps.

Contribution

It introduces a comprehensive classification scheme for ZGNR-C electronic states based on structural parameters, advancing understanding of structure-electronic structure relationships.

Findings

Classified ZGNR-C as metallic, topological insulators, or semiconductors based on structure.

Derived an empirical formula to estimate band gaps from structural parameters.

Provided rules for constructing ZGNR-C with desired electronic properties.

Abstract

In cove-edged zigzag graphene nanoribbons (ZGNR-C), one terminal CH group per length unit is removed on each zigzag edge, forming a regular pattern of coves which controls their electronic structure. Based on three structural parameters that unambiguously characterize the atomistic structure of ZGNR-C, we present a scheme that classifies their electronic state, i.e., if they are metallic, topological insulators or trivial semiconductors, for all possible widths N, unit lengths a and cove position offsets at both edges b, thus showing the direct structure-electronic structure relation. We further present an empirical formula to estimate the band gap of the semiconducting ribbons from N, a, and b. Finally, we identify all geometrically possible ribbon terminations and provide rules to construct ZGNR-C with well-defined electronic structure.