Unveiling and Manipulating Hidden Symmetries in Graphene Nanoribbons

TL;DR

This paper reveals hidden symmetries in armchair graphene nanoribbons that influence their electronic properties and demonstrates how strain can manipulate their energy gaps and topological phases.

Contribution

It uncovers a previously unidentified hidden symmetry affecting nanoribbon electronic structure and shows how strain can control this symmetry to tune properties.

Findings

Energy-gap opening linked to breaking of hidden symmetry

Strain enables continuous energy-gap tuning

Emergence of Dirac points and topological transitions

Abstract

Armchair graphene nanoribbons are a highly promising class of semiconductors for all-carbon nanocircuitry. Here, we present a new perspective on their electronic structure from simple model Hamiltonians and $\textit{ab initio}$ calculations. We focus on a specific set of nanoribbons of width $n = 3p+2$, where $n$ is the number of carbon atoms across the nanoribbon axis and $p$ is a positive integer. We demonstrate that the energy-gap opening in these nanoribbons originates from the breaking of a previously unidentified hidden symmetry by long-ranged hopping of $\pi$-electrons and structural distortions occurring at the edges. This hidden symmetry can be restored or manipulated through the application of in-plane lattice strain, which enables continuous energy-gap tuning, the emergence of Dirac points at the Fermi level, and topological quantum phase transitions. Our work establishes an original interpretation of the semiconducting character of armchair graphene nanoribbons and offers guidelines for rationally designing their electronic structure.