Hidden symmetries, Dirac fermions, and topological phase transitions in graphene nanoribbons

We present a theory of the semiconducting state in armchair graphene nanoribbons (AGNRs), a promising class of materials for post-silicon logic electronics. We focus on a specific class of AGNRs of width n=3p+2, where n is the number of carbon atoms across the nanoribbon and p is an integer. Using tight-binding model Hamiltonians and first-principles calculations, we show that the energy gap in such AGNRs originates from the breaking of a previously overlooked hidden symmetry by long-range hopping interactions and structural distortions at the nanoribbon edges. This hidden symmetry can be manipulated through the application of in-plane lattice strain, which can be used to fine tune the energy gap. We further show that lattice strain exceeding a critical value leads to the emergence of Dirac points at the Fermi level and a topological phase transition. Our findings thus establish a novel interpretation of the semiconducting nature of this class of graphene nanoribbons and open new avenues for engineering their topological quantum phases.