Quantum nonlocal effects in individual and interacting graphene nanoribbons

We show that highly doped graphene ribbons can support surface plasmons at near-infrared frequencies when their width is in the nanometer range,leading to important nonlocal and finite quantum-size corrections,such as sizable blueshifts.The magnitude of these effects is assessed by comparing classical and quantum-mechanical models to describe graphene plasmons.More precisely,we examine individual and interacting 6–8 nm wide zigzag and armchair ribbons doped to 0.4–1.5 eV Fermi energies.We find a strong influence of nonlocal effects on the orientation of graphene edges,with plasmons in zigzag ribbons undergoing strong quenching when their energy is below the Fermi level.Nonlocality is also affecting the hybridization between ribbon plasmons in dimers and arrays for separations below a few nanometers.Remarkably,the removal of a single row of atomic bonds in a ribbon produces a strong plasmon frequency shift,whereas the removal of bonds along an array of rows separated by several nanometers in an extended sheet causes a dramatic increase in the absorption.Besides the fundamental interest of these results,our work supports the use of narrow ribbons to achieve electro-optical modulation in the near infrared.