First-principles study of the terahertz third-order nonlinear response of metallic armchair graphene nanoribbons

We compute the terahertz third-order nonlinear conductance of metallic armchair graphene nanoribbons using time-dependent perturbation theory. Significant enhancement of the intrinsic third-order conductance over the result for instrinsic 2D single-layer graphene is observed over a wide range of temperatures. We also investigate the nonlinear response of extrinsic metallic acGNR with $|{E}_F|\ensuremath{\ll}200\phantom{\rule{4pt}{0ex}}\mathrm{meV}$. We find that the third-order conductance exhibits a strong Fermi level dependence at low temperatures. A third-order critical field strength of between $\ensuremath{\sim}1$ and $5\phantom{\rule{4pt}{0ex}}\mathrm{kV}/\mathrm{m}$ is computed for the Kerr conductance as a function of temperature. For the third-harmonic conductance, the minimum critical field is computed to be $\ensuremath{\sim}5\phantom{\rule{4pt}{0ex}}\mathrm{kV}/\mathrm{m}$.