We report that for graphene with a finite band gap (such as semihydrogenated graphene or graphene with spin-orbit coupling), there exists a strong nonlinear optical response for energies lower than the band gap where the linear response is forbidden. At low temperatures, the nonlinear current in graphene with a gap is much stronger than that in gapless graphene. Our result suggests that semihydrogenated graphene can have a unique potential as a two-color nonlinear material in the terahertz frequency region. The relative intensity of the two colors can be tuned with the electric field.
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