Fig. 2: Intensity of the fifth harmonics as a function of the chemical potential (μ).

a Electrical transport measurement of the graphene channel. Resistance (blue solid line) shows the maximum at the gate voltage \({V}_{{{{{{\rm{G}}}}}}}\) of 0.95 V, identifying the charge-neutral case (\(\mu\) = 0 eV). b Infrared transmission measurement of the graphene device. As \({V}_{{{{{{\rm{G}}}}}}}\) decreases from 0.1 V to −1.3 V, a step-like absorption edge moves to higher energy. Fitting to the model based on Kubo formula (gray solid lines) determines \(\mu\) which is summarized in a with black squares. c–e Harmonic intensity as a function of \(2\left|\mu \right|\) (or \(2\left|\mu \right|/{E}_{{{{{{\rm{ph}}}}}}}\) where \({E}_{{{{{{\rm{ph}}}}}}}\) is laser photon energy). \({I}_{{{{{{\rm{x}}}}}}}^{(5\omega )}\) (red circles) and \({I}_{{{{{{\rm{y}}}}}}}^{(5\omega )}\) (blue circles) represent harmonic intensity along the x-direction and y-direction, respectively. \({I}_{{{{{{\rm{x}}}}}}}^{(5\omega )}\) + \({I}_{{{{{{\rm{y}}}}}}}^{(5\omega )}\) (black squares) represents total intensity of the harmonics. Under linearly-polarized excitation (c), \({I}_{{{{{{\rm{x}}}}}}}^{(5\omega )}\) shows a resonance-like profile with the maximum intensity as \(2\left|\mu \right|\) = 0.87 eV while \({I}_{{{{{{\rm{y}}}}}}}^{(5\omega )}\) is absent beyond the noise level. Under elliptically polarized excitation with ellipticity \({\varepsilon }_{{{{{{\rm{exc}}}}}}}\) = 0.2 (d) and \({\varepsilon }_{{{{{{\rm{exc}}}}}}}\) = 0.4 (e), the fifth harmonics shows \(I\)_x^(5ω) and \(I\)_y^(5ω) with a resonance-like profile and a step-like profile, respectively.