We calculate the dc current induced second harmonic generation in doped graphene using the semiconductor Bloch equations under relaxation time approximations. We find that the maximum value of the effective second order susceptibility appears when the fundamental photon energy matches the chemical potential. For a surface current density 1.1 × 10(3) A/m and a relaxation time at optical frequencies of 13 fs, the effective second order susceptibility χeff(2);xxx can be as large as 10(-7)m/V for h̄ω = 0.2 eV or 10(-8) m/V for h̄ω = 0.53 eV.
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Cheng et al. (2014) studied this question.
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