Quantum theory of the third-order nonlinear electrodynamic effects in graphene

Abstract

The linear energy dispersion of graphene electrons leads to a strongly nonlinear electromagnetic response of this material. We develop a general quantum theory of the third-order nonlinear local dynamic conductivity of graphene ${\sigma }_{\alpha \beta \gamma \delta }({\omega }_1,{\omega }_2,{\omega }_3)$, which describes its nonlinear response to a uniform electromagnetic radiation. The derived analytical formulas describe a large number of different nonlinear phenomena such as the third harmonic generation, the four wave mixing, the saturable absorption, the second harmonic generation stimulated by a dc electric current, etc., which may be used in different terahertz and optoelectronic devices.

36 pages, 10 figures; slightly shortened as compared to the previous version, some details are added; accepted for publication version

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