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The recent demonstration of gate tuneable third harmonic generation (THG) in single layer graphene (SLG) has sparked renewed interest in the study of the nonlinear optical properties of 2D materials and Dirac semimetals. Interestingly, our results also suggest new routes towards the realization of on-chip integrated nonlinear devices based on SLG, such as broadband gate tuneable nonlinear optical switches. However, a major limiting factor in this regard, which heavily suppresses the efficiency of such devices, is the increase of the SLG electronic temperature that follows from interaction with ultrashort (fs-ps) pulses. The study of the ultrafast hot electron dynamics in SLG is thus crucial both for the understanding of its nonlinear optical properties and for the realization of nonlinear optical devices such as frequency converters and saturable absorbers. In this talk I will discuss our current understanding of the interplay between hot electrons and nonlinear optics in SLG, focusing in particular on the process of THG. In SLG, the THG intensity can be tuned by over one order of magnitude by externally applied gate voltages. This enhancement is due to logarithmic resonances in the imaginary part of the nonlinear optical conductivity arising from multiphoton resonant transitions. However, both the THG intensity and its power dependence are heavily affected by an increase in the electronic temperature. I will demonstrate that hot electrons are responsible of a two-orders of magnitude reduction of the THG intensity and of a stark deviation from the cubic power law expected for THG. Finally, I will discuss possible configurations to control the hot electron recombination dynamics. These include interlayer electron-phonon interactions and gate tuning of the SLG chemical potential due to phase-space suppression of the hot electron scattering with optical phonons.
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