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Graphene possesses remarkable electronic, optical and mechanical properties that have taken the research of two-dimensional relativistic condensed matter systems to prolific levels. However, the understanding of how its nonlinear optical properties are affected by relativistic-like effects has been broadly uncharted. It has been recently shown that highly-nontrivial currents can be generated in free-standing samples, notably leading to the generation of even harmonics. Since graphene monolayers are centrosymmetric media, for which such harmonic generation is deemed inaccessible, this light-driven phenomenon is both startling and promising. More realistically, graphene samples are often deposited on a dielectric substrate, leading to additional intricate interactions. Here, we present a treatment to study this instance by gapping the spectrum and we show this leads to the appearance of a Berry phase in the carrier dynamics. We analyse the role of such a phase in the generated nonlinear current and conclude that it suppresses odd-harmonic generation. The pump energy can be tuned to the energy gap to yield interference among odd harmonics mediated by interband transitions, allowing even harmonics to be generated. Our results and general methodology pave the way for understanding the role of gap-opening physical factors in the nonlinear optics of hexagonal two-dimensional lattices.arXiv:1710.04581v1 [cond-mat.mes-hall]

Abstract:The usually-held notion that monolayer graphene, a centrosymmetric system, does not allow even-harmonic generation when illuminated at normal incidence is challenged by the discovery of a peculiar e ect we term the dynamical centrosymmetry breaking mechanism. This e ect results in a global pulse-induced oscillation of the Dirac cones which in turn produces second harmonic waves. We prove that this result can only be found by using the full Dirac equation and show that the widely used semiconductor Bloch equations fail to reproduce this and some other important physics of graphene. These results clear the way for further investigation concerning nonlinear light-matter interactions in a wide range of two-dimensional materials admitting either a gapped or ungapped Dirac-like spectrum.

We present a comprehensive review of the optical response of graphene, in both the linear and nonlinear regime. This will serve as a reference for both beginners and more experienced researchers in the field. We introduce, derive, and extensively discuss the Dirac–Bloch equations framework, central to describing electron–photon interaction in nonperturbative, gapless materials. We use this model to re-derive several known results in the linear regime, such as the universal absorption law, and to describe the nonlinear interaction of ultrashort pulses with graphene. We compare the validity of the Dirac–Bloch equations model with the traditional Semiconductor-Bloch equations and point out advantages and shortcomings of the two models. Lastly, we present a cutting-edge model for describing the nonlinear optical response of graphene when bending becomes important, a situation that deeply affects the output spectra, and can provide insight to a novel, effective way to manipulate light in two-dimensional media.

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