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Non-linear response of two dimensional crystals and layered materials

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Starting since 2013 we have been developing a real-time approach to study nonlinear optical properties in periodic systems [1]. In this approach the non-linear response is obtained from the time evolution of an effective Schroedinger equation. In this talk I will introduce non-linear response in solids and show how it can be calculated by means of Modern Theory of Polarization plus a real-time dynamics. Then I will present different applications to the second harmonic generation (SHG) in hBN and MoS2 [2], where the inclusion of excitonic effect is crucial to reproduce the experimental results. A final example will be the two-photon absorption (TPA) in bulk and single layer hexagonal boron nitride (hBN) [3]. The TPA obeys to different selection rules from those governing linear optics and therefore provides complementary information on the electronic excitations of hBN. Combining the results from the simulations with a symmetry analysis we show that two-photon absorption is able to probe lowest dark degenerate states of bulk hBN.

[1] Nonlinear optics from an ab initio approach by means of the dynamical Berry phase: Application to second-and third-harmonic generation in semiconductors C Attaccalite, M Grüning, Physical Review B 88 (23), 235113 (2013)

[2] Second harmonic generation in h-BN and MoS2 monolayers: Role of electron-hole interaction M Grüning, C Attaccalite, Physical Review B 89 (8), 081102 (2014)

[3] Two-photon absorption in two-dimensional materials: The case of hexagonal boron nitride C Attaccalite, M Grüning, H Amara, S Latil, F Ducastelle Physical Review B 98 , 165126 (2018)

This talk is part of the Theory of Condensed Matter series.

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