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arXiv · 2208.10213

Floquet formulation of the dynamical Berry-phase approach to non-linear optics in extended systems

Ignacio M. Alliati·Myrta Grüning
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Abstract

We present a Floquet scheme for the ab-initio calculation of nonlinear optical properties in extended systems. This entails a reformulation of the real-time approach based on the dynamical Berry-phase polarisation [Attaccalite & Gr\"uning, PRB 88, 1-9 (2013)] and retains the advantage of being non-perturbative in the electric field. The proposed method applies to periodically-driven Hamiltonians and makes use of this symmetry to turn a time-dependent problem into a self-consistent time-independent eigenvalue problem. We implemented this Floquet scheme at the independent particle level and compared it with the real-time approach. Our reformulation reproduces real-time-calculated $2^{nd}$ and $3^{rd}$ order susceptibilities for a number of bulk and two-dimensional materials, while reducing the associated computational cost by one or two orders of magnitude.

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Ignacio M. Alliati, Myrta Grüning. 2022-08-22. Floquet formulation of the dynamical Berry-phase approach to non-linear optics in extended systems. https://doi.org/10.1088/2516-1075%2Facbc5e

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