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

TL;DR

This paper introduces a Floquet-based method for calculating nonlinear optical properties in extended systems, transforming a time-dependent problem into a more efficient time-independent eigenvalue problem, and demonstrating its accuracy and computational advantages.

Contribution

It presents a novel Floquet formulation of the dynamical Berry-phase approach that is non-perturbative and computationally more efficient for nonlinear optics in extended systems.

Findings

Reproduces second and third order susceptibilities accurately.

Reduces computational cost by one or two orders of magnitude.

Applicable to periodically-driven Hamiltonians.

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.