Enhancement of High Harmonic Generation in Bulk Floquet Systems

TL;DR

This paper develops a Floquet-based theoretical framework for high harmonic generation in bulk periodically driven systems, revealing how external drives and symmetries influence harmonic spectra and enabling enhanced harmonic generation even at low field amplitudes.

Contribution

It introduces a unified Floquet approach to nonlinear optical responses in driven solids, connecting symmetries to harmonic selection rules and providing analytical and numerical insights into harmonic enhancement.

Findings

Drive-induced symmetry breaking enables forbidden harmonics.

Significant harmonic enhancement occurs even at low field amplitudes.

Analytical expressions for high-frequency, low-amplitude regimes are derived.

Abstract

We formulate a theory of bulk optical current for a periodically driven system, which accounts for the mixing of external drive and laser field frequencies and, therefore, the broadening of the harmonic spectrum compared to the undriven system. We express the current in terms of Floquet-Bloch bands and their non-adiabatic Berry connection and curvature. Using this expression, we relate spatio-temporal symmetries of the driven model to selection rules for current harmonics. We illustrate the application of this theory by studying high harmonic generation in the periodically driven Su-Schrieffer-Heeger model. In the high frequency and low field amplitude limit, we find analytical expressions for current harmonics. We also calculate the current numerically beyond the high frequency limit and verify that when the drive breaks a temporal symmetry, harmonics forbidden in the undriven model become available. Moreover, we find significant enhancement in higher harmonics when the system is driven, even for low field amplitudes. Our work offers a unified Floquet approach to nonlinear optical properties of solids, which is useful for realistic calculations of high harmonic spectra of electronic systems subject to multiple periodic drives.