Berry curvature and shift vector effects at high-order wave mixing in biased bilayer graphene

TL;DR

This paper develops a quantum theory to analyze how Berry curvature and shift vector influence high-order wave mixing and harmonic generation in biased bilayer graphene under strong bichromatic laser fields.

Contribution

It introduces a microscopic, nonperturbative model incorporating Berry curvature and shift vector effects for high-order nonlinear optical responses in bilayer graphene.

Findings

Berry curvature and shift vector significantly alter high-order harmonic spectra.

High-order wave mixing can be modeled with classical electron-hole trajectories.

Resonant electron-hole pair generation affects spectral features.

Abstract

In this work, we present a microscopic quantum theory that elucidates the nonlinear and nonperturbative optical response of biased bilayer graphene subjected to bichromatic strong laser fields. This response is analyzed using a four-band Hamiltonian derived from \textit{ab initio} calculations. For the laser-stimulated dynamics, we employ structure gauge-invariant evolutionary equations to accurately describe the evolution of the single-particle density matrix across the entire Brillouin zone. The resonant generation of electron-hole pairs by the high-frequency component of the field, combined with the induction of high-order harmonic generation and high-order wave mixing by the strong low-frequency field component, leads to significant alterations in the resulting spectra. These changes are driven by the effects of Berry curvature and the shift vector, which modify the relative contributions of interband and intraband channels, thereby fundamentally reshaping the radiation spectra at high-order frequency multiplication. The numerical results are further supported by approximate analytical calculations, demonstrating that high-order wave mixing can be modeled using the classical trajectory analysis of electron-hole pairs, with Berry curvature and the shift vector significantly influencing the saddle-point equations.