A comparative study of perturbative and nonequilibrium Green's function approaches for Floquet sidebands in periodically driven quantum systems

TL;DR

This paper compares perturbative and nonequilibrium Green's function methods for analyzing Floquet sidebands in driven quantum systems, demonstrating their respective strengths and limitations through graphene models.

Contribution

It provides a detailed comparison of two theoretical approaches for Floquet sidebands, highlighting their applicability and differences in modeling driven quantum materials.

Findings

PB1 yields analytical sideband intensity expressions.

tdNEGF accurately reproduces full spectra including hybridization gaps.

Qualitative agreement between methods with quantitative differences near complex regions.

Abstract

We compare two complementary theoretical approaches to compute and interpret Floquet sidebands in periodically driven quantum materials: a first-order perturbative approach (first-order perturbative Born approximation, PB1) and time-dependent nonequilibrium Green's functions (tdNEGF). Using graphene as a model Dirac system, we disentangle in pump-probe setups Floquet-dressed initial states, Volkov-dressed final states (also known as laser-assisted photoelectric effect, LAPE), and their interference. We quantify how photoemission matrix elements, polarization, incidence angle, and near-surface screening shape the momentum-resolved sideband intensity observed in tr-ARPES. PB1 yields an analytical expression for the momentum-dependent sideband intensity, and for graphene it captures the correct symmetry trends, such as the magnitude of the intensities when considering the interference between the Floquet and Volkov states and photoemission matrix elements. tdNEGF reproduces the full energy-momentum-resolved spectra, including hybridization gaps and spectral-weight redistribution. We find qualitative agreement between PB1 and tdNEGF once matrix elements are included; quantitative differences arise near hybridization regions and at specific angles where higher-order processes and self-energies are essential. Thus, for systems with simple band structures and away from these regions, the two approaches can be used in a complementary way.