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

Karun Gadge1,*, Marco Merboldt2, Michael Schüler3,4, Jan Philipp Bange2, Wiebke Bennecke2, Michael A. Sentef5,6, Marcel Reutzel2,7,8, Stefan Mathias2,9, and Salvatore R. Manmana1,†

  • 1Institute for Theoretical Physics, Georg-August-University Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
  • 2I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
  • 3PSI Center for Scientific Computing, Theory and Data, Paul Scherrer Institute, Villigen PSI, Switzerland
  • 4Department of Physics, University of Fribourg, Fribourg, Switzerland
  • 5Institute for Theoretical Physics and Bremen Center for Computational Materials Science, University of Bremen, 28359 Bremen, Germany
  • 6Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
  • 7Department of Physics, Philipps-Universität Marburg, D-35032 Marburg, Germany
  • 8mar.quest — Marburg Center for Quantum Materials and Sustainable Technologies, Hans-Meerwein-Straße 6, D-35032 Marburg, Germany
  • 9International Center for Advanced Studies of Energy Conversion (ICASEC), University of Göttingen, Göttingen, Germany

  • *Contact author: karun.gadge@uni-goettingen.de
  • †Contact author: salvatore.manmana@uni-goettingen.de
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Phys. Rev. B 114, 125402 – Published 3 August, 2026

DOI: https://doi.org/10.1103/h59r-hyc4

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), 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 the 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.

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Phys. Rev. B 114, 125402– Published 3 August, 2026
  • Received 23 January 2026
  • Revised 9 June 2026
  • Accepted 6 July 2026
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