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Graphene lattice recoil in hard x-ray photoemission: Experiment and theory

Simone Ritarossi1,2,*, Alice Apponi1,2, Orlando Castellano1,2, José Lorenzana3, Domenica Convertino4, Camilla Coletti4,5, Tien-Lin Lee6, Francesco Offi1,2, and Alessandro Ruocco1,2

  • *Contact author: simone.ritarossi@uniroma3.it
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Phys. Rev. B 114, 194307 – Published 27 October, 2026

DOI: https://doi.org/10.1103/s8w3-plc1

Abstract

Hard-x-ray C 1s photoemission from monolayer graphene probes a regime in which nuclear recoil and intrinsic electronic asymmetry contribute on comparable energy scales to the observed spectral line shape. Here we combine experiment and modeling over the photon-energy range 0.8–8keV to resolve this interplay quantitatively. A graphene-specific implementation of the Fujikawa-Takata cumulant formalism, based on an anisotropic vibrational density of states constrained by first-principles phonon calculations, captures the expected recoil scaling with photon energy and emission geometry but fails to reproduce the pronounced asymmetric tails of the measured spectra. To overcome this limitation, we introduce an explicit electronic convolution model in which a photon-energy-independent reference response, dominated by the electronic line shape and extracted from the low-recoil 0.8keV data through a recoil-inclusive fit, is convolved with a phonon recoil kernel carrying the full dependence on photon energy and emission angle. This approach reproduces both the measured line-shape evolution and the observed peak shifts across the explored energy range without refitting the spectra at higher photon energies. The results show that recoil in graphene cannot be described by a baseline treatment in which the phonon recoil kernel is combined only with symmetric lifetime broadening, but must be treated together with the intrinsic many-body electronic response of the C 1s line.

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Information

Phys. Rev. B 114, 194307– Published 27 October, 2026
  • Received 14 May 2026
  • Accepted 2 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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