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  • Open Access

Turning graphene into an intensity gauge for Angle-Resolved Photoemission Spectroscopy

Cedric Schmitt1,2, Hans Kirschner3, Jonas Erhardt1,2, Lukas Gehrig1,2, Philipp Keßler1,2, Kilian Strauß1,2, Merit Spring1,2, Bing Liu1,2, Stefan Enzner2,4 et al.

Alexander Gottwald3, Vitaliy Feyer5,6, Timur Kim7, Cephise Cacho7, Chris Jozwiak8, Aaron Bostwick8, Eli Rotenberg8, Lukasz Plucinski5,9, F. Stefan Tautz10,11,12, Ralph Claessen1,2, Serguei Soubatch10,11, and Simon Moser1,2,13,14,*

  • *Contact author: simon.moser@uni-bielefeld.de
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Phys. Rev. Research 8, 043081 – Published 22 October, 2026

DOI: https://doi.org/10.1103/7ddz-xy1y

Abstract

Angle-resolved photoemission spectroscopy (ARPES) provides the most direct experimental access to electronic band structures and many-body interactions in solids. Beyond energy and momentum, the measured intensity also carries detailed information about the initial-state wavefunction through the complex photoemission matrix element governing the transition to—and scattering character of—the photoelectron final state. Orbital tomography seeks to exploit this sensitivity to reconstruct electronic wavefunctions. However, its quantitative implementation has been hindered by the lack of direct information on the phase of the matrix element and by the nontrivial role of solid-state scattering. Here, we overcome these limitations by achieving an experimental reconstruction of the complex photoemission matrix element in quasi-freestanding monolayer graphene (QFMLG), including both amplitude and phase. By combining circular-dichroism ARPES with linearly polarized measurements within a controlled scattered-wave framework, we determine the full matrix element over a broad kinetic-energy range. The reconstructed amplitudes exhibit pronounced channel-selective resonances and Cooper minima, directly revealing substantial solid-state modifications beyond commonly used simplified models. Leveraging this quantitative reconstruction, we establish QFMLG as an easily available in situ intensity reference for ARPES. Its known complex matrix element enables direct normalization for the product of photon flux and detector response, allowing the determination of photoemission cross sections in other materials under identical experimental geometries. This advances orbital tomography by ARPES to a quantitatively normalized approach that separates the initial-state wavefunction from final-state scattering contributions, and more broadly may provide access to the associated quantum geometry.

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References (49)

  1. S. Moser, An experimentalist's guide to the matrix element in angle resolved photoemission, J. Electron Spectrosc. Relat. Phenom. 214, 29 (2017).
  2. D. Lüftner et al., Imaging the wave functions of adsorbed molecules, Proc. Natl. Acad. Sci. USA 111, 605 (2014).
  3. P. Puschnig and M. Ramsey, Photoemission tomography: Valence band photoemission as a quantitative method for investigating molecular films, edited by K. Wandelt Encyclopedia of Interfacial Chemistry (Elsevier, Oxford, 2018), p. 380.
  4. J. Erhardt et al., Bias-free access to orbital angular momentum in two-dimensional quantum materials, Phys. Rev. Lett. 132, 196401 (2024).
  5. M. Schüler et al., Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials, Sci. Adv. 6, eaay2730 (2020).
  6. M. Kang et al., Measurements of the quantum geometric tensor in solids, Nat. Phys. 21, 110 (2025).
  7. S. Weiß et al., Exploring three-dimensional orbital imaging with energy-dependent photoemission tomography, Nat. Commun. 6, 8287 (2015).
  8. P. J. Feibelman and D. E. Eastman, Photoemission spectroscopy—Correspondence between quantum theory and experimental phenomenology, Phys. Rev. B 10, 4932 (1974).
  9. J. W. Gadzuk, Surface molecules and chemisorption. II. Photoemission angular distributions, Phys. Rev. B 10, 5030 (1974).
  10. G. D. Mahan, Theory of photoemission in simple metals, Phys. Rev. B 2, 4334 (1970).
  11. N. V. Smith, M. M. Traum, J. A. Knapp, J. Anderson, and G. J. Lapeyre, Polarization effects in angle-resolved photoemission using synchrotron radiation, Phys. Rev. B 13, 4462 (1976).
  12. G. Lapeyre, J. Anderson, and R. Smith, Initial state symmetries from polarization effects in angular resolved photoemission, Surf. Sci. 89, 304 (1979).
  13. A. Bansil and M. Lindroos, Importance of matrix elements in the ARPES spectra of BISCO, Phys. Rev. Lett. 83, 5154 (1999).
  14. A. Bansil and M. Lindroos, Matrix element effects in the angle-resolved photoemission spectrum of BISCO, J. Phys. Chem. Solids 59, 1879 (1998).
  15. P. Puschnig et al., Orbital tomography: Deconvoluting photoemission spectra of organic molecules, Phys. Rev. B 84, 235427 (2011).
  16. W. S. Jung et al., Imaging the electron density in solids by using multi-Brillouin-zone angle resolved photoelectron spectroscopy, Phys. Rev. B 82, 235105 (2010).
  17. D. Lee and C. Kim, Method to map one-dimensional electronic wave function by using multiple Brillouin zone angle resolved photoemission, JAST 1, 118 (2010).
  18. S. Moser, A toy model for dichroism in angle resolved photoemission, J. Electron Spectrosc. Relat. Phenom. 262, 147278 (2023).
  19. E. E. Krasovskii, Character of the outgoing wave in soft x-ray photoemission, Phys. Rev. B 102, 245139 (2020).
  20. V. N. Strocov et al., High-energy photoemission final states beyond the free-electron approximation, Nat. Commun. 14, 4827 (2023).
  21. C. S. Kern et al., Simple extension of the plane-wave final state in photoemission: Bringing understanding to the photon-energy dependence of two-dimensional materials, Phys. Rev. Res. 5, 033075 (2023).
  22. J. Erhardt et al., Indium epitaxy on SiC(0001): A roadmap to large scale growth of the quantum spin Hall insulator indenene, J. Phys. Chem. C 126, 16289 (2022).
  23. A. K. Geim, Graphene: Status and prospects, Science 324, 1530 (2009).
  24. C. Riedl, C. Coletti, and U. Starke, Structural and electronic properties of epitaxial graphene on SiC(0001): A review of growth, characterization, transfer doping and hydrogen intercalation, J. Phys. D: Appl. Phys. 43, 374009 (2010).
  25. A. Gottwald et al., Current capabilities at the Metrology Light Source, Metrologia 49, S146 (2012).
  26. C. Schmitt et al., Achieving environmental stability in an atomically thin quantum spin Hall insulator via graphene intercalation, Nat. Commun. 15, 1486 (2024).
  27. S. Glass et al., Atomic-scale mapping of layer-by-layer hydrogen etching and passivation of SiC(0001) substrates, J. Phys. Chem. C 120, 10361 (2016).
  28. T. Seyller, Passivation of hexagonal SiC surfaces by hydrogen termination, J. Phys.: Condens. Matter 16, S1755 (2004).
  29. N. Briggs et al., Atomically thin half-van der Waals metals enabled by confinement heteroepitaxy, Nat. Mater. 19, 637 (2020).
  30. H. Kim, N. Tsogtbaatar, B. Tuvdendorj, A. Lkhagvasuren, and J. M. Seo, Effects of two kinds of intercalated In films on quasi-free-standing monolayer graphene formed above SiC(0001), Carbon 159, 229 (2020).
  31. L. Broekman et al., First results from a second generation toroidal electron spectrometer, J. Electron Spectrosc. Relat. Phenom. 144–147, 1001 (2005).
  32. H. Boban et al., Scattering makes a difference in circular dichroic angle-resolved photoemission, Phys. Rev. B 111, 115127 (2025).
  33. M. Bauernfeind et al., Design and realization of topological Dirac fermions on a triangular lattice, Nat. Commun. 12, 5396 (2021).
  34. J. Sforzini et al., Approaching truly freestanding graphene: The structure of hydrogen-intercalated graphene on 6H-SiC(0001), Phys. Rev. Lett. 114, 106804 (2015).
  35. C. S. Kern et al., Circular dichroism in the photoelectron angular distribution of achiral molecules, Phys. Rev. Res. 8, 023275 (2026).
  36. I. Gierz, M. Lindroos, H. Höchst, C. R. Ast, and K. Kern, Graphene sublattice symmetry and isospin determined by circular dichroism in angle-resolved photoemission spectroscopy, Nano Lett. 12, 3900 (2012).
  37. Y. Liu, G. Bian, T. Miller, and T.-C. Chiang, Visualizing electronic chirality and Berry phases in graphene systems using photoemission with circularly polarized light, Phys. Rev. Lett. 107, 166803 (2011).
  38. C. Hwang et al., Direct measurement of quantum phases in graphene via photoemission spectroscopy, Phys. Rev. B 84, 125422 (2011).
  39. H. Daimon et al., Strong circular dichroism in photoelectron diffraction from nonchiral, nonmagnetic material–direct observation of rotational motion of electrons, Jpn. J. Appl. Phys. 32, L1480 (1993).
  40. C. Schmitt, R. Claessen, and S. Moser, Dataset: Turning graphene into an intensity gauge for ARPES, University of Würzburg, WueData, 2026, doi: 10.58160/uaabat31rcvf42nu.
  41. J. W. Cooper, Photoionization from outer atomic subshells. A model study, Phys. Rev. 128, 681 (1962).
  42. S. Moser et al., Polarization control at the microscopic and electronic structure observatory, Nucl. Instrum. Methods Phys. Res. Sect. A 914, 156 (2019).
  43. M. Mulazzi et al., Understanding intensities of angle-resolved photoemission with circularly polarized radiation from a Cu(111) surface state, Phys. Rev. B 79, 165421 (2009).
  44. J. Avery, Many-center Coulomb Sturmians and Shibuya-Wulfman integrals, Int. J. Quantum Chem. 100, 121 (2004).
  45. V. Aquilanti and A. Caligiana, Sturmian approach to one-electron many-center systems: Integrals and iteration schemes, Chem. Phys. Lett. 366, 157 (2002).
  46. P. Krüger and F. Matsui, Observation and theory of strong circular dichroism in angle-revolved photoemission from graphite, J. Electron Spectrosc. Relat. Phenom. 258, 147219 (2022).
  47. G. H. Golub and C. Reinsch, Singular value decomposition and least squares solutions, Numer. Math. 14, 403 (1970).
  48. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  49. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).

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Phys. Rev. Research 8, 043081– Published 22 October, 2026
  • Received 23 March 2026
  • Accepted 5 September 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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