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  • Open Access

Excitonic contributions to dark matter-electron scattering

Nora Taufertshöfer1,*, Vanessa Zema2,3, Riccardo Catena4, Valerio Olevano5, and Nicola A. Spaldin1

  • *Contact author: nora.taufertshoefer@mat.ethz.ch

Phys. Rev. Research 8, 013056 – Published 20 January, 2026

DOI: https://doi.org/10.1103/9b1j-fcvw

Abstract

We determine whether excitonic effects affect predictions of dark matter (DM)-electron scattering rates by calculating the energy- and momentum-dependent energy-loss function, including electron-hole interaction excitonic effects, for the DM scintillating detector materials GaAs and NaI. By comparing our results using the Bethe-Salpeter equation in the framework of many-body perturbation theory, which explicitly includes excitonic effects, with those using the quasiparticle random-phase approximation, which includes only electron-electron interaction and crystal local-field effects, we find that excitonic effects in NaI significantly increase the predicted scattering rate at low energy and as a result improve the cross-section sensitivity considering a realistic background. In contrast, the predicted scattering rate and the DM-electron scattering cross section for GaAs are minimally affected by excitonic effects.

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References (53)

  1. J. Billard, M. Boulay, S. Cebrián, L. Covi, G. Fiorillo, A. Green, J. Kopp, B. Majorovits, K. Palladino, F. Petricca, L. Roszkowski, and M. Schumann, Direct detection of dark matter—APPEC committee report, Rep. Prog. Phys. 85, 056201 (2022).
  2. R. Essig, Some progress & challenges for the direct-detection of sub-GeV dark matter, Nucl. Phys. B 1003, 116484 (2024).
  3. J. Kopp, V. Niro, T. Schwetz, and J. Zupan, DAMA/LIBRA data and leptonically interacting dark matter, Phys. Rev. D 80, 083502 (2009).
  4. A. Dedes, I. Giomataris, K. Suxho, and J. Vergados, Searching for secluded dark matter via direct detection of recoiling nuclei as well as low energy electrons, Nucl. Phys. B 826, 148 (2010).
  5. R. Essig, J. Mardon, and T. Volansky, Direct detection of sub-GeV dark matter, Phys. Rev. D 85, 076007 (2012).
  6. R. Essig, M. Fernández-Serra, J. Mardon, A. Soto, T. Volansky, and T.-T. Yu, Direct detection of sub-GeV dark matter with semiconductor targets, J. High Energy Phys. 05 (2016) 046.
  7. S. M. Griffin, K. Inzani, T. Trickle, Z. Zhang, and K. M. Zurek, Multichannel direct detection of light dark matter: Target comparison, Phys. Rev. D 101, 055004 (2020).
  8. S. M. Griffin, Y. Hochberg, K. Inzani, N. Kurinsky, T. Lin, and T. C. Yu, Silicon carbide detectors for sub-GeV dark matter, Phys. Rev. D 103, 075002 (2021).
  9. S. M. Griffin, K. Inzani, T. Trickle, Z. Zhang, and K. M. Zurek, Extended calculation of dark matter-electron scattering in crystal targets, Phys. Rev. D 104, 095015 (2021).
  10. H.-Y. Chen, A. Mitridate, T. Trickle, Z. Zhang, M. Bernardi, and K. M. Zurek, Dark matter direct detection in materials with spin-orbit coupling, Phys. Rev. D 106, 015024 (2022).
  11. C. E. Dreyer, R. Essig, M. Fernandez-Serra, A. Singal, and C. Zhen, Fully ab-initio all-electron calculation of dark matter-electron scattering in crystals with evaluation of systematic uncertainties, Phys. Rev. D 109, 115008 (2024).
  12. R. Catena, T. Emken, N. A. Spaldin, and W. Tarantino, Atomic responses to general dark matter-electron interactions, Phys. Rev. Res. 2, 033195 (2020).
  13. R. Catena, T. Emken, M. Matas, N. A. Spaldin, and E. Urdshals, Crystal responses to general dark matter-electron interactions, Phys. Rev. Res. 3, 033149 (2021).
  14. S. Knapen, J. Kozaczuk, and T. Lin, Dark matter-electron scattering in dielectrics, Phys. Rev. D 104, 015031 (2021).
  15. Y. Hochberg, Y. Kahn, N. Kurinsky, B. V. Lehmann, T. C. Yu, and K. K. Berggren, Determining dark-matter–electron scattering rates from the dielectric function, Phys. Rev. Lett. 127, 151802 (2021).
  16. J. Lindhard, On the properties of a gas of charged particles, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 28, 21 (1954).
  17. S. Knapen, J. Kozaczuk, and T. Lin, Python package for dark matter scattering in dielectric targets, Phys. Rev. D 105, 015014 (2022).
  18. E. A. Peterson, S. L. Watkins, C. Lane, and J.-X. Zhu, Beyond-DFT ab initio calculations for accurate prediction of sub-GeV dark matter experimental reach, arXiv:2310.00147.
  19. S. Derenzo, R. Essig, A. Massari, A. Soto, and T.-T. Yu, Direct detection of sub-GeV dark matter with scintillating targets, Phys. Rev. D 96, 016026 (2017).
  20. V. Zema, P. Figueroa, G. Angloher, M. R. Bharadwaj, T. Frank, M. N. Hughes, M. Kellermann, F. Pröbst, K. Schäffner, K. Shera, and M. Stahlberg, Dark matter-electron scattering search using cryogenic light detectors, Phys. Rev. D 110, 123012 (2024).
  21. M. Gatti and F. Sottile, Exciton dispersion from first principles, Phys. Rev. B 88, 155113 (2013).
  22. H.-C. Weissker, J. Serrano, S. Huotari, E. Luppi, M. Cazzaniga, F. Bruneval, F. Sottile, G. Monaco, V. Olevano, and L. Reining, Dynamic structure factor and dielectric function of silicon for finite momentum transfer: Inelastic x-ray scattering experiments and ab initio calculations, Phys. Rev. B 81, 085104 (2010).
  23. P. Abbamonte, T. Graber, J. P. Reed, S. Smadici, C.-L. Yeh, A. Shukla, J.-P. Rueff, and W. Ku, Dynamical reconstruction of the exciton in LiF with inelastic x-ray scattering, Proc. Natl. Acad. Sci. USA 105, 12159 (2008).
  24. G. Angloher, M. R. Bharadwaj, I. Dafinei, N. Di Marco, L. Einfalt, F. Ferroni, S. Fichtinger, A. Filipponi, T. Frank, M. Friedl, A. Fuss, Z. Ge, M. Heikinheimo, M. N. Hughes, K. Huitu, M. Kellermann, R. Maji, M. Mancuso, L. Pagnanini, and F. Petricca (COSINUS Collaboration), Deep-underground dark matter search with a COSINUS detector prototype, Phys. Rev. D 110, 043010 (2024).
  25. G. Angloher, M. R. Bharadwaj, A. Böhmer, M. Cababie, I. Colantoni, I. Dafinei, N. D. Marco, C. Dittmar, L. Einfalt, F. Ferella, et al., COSINUS—A model-independent challenge of the DAMA/LIBRA dark matter claim with cryogenic NaI detectors operated in a new low-background facility, arXiv:2507.02429.
  26. R. Essig, G. K. Giovanetti, N. Kurinsky, D. McKinsey, K. Ramanathan, K. Stifter, T.-T. Yu, A. Aboubrahim, D. Adams, D. S. M. Alves, et al., Snowmass2021 Cosmic Frontier: The landscape of low-threshold dark matter direct detection in the next decade, arXiv:2203.08297.
  27. D. L. Helis, A. Melchiorre, A. Puiu, G. Benato, P. Carniti, A. Continenza, N. Di Marco, A. Ferella, C. Ferrari, F. Giannessi, et al., First measurement of gallium arsenide as a low-temperature calorimeter, Eur. Phys. J. C 84, 749 (2024).
  28. E. E. Salpeter and H. A. Bethe, A relativistic equation for bound-state problems, Phys. Rev. 84, 1232 (1951).
  29. W. Hanke and L. J. Sham, Many-particle effects in the optical excitations of a semiconductor, Phys. Rev. Lett. 43, 387 (1979).
  30. G. Strinati, Application of the Green's functions method to the study of the optical properties of semiconductors, Riv. Nuovo Cimento 11, 1 (1988).
  31. G. Onida, L. Reining, R. W. Godby, R. Del Sole, and W. Andreoni, Ab initio calculations of the quasiparticle and absorption spectra of clusters: The sodium tetramer, Phys. Rev. Lett. 75, 818 (1995).
  32. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9b1j-fcvw for additional details on the electronic structure calculations, the dark matter model, and the reach calculations, which includes Refs.  [50, 51, 52, 53].
  33. In principle, we can also consider the coupling with the electron current for the case, e.g., of a vector boson mediator. This case requires the calculation of the full dielectric tensor, including transverse components.
  34. A. Gulans, S. Kontur, C. Meisenbichler, D. Nabok, P. Pavone, S. Rigamonti, S. Sagmeister, U. Werner, and C. Draxl, Exciting: A full-potential all-electron package implementing density-functional theory and many-body perturbation theory, J. Phys.: Condens. Matter 26, 363202 (2014).
  35. C. Vorwerk, B. Aurich, C. Cocchi, and C. Draxl, Bethe–Salpeter equation for absorption and scattering spectroscopy: Implementation in the exciting code, Electron. Struct. 1, 037001 (2019).
  36. E. Grilli, M. Guzzi, R. Zamboni, and L. Pavesi, High-precision determination of the temperature dependence of the fundamental energy gap in Gallium arsenide, Phys. Rev. B 45, 1638 (1992).
  37. F. C. Brown, C. Gähwiller, H. Fujita, A. B. Kunz, W. Scheifley, and N. Carrera, Extreme-ultraviolet spectra of ionic crystals, Phys. Rev. B 2, 2126 (1970).
  38. B. Campbell-Deem, S. Knapen, J. Kozaczuk, T. Lin, C. Stratman, and E. Villarama, DarkELF Python code, GitHub (2022, https://github.com/tongylin/DarkELF.
  39. G. Angloher, S. Banik, G. Benato, A. Bento, A. Bertolini, R. Breier, C. Bucci, J. Burkhart, L. Canonica, A. D'Addabbo, S. Di Lorenzo, L. Einfalt, A. Erb, F. v. Feilitzsch, N. Ferreiro Iachellini, S. Fichtinger, D. Fuchs, A. Fuss, A. Garai, and V. M. Ghete (CRESST Collaboration), Results on sub-GeV dark matter from a 10 eV threshold CRESST-III silicon detector, Phys. Rev. D 107, 122003 (2023).
  40. K. Teegarden and G. Baldini, Optical absorption spectra of the alkali halides at 10°K, Phys. Rev. 155, 896 (1967).
  41. R. Williams and K. Song, The self-trapped exciton, J. Phys. Chem. Solids 51, 679 (1990).
  42. M. D. Sturge, Optical absorption of Gallium arsenide between 0.6 and 2.75 eV, Phys. Rev. 127, 768 (1962).
  43. S. Vasiukov, F. Chiossi, C. Braggio, G. Carugno, F. Moretti, E. Bourret, and S. Derenzo, GaAs as a bright cryogenic scintillator for the detection of low-energy electron recoils from MeV/c2 dark matter, IEEE Trans. Nucl. Sci. 66, 2333 (2019).
  44. F. Reindl, G. Angloher, P. Carniti, L. Cassina, L. Gironi, C. Gotti, A. Gütlein, M. Maino, M. Mancuso, N. D. Marco, L. Pagnanini, G. Pessina, F. Petricca, S. Pirro, F. Pröbst, R. Puig, K. Schäffner, and J. Schieck, Results of the first NaI scintillating calorimeter prototypes by COSINUS, J. Phys.: Conf. Ser. 1342, 012099 (2020).
  45. J. E. Eby, K. J. Teegarden, and D. B. Dutton, Ultraviolet absorption of Alkali Halides, Phys. Rev. 116, 1099 (1959).
  46. M. Grunert, M. Großmann, and E. Runge, Predicting exciton binding energies from ground-state properties, Phys. Rev. B 110, 075204 (2024).
  47. S. Nagata, K. Fujiwara, and H. Nishimura, Dynamical aspects of excitons in NaI, J. Lumin. 47, 147 (1990).
  48. Z. Dai, C. Lian, J. Lafuente-Bartolome, and F. Giustino, Excitonic polarons and self-trapped excitons from first-principles exciton-phonon couplings, Phys. Rev. Lett. 132, 036902 (2024).
  49. N. Taufertshöfer, V. Zema, R. Catena, V. Olevano, and N. A. Spaldin, Replication data and input files for “Excitonic contributions to dark matter-electron scattering” [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.17733600.
  50. D. Zhou and B. F. Usher, Deviation of the AlGaAs lattice constant from Vegard's law, J. Phys. D: Appl. Phys. 34, 1461 (2001).
  51. Handbook of Optics: Design, Fabrication, and Testing; Sources and Detectors; Radiometry and Photometry, 3rd ed. edited by M. Bass (McGraw-Hill Education, New York, 2010), Vol. 2.
  52. K. Momma and F. Izumi, Vesta: A three-dimensional visualization system for electronic and structural analysis, J. Appl. Crystallogr. 41, 653 (2008).
  53. K. Aggarwal, I. Arnquist, N. Avalos, X. Bertou, N. Castelló-Mor, A. E. Chavarria, J. Cuevas-Zepeda, A. Dastgheibi-Fard, C. D. Dominicis, O. Deligny, et al., Probing benchmark models of hidden-sector dark matter with DAMIC-M, Phys. Rev. Lett. 135, 071002 (2025).

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