- Open Access
Excitonic contributions to dark matter-electron scattering
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.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (53)
- 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).
- R. Essig, Some progress & challenges for the direct-detection of sub-GeV dark matter, Nucl. Phys. B 1003, 116484 (2024).
- J. Kopp, V. Niro, T. Schwetz, and J. Zupan, DAMA/LIBRA data and leptonically interacting dark matter, Phys. Rev. D 80, 083502 (2009).
- 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).
- R. Essig, J. Mardon, and T. Volansky, Direct detection of sub-GeV dark matter, Phys. Rev. D 85, 076007 (2012).
- 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.
- 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).
- 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).
- 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).
- 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).
- 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).
- R. Catena, T. Emken, N. A. Spaldin, and W. Tarantino, Atomic responses to general dark matter-electron interactions, Phys. Rev. Res. 2, 033195 (2020).
- 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).
- S. Knapen, J. Kozaczuk, and T. Lin, Dark matter-electron scattering in dielectrics, Phys. Rev. D 104, 015031 (2021).
- 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).
- J. Lindhard, On the properties of a gas of charged particles, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 28, 21 (1954).
- S. Knapen, J. Kozaczuk, and T. Lin, Python package for dark matter scattering in dielectric targets, Phys. Rev. D 105, 015014 (2022).
- 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.
- 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).
- 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).
- M. Gatti and F. Sottile, Exciton dispersion from first principles, Phys. Rev. B 88, 155113 (2013).
- 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).
- 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).
- 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).
- 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.
- 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.
- 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).
- E. E. Salpeter and H. A. Bethe, A relativistic equation for bound-state problems, Phys. Rev. 84, 1232 (1951).
- W. Hanke and L. J. Sham, Many-particle effects in the optical excitations of a semiconductor, Phys. Rev. Lett. 43, 387 (1979).
- G. Strinati, Application of the Green's functions method to the study of the optical properties of semiconductors, Riv. Nuovo Cimento 11, 1 (1988).
- 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).
- 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].
- 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.
- 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).
- 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).
- 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).
- 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).
- B. Campbell-Deem, S. Knapen, J. Kozaczuk, T. Lin, C. Stratman, and E. Villarama, DarkELF Python code, GitHub (2022, https://github.com/tongylin/DarkELF.
- 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).
- K. Teegarden and G. Baldini, Optical absorption spectra of the alkali halides at 10°K, Phys. Rev. 155, 896 (1967).
- R. Williams and K. Song, The self-trapped exciton, J. Phys. Chem. Solids 51, 679 (1990).
- M. D. Sturge, Optical absorption of Gallium arsenide between 0.6 and 2.75 eV, Phys. Rev. 127, 768 (1962).
- 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 dark matter, IEEE Trans. Nucl. Sci. 66, 2333 (2019).
- 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).
- J. E. Eby, K. J. Teegarden, and D. B. Dutton, Ultraviolet absorption of Alkali Halides, Phys. Rev. 116, 1099 (1959).
- M. Grunert, M. Großmann, and E. Runge, Predicting exciton binding energies from ground-state properties, Phys. Rev. B 110, 075204 (2024).
- S. Nagata, K. Fujiwara, and H. Nishimura, Dynamical aspects of excitons in NaI, J. Lumin. 47, 147 (1990).
- 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).
- 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.
- D. Zhou and B. F. Usher, Deviation of the AlGaAs lattice constant from Vegard's law, J. Phys. D: Appl. Phys. 34, 1461 (2001).
- 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.
- K. Momma and F. Izumi, Vesta: A three-dimensional visualization system for electronic and structural analysis, J. Appl. Crystallogr. 41, 653 (2008).
- 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).