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All-electron dark matter-electron scattering with random-phase approximation dielectric screening and local field effects

Cyrus E. Dreyer1,2, Rouven Essig3, Marivi Fernandez-Serra1,4, Megan Hott1,3,4,*, and Aman Singal1,3,4

  • *Contact author: megan.hott@stonybrook.edu
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Phys. Rev. D 114, 035003 – Published 3 August, 2026

DOI: https://doi.org/10.1103/rvzm-31vc

Abstract

Accurate predictions for dark matter-electron scattering in solids require an all-electron treatment together with a faithful description of dielectric screening beyond simple approximations. In particular, local field effects, arising from microscopic inhomogeneities of the electronic response, can significantly modify scattering rates across relevant momentum and energy scales. We present an all-electron framework for computing dark matter-electron scattering rates that incorporates dielectric screening at the random-phase approximation (RPA) level, including local field effects. Using crystalline silicon as a benchmark, we show that local field effects play an important role both at large momentum transfers, spanning multiple Brillouin zones, and at low momentum near the plasmon resonance. We compute electron recoil spectra and projected sensitivities for nonrelativistic halo dark matter and for boosted dark matter or other dark-sector particles, which are sensitive to the impact of local field effects in these high and low momentum regimes, respectively. We further present RPA dielectric functions including local field effects for Ge, GaAs, SiC, and diamond, enabling a systematic comparison across target materials. These developments are implemented in the open source code qcdark2.

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References (120)

  1. R. Essig, J. Mardon, and T. Volansky, Direct detection of sub-GeV dark matter, Phys. Rev. D 85, 076007 (2012).
  2. J. Tiffenberg, M. Sofo-Haro, A. Drlica-Wagner, R. Essig, Y. Guardincerri, S. Holland, T. Volansky, and T.-T. Yu (SENSEI Collaboration), Single-electron and single-photon sensitivity with a silicon skipper CCD, Phys. Rev. Lett. 119, 131802 (2017).
  3. M. Crisler, R. Essig, J. Estrada, G. Fernandez, J. Tiffenberg, M. Sofo haro, T. Volansky, and T.-T. Yu (SENSEI Collaboration), SENSEI: First direct-detection constraints on sub-GeV Dark Matter from a surface run, Phys. Rev. Lett. 121, 061803 (2018).
  4. O. Abramoff et al. (SENSEI Collaboration), SENSEI: Direct-detection constraints on sub-GeV Dark Matter from a shallow underground run using a prototype skipper-CCD, Phys. Rev. Lett. 122, 161801 (2019).
  5. L. Barak et al. (SENSEI Collaboration), SENSEI: Direct-detection results on sub-GeV Dark Matter from a new skipper-CCD, Phys. Rev. Lett. 125, 171802 (2020).
  6. L. Barak et al. (SENSEI Collaboration), SENSEI: Characterization of single-electron events using a skipper charge-coupled device, Phys. Rev. Appl. 17, 014022 (2022).
  7. P. Adari et al. (SENSEI Collaboration), First direct-detection results on sub-GeV Dark Matter using the SENSEI detector at SNOLAB, Phys. Rev. Lett. 134, 011804 (2025).
  8. I. M. Bloch et al. (SENSEI Collaboration), SENSEI at SNOLAB: Single-electron event rate and implications for Dark Matter, Phys. Rev. Lett. 134, 161002 (2025).
  9. I. M. Bloch et al. (SENSEI Collaboration), SENSEI: A search for diurnal modulation in sub-GeV Dark Matter scattering, Phys. Rev. Lett. 136, 211001 (2026).
  10. I. Arnquist et al. (DAMIC-M Collaboration), First constraints from DAMIC-M on sub-GeV Dark-Matter particles interacting with electrons, Phys. Rev. Lett. 130, 171003 (2023).
  11. I. Arnquist et al. (DAMIC-M Collaboration), Search for daily modulation of MeV Dark Matter signals with DAMIC-M, Phys. Rev. Lett. 132, 101006 (2024).
  12. K. Aggarwal et al. (DAMIC-M Collaboration), Daily modulation constraints on light Dark Matter with DAMIC-M, arXiv:2511.13962.
  13. K. Aggarwal et al. (DAMIC-M Collaboration), Probing benchmark models of hidden-sector dark matter with DAMIC-M, Phys. Rev. Lett. 135, 071002 (2025).
  14. R. Agnese et al. (SuperCDMS Collaboration), First Dark Matter constraints from a SuperCDMS single-charge sensitive detector, Phys. Rev. Lett. 121, 051301 (2018); 122, 069901(E) (2019).
  15. D. W. Amaral et al. (SuperCDMS Collaboration), Constraints on low-mass, relic dark matter candidates from a surface-operated SuperCDMS single-charge sensitive detector, Phys. Rev. D 102, 091101 (2020).
  16. M. F. Albakry et al. (SuperCDMS Collaboration), Light dark matter constraints from SuperCDMS HVeV detectors operated underground with an anticoincidence event selection, Phys. Rev. D 111, 012006 (2025).
  17. M. F. Albakry et al. (SuperCDMS Collaboration), Search for low-mass electron-recoil dark matter using a single-charge sensitive SuperCDMS-HVeV detector, Phys. Rev. D 113, 032001 (2026).
  18. Q. Arnaud et al. (EDELWEISS Collaboration), First Germanium-based constraints on sub-MeV Dark Matter with the EDELWEISS Experiment, Phys. Rev. Lett. 125, 141301 (2020).
  19. A. Aguilar-Arevalo et al. (Oscura Collaboration), The Oscura experiment, arXiv:2202.10518.
  20. 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).
  21. 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).
  22. S. Knapen, J. Kozaczuk, and T. Lin, Dark matter-electron scattering in dielectrics, Phys. Rev. D 104, 015031 (2021).
  23. 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).
  24. R. Essig, M. Fernandez-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.
  25. P. Giannozzi et al., Advanced capabilities for materials modelling with quantum espresso, J. Phys. Condens. Matter 29, 465901 (2017).
  26. T. Trickle, Extended calculation of electronic excitations for direct detection of dark matter, Phys. Rev. D 107, 035035 (2023).
  27. S. Knapen, J. Kozaczuk, and T. Lin, python package for dark matter scattering in dielectric targets, Phys. Rev. D 105, 015014 (2022).
  28. J. J. Mortensen et al., gpaw: An open python package for electronic structure calculations, J. Chem. Phys. 160, 092503 (2024).
  29. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  30. Q. Sun et al., Recent developments in the pyscf program package, J. Chem. Phys. 153, 024109 (2020).
  31. N. Kurinsky, D. Baxter, Y. Kahn, and G. Krnjaic, Dark matter interpretation of excesses in multiple direct detection experiments, Phys. Rev. D 102, 015017 (2020).
  32. S. Knapen, J. Kozaczuk, and T. Lin, Migdal Effect in semiconductors, Phys. Rev. Lett. 127, 081805 (2021).
  33. R. Essig, R. Plestid, and A. Singal, Collective excitations and low-energy ionization signatures of relativistic particles in silicon detectors, Commun. Phys. 7, 416 (2024).
  34. Z.-L. Liang, L. Su, L. Wu, and B. Zhu, Plasmon-enhanced direct-detection method for boosted sub-MeV Dark Matter, Phys. Rev. Lett. 134, 071001 (2025).
  35. T. Emken, C. Kouvaris, and N. G. Nielsen, The sun as a sub-GeV Dark Matter accelerator, Phys. Rev. D 97, 063007 (2018).
  36. H. An, M. Pospelov, J. Pradler, and A. Ritz, Directly detecting MeV-Scale Dark Matter via solar reflection, Phys. Rev. Lett. 120, 141801 (2018).
  37. T. Emken, Solar reflection of light dark matter with heavy mediators, Phys. Rev. D 105, 063020 (2022).
  38. H. An, H. Nie, M. Pospelov, J. Pradler, and A. Ritz, Solar reflection of dark matter, Phys. Rev. D 104, 103026 (2021).
  39. T. Emken, R. Essig, and H. Xu, Solar reflection of dark matter with dark-photon mediators, J. Cosmol. Astropart. Phys. 07 (2024) 023.
  40. T. Bringmann and M. Pospelov, Novel direct detection constraints on light dark matter, Phys. Rev. Lett. 122, 171801 (2019).
  41. Y. Ema, F. Sala, and R. Sato, Light dark matter at neutrino experiments, Phys. Rev. Lett. 122, 181802 (2019).
  42. J. Alvey, M. D. Campos, M. Fairbairn, and T. You, Detecting light dark matter via inelastic cosmic ray collisions, Phys. Rev. Lett. 123, 261802 (2019).
  43. L. Su, W. Wang, L. Wu, J. M. Yang, and B. Zhu, Atmospheric dark matter and XENON1T excess, Phys. Rev. D 102, 115028 (2020).
  44. Y. Jho, J.-C. Park, S. C. Park, and P.-Y. Tseng, Cosmic-neutrino-boosted Dark Matter (νBDM), arXiv:2101.11262.
  45. A. Das and M. Sen, Boosted dark matter from diffuse supernova neutrinos, Phys. Rev. D 104, 075029 (2021).
  46. J.-W. Sun, L. Wu, Y.-H. Xu, and B. Zhu, Probing supernova neutrino boosted dark matter with collective excitations, Phys. Rev. D 112, 015014 (2025).
  47. L. Barak et al. (SENSEI Collaboration), Search by the SENSEI experiment for Millicharged particles produced in the NuMI beam, Phys. Rev. Lett. 133, 071801 (2024).
  48. S. Perez et al. (Oscura Collaboration), Searching for millicharged particles with 1 kg of Skipper-CCDs using the NuMI beam at Fermilab, J. High Energy Phys. 02 (2024) 072.
  49. A. A. Aguilar-Arevalo et al. (CONNIE Collaboration and Atucha-II Collaboration), Search for reactor-produced millicharged particles with skipper-CCDs at the CONNIE and Atucha-II experiments, Phys. Rev. Lett. 134, 071801 (2025).
  50. A. A. Aguilar-Arevalo et al. (CONNIE Collaboration), Searches for CEνNS and physics beyond the Standard Model using skipper-CCDs at CONNIE, Phys. Rev. D 113, 092017 (2026).
  51. R. Essig, P. Li, Z. Liu, M. McDuffie, R. Plestid, and H. Xu, Probing millicharged particles at an electron beam dump with ultralow-threshold sensors, J. High Energy Phys. 04 (2025) 057.
  52. T. Trickle, Z. Zhang, K. M. Zurek, K. Inzani, and S. M. Griffin, Multi-channel direct detection of light dark matter: Theoretical framework, J. High Energy Phys. 03 (2020) 036.
  53. D. Baxter et al., Recommended conventions for reporting results from direct dark matter searches, Eur. Phys. J. C 81, 907 (2021).
  54. K. Agashe, Y. Cui, L. Necib, and J. Thaler, (In)direct detection of boosted dark matter, J. Cosmol. Astropart. Phys. 10 (2014) 062.
  55. C. Boyd, Y. Hochberg, Y. Kahn, E. D. Kramer, N. Kurinsky, B. V. Lehmann, and T. C. Yu, Directional detection of dark matter with anisotropic response functions, Phys. Rev. D 108, 015015 (2023).
  56. K. Ramanathan and N. Kurinsky, Ionization yield in silicon for eV-scale electron-recoil processes, Phys. Rev. D 102, 063026 (2020).
  57. D. Pines and D. Bohm, A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions, Phys. Rev. 85, 338 (1952).
  58. H. Ehrenreich and M. H. Cohen, Self-consistent field approach to the many-electron problem, Phys. Rev. 115, 786 (1959).
  59. S. L. Adler, Quantum theory of the dielectric constant in real solids, Phys. Rev. 126, 413 (1962).
  60. N. Wiser, Dielectric constant with local field effects included, Phys. Rev. 129, 62 (1963).
  61. M. S. Hybertsen and S. G. Louie, Ab initio static dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators, Phys. Rev. B 35, 5585 (1987).
  62. M. Shishkin and G. Kresse, Implementation and performance of the frequency-dependent GW method within the PAW framework, Phys. Rev. B 74, 035101 (2006).
  63. T. Miyake and F. Aryasetiawan, Efficient algorithm for calculating noninteracting frequency-dependent linear response functions, Phys. Rev. B 61, 7172 (2000).
  64. R. M. Martin, L. Reining, and D. M. Ceperley, Interacting Electrons: Theory and Computational Approaches (Cambridge University Press, Cambridge, England, 2016).
  65. J. Yan, J. J. Mortensen, K. W. Jacobsen, and K. S. Thygesen, Linear density response function in the projector augmented wave method: Applications to solids, surfaces, and interfaces, Phys. Rev. B 83, 245122 (2011).
  66. I. Timrov, N. Vast, R. Gebauer, and S. Baroni, turboeels—A code for the simulation of the electron energy loss and inelastic X-ray scattering spectra using the Liouville–Lanczos approach to time-dependent density-functional perturbation theory, Comput. Phys. Commun. 196, 460 (2015).
  67. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  68. J. Dunning, Thom H., K. A. Peterson, and A. K. Wilson, Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited, J. Chem. Phys. 114, 9244 (2001).
  69. J. Dunning and Thom H., Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen, J. Chem. Phys. 90, 1007 (1989).
  70. D. E. Woon and J. Dunning, Thom H., Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon, J. Chem. Phys. 98, 1358 (1993).
  71. A. K. Wilson, D. E. Woon, K. A. Peterson, and J. Dunning, Thom H., Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton, J. Chem. Phys. 110, 7667 (1999).
  72. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  73. C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, New York, 1996).
  74. M. E. Levinshteĭn, S. L. Rumyantsev, and M. Shur, Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, SiGe (Wiley, New York, 2001).
  75. O. Madelung, Semiconductors. Group IV Elements and III-V Compounds, Data in science and technology (Springer-Verlag, Berlin, 1991).
  76. S. G. Louie, J. R. Chelikowsky, and M. L. Cohen, Local-field effects in the optical spectrum of silicon, Phys. Rev. Lett. 34, 155 (1975).
  77. D. F. Edwards, Silicon, in Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic Press, New York, 1985), Vol. 1, pp. 547–568.
  78. L. Marton and J. Toots, Optical properties of germanium in the far ultraviolet, Phys. Rev. 160, 602 (1967).
  79. G. Brockt and H. Lakner, Nanoscale EELS analysis of dielectric function and bandgap properties in GaN and related materials, Micron 31, 435 (2000).
  80. J.-M. Costantini and J. Ribis, Analysis of plasmon loss peaks of oxides and semiconductors with the energy loss function, Materials 16, 7610 (2023).
  81. V. Serin, E. Beche, R. Berjoan, O. Abidate, D. Rats, J. Fontaine, L.Vandenbulcke, C. Germain, and A. Catherinot, in XAES, XPS, EELS and RAMAN spectroscopy of polycrystalline to amorphous carbon films with various sp3 to sp2 bondings, in Proceedings of the Fifth International Symposium on Diamond Materials, edited by J. L. Davidson, W. D. Brown, A. Gicquel, B. Spytsin, and J. Angus (The Electrochemical Society, Pennington, NJ, 1998), pp. 126–141.
  82. P. Ewels, T. Sikora, V. Serin, C. P. Ewels, and L. Lajaunie, A complete overhaul of the electron energy-loss spectroscopy and x-ray absorption spectroscopy database: eelsdb.eu, Microsc. Microanal. 22, 717 (2016).
  83. 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).
  84. E. Runge and E. K. U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett. 52, 997 (1984).
  85. E. K. U. Gross and W. Kohn, Local density-functional theory of frequency-dependent linear response, Phys. Rev. Lett. 55, 2850 (1985).
  86. N. Taufertshöfer, V. Zema, R. Catena, V. Olevano, and N. A. Spaldin, Excitonic contributions to dark matter-electron scattering, Phys. Rev. Res. 8, 013056 (2026).
  87. X. Chu, T. Hambye, and M. H. G. Tytgat, The four basic ways of creating Dark Matter through a portal, J. Cosmol. Astropart. Phys. 05 (2012) 034.
  88. C. Dvorkin, T. Lin, and K. Schutz, Making dark matter out of light: Freeze-in from plasma effects, Phys. Rev. D 99, 115009 (2019); 105, 119901(E) (2022).
  89. P. Sellin and J. Vaitkus, New materials for radiation hard semiconductor dectectors, Nucl. Instrum. Methods Phys. Res., Sect. A 557, 479 (2006).
  90. D. Rodrigues et al., Absolute measurement of the Fano factor using a Skipper-CCD, Nucl. Instrum. Methods Phys. Res., Sect. A 1010, 165511 (2021).
  91. G. Cappellini, R. Del Sole, L. Reining, and F. Bechstedt, Model dielectric function for semiconductors, Phys. Rev. B 47, 9892 (1993).
  92. J. Lindhard, On the properties of a gas of charged particles, Kgl. Danske Videnskab. Selskab Mat.-fys. Medd. 28, 1 (1953).
  93. M. Vos and P. L. Grande, RPA Dielectric functions: Streamlined approach to relaxation effects, binding and high momentum dispersion, J. Phys. Chem. Solids 198, 112470 (2025).
  94. R. Essig, Y. Hochberg, Y. Shoji, A. Singal, and G. Suczewski, Low-energy compton scattering in materials, Phys. Rev. D 109, 116011 (2024).
  95. C. Boehm, M. J. Dolan, and C. McCabe, A lower bound on the mass of cold thermal Dark Matter from Planck, J. Cosmol. Astropart. Phys. 08 (2013) 041.
  96. M. L. Cohen and S. G. Louie, Fundamentals of Condensed Matter Physics (Cambridge University Press, Cambridge, England, 2016).
  97. S. K. Lee, M. Lisanti, S. Mishra-Sharma, and B. R. Safdi, Modulation effects in Dark Matter-electron scattering experiments, Phys. Rev. D 92, 083517 (2015).
  98. 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).
  99. 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.
  100. G. Krnjaic, D. Rocha, and T. Trickle, The non-relativistic effective field theory of dark matter-electron interactions, J. High Energy Phys. 03 (2025) 165.
  101. Y. Hochberg, M. Khalaf, A. Lenoci, and R. Ovadia, Determining (all) Dark Matter-electron scattering rates from material properties, arXiv:2510.25835.
  102. qedark-eft (2021), github.com/urdshals/QEdark-EFT.
  103. W. W. M. Allison and J. H. Cobb, Relativistic charged particle identification by energy loss, Annu. Rev. Nucl. Part. Sci. 30, 253 (1980).
  104. U. Fano, Penetration of protons, alpha particles, and mesons, Annu. Rev. Nucl. Part. Sci. 13, 1 (1963).
  105. H. Bichsel and H. Schindler, The Interaction of Radiation with Matter, in Particle Physics Reference Library: Volume 2: Detectors for Particles and Radiation, edited by C. W. Fabjan and H. Schopper (Springer International Publishing, New York, 2020).
  106. M. Dressel and G. Grüner, Electrodynamics of Solids: Optical Properties of Electrons in Matter (Cambridge University Press, Cambridge, England, 2002), pp. 47–56.
  107. J. Kozaczuk and T. Lin, Plasmon production from dark matter scattering, Phys. Rev. D 101, 123012 (2020).
  108. A. C. Sharma and S. Auluck, Transverse dielectric function for a model semiconductor, Phys. Rev. B 24, 4729 (1981).
  109. R. Essig, M. Sholapurkar, and T.-T. Yu, Solar neutrinos as a signal and background in direct-detection experiments searching for sub-GeV dark matter with electron recoils, Phys. Rev. D 97, 095029 (2018).
  110. J. Wyenberg and I. M. Shoemaker, Mapping the neutrino floor for direct detection experiments based on dark matter-electron scattering, Phys. Rev. D 97, 115026 (2018).
  111. B. Carew, A. R. Caddell, T. N. Maity, and C. A. J. O’Hare, Neutrino fog for dark matter-electron scattering experiments, Phys. Rev. D 109, 083016 (2024).
  112. J. B. Dent, B. A. Friedman, J. L. Newstead, and S. Sabharwal, Nuclear and electron scattering by neutrinos and dark matter in condensed systems, Phys. Rev. D 113, 116016 (2026).
  113. A. Migdal, Ionizatsiya atomov pri yadernykh reaktsiyakh, Zh. Eksp. Teor. Fiz. 9, 1163 (1939).
  114. M. Ibe, W. Nakano, Y. Shoji, and K. Suzuki, Migdal effect in dark matter direct detection experiments, J. High Energy Phys. 03 (2018) 194.
  115. S. Knapen, J. Kozaczuk, and T. Lin, Migdal effect in semiconductors, Phys. Rev. Lett. 127, 081805 (2021).
  116. Z.-L. Liang, C. Mo, F. Zheng, and P. Zhang, Describing the Migdal effect with a bremsstrahlung-like process and many-body effects, Phys. Rev. D 104, 056009 (2021).
  117. K. V. Berghaus, A. Esposito, R. Essig, and M. Sholapurkar, The Migdal effect in semiconductors for dark matter with masses below ∼100  MeV, J. High Energy Phys. 01 (2023) 023.
  118. https://github.com/meganhott/QCDark2.
  119. S. Baroni and R. Resta, Ab initio calculation of the macroscopic dielectric constant in silicon, Phys. Rev. B 33, 7017 (1986).
  120. M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, Linear optical properties in the projector-augmented wave methodology, Phys. Rev. B 73, 045112 (2006).

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Phys. Rev. D 114, 035003– Published 3 August, 2026
  • Received 8 April 2026
  • Accepted 30 June 2026
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