The Migdal Effect in Semiconductors for Dark Matter with Masses below $\sim$100 MeV

Abstract

Dark matter scattering off a nucleus has a small probability of inducing an observable ionization through the inelastic excitation of an electron, called the Migdal effect. We use an effective field theory to extend the computation of the Migdal effect in semiconductors to regions of small momentum transfer to the nucleus, where the final state of the nucleus is no longer well described by a plane wave. Our analytical result can be fully quantified by the measurable dynamic structure factor of the semiconductor, which accounts for the vibrational degrees of freedom (phonons) in a crystal. We show that, due to the sum rules obeyed by the structure factor, the inclusive Migdal rate and the shape of the electron recoil spectrum is well captured by approximating the nuclei in the crystal as free ions; however, the exclusive differential rate with respect to energy depositions to the crystal depends on the phonon dynamics encoded in the dynamic structure function of the specific material. Our results now allow the Migdal effect in semiconductors to be evaluated even for the lightest dark matter candidates ($m_{\chi }\gtrsim 1$ MeV) that can kinematically excite electrons.

30 pages, 8 figures

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Cited by in corpus (14)

• SENSEI: First Direct-Detection Results on sub-GeV Dark Matter from SENSEI at SNOLAB
• Probing Benchmark Models of Hidden-Sector Dark Matter with DAMIC-M
• A neutrino floor for the Migdal effect
• Measuring the Migdal effect in semiconductors for dark matter detection
• Spin-dependent sub-GeV Inelastic Dark Matter-electron scattering and Migdal effect: (I). Velocity Independent Operator
• Optimal anti-ferromagnets for light dark matter detection
• An Improved Bound on Accelerated Light Dark Matter
• Exploring light dark matter with the Migdal effect in hydrogen-doped liquid xenon
• The Non-Relativistic Effective Field Theory Of Dark Matter-Electron Interactions
• Low-mass constraints on WIMP effective models of inelastic scattering using the Migdal effect
• Measuring the molecular Migdal effect with neutron scattering on diatomic gases
• Semi-Visible Dark Photon Phenomenology at the GeV Scale
• The Migdal effect in solid crystals and the role of non-adiabaticity
• Comparison of the Migdal transition probabilities in electron-atom inelastic cross sections