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

TL;DR

This paper extends the theoretical understanding of the Migdal effect in semiconductors, enabling the detection of lighter dark matter particles below 100 MeV by relating the effect to measurable crystal properties.

Contribution

We develop an effective field theory framework that incorporates phonon dynamics to accurately compute the Migdal effect in semiconductors at small momentum transfer.

Findings

Inclusive Migdal rate is well approximated by free ion models.

The shape of the electron recoil spectrum depends on phonon dynamics.

Results enable analysis of dark matter as light as 1 MeV in semiconductors.

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.