The Migdal effect in solid crystals and the role of non-adiabaticity

TL;DR

This paper presents a systematic Born–Oppenheimer analysis of the Migdal effect in solid crystals, showing that in the formally infinite lattice the adiabatic contribution cancels and the entire effect arises from non-adiabatic electron–nucleus couplings. By expanding in the small parameter $ε = (m/M)^{1/4}$ and carefully separating the electronic and nuclear components, the authors derive the non-adiabatic matrix element and demonstrate that it matches the matrix element obtained in the Berghaus:2022pbu effective theory. This cross-check supports the experimental bounds on dark matter–nucleus interactions derived by SENSEI and clarifies the role of non-adiabaticity in semiconductors. The work also situates the crystal case within a broader pattern: adiabatic contributions dominate atomic targets, both adiabatic and non-adiabatic can matter for molecules, while crystals are governed by non-adiabatic effects, suggesting avenues for applying the framework to more complex systems in the future.

Abstract

We systematically apply the Born-Oppenheimer approximation to show that the Migdal effect in a solid crystal is entirely due to non-adiabatic effects, namely the deviation of the wave function from exact factorization of the electronic and nuclear contributions. The matrix element obtained this way matches exactly the result found by means of a previously derived low energy effective theory.