Defect Formation in NaI Crystals: A Novel Pathway to Dark Matter Detection

TL;DR

The paper investigates whether dark matter collisions can create lattice defects in NaI crystals and how such defects affect detection channels in NaI-based detectors. It combines molecular dynamics (MD, via LAMMPS) and first-principles density functional theory (DFT, via VASP) to quantify defect formation energies, threshold displacement energies, and defect-induced electronic states, reporting $E_{ ext{Def,Na}} \sim 4$ eV, $E_{ ext{Def,I}} \sim 16$ eV, and direction-dependent $TDE$ values such as $TDE^{[110]}_{ ext{Na}} = 24$ eV and $TDE^{[110]}_{ ext{I}} = 51$ eV. A key finding is that iodine Frenkel pairs generate in-gap states around $1$ eV (occupied) and $3$ eV (empty), enabling lower-energy electronic transitions and suggesting defect-enabled electronic or luminescent detection channels. The work also shows that defect formation can alter the phonon and scintillation signals, providing DM-rate predictions that identify specific mass ranges where defect-related channels become relevant, with iodine contributions often dominating at larger masses.

Abstract

Sodium iodide (NaI) is a widely used scintillator in direct dark matter searches. In particular, NaI-based cryogenic scintillating calorimeters have emerged as promising candidates, like in the COSINUS experiment, for testing the annually modulating signal reported by DAMA/LIBRA. In this study, we investigate defect formation within NaI crystals and its impact on the dark matter detection signal. Using molecular dynamics simulations and density functional theory techniques, we simulate a DM particle collision on an NaI crystal, focusing on the possible defects formation and their structural and electronic properties. Our analysis includes a detailed study of the electronic states associated with the interstitial atoms and vacancies, the energetic cost of defect formation, and the anisotropic threshold displacement energy. Finally, we highlight the potential to exploit dark matter-induced defects as a novel detection channel, enabled by the introduction of new states within the electronic band gap.

Figures (5)

• Figure 1: (a-b) Iodine interstitial atom and its corresponding vacancy. Na atoms are shown in red while I atoms are in blue. The yellow surfaces indicate the charge density associated to the states present in the electronic band gap, induced by the I defect. (c) Comparison of the electronic density of states between the ideal NaI system in absence of defects (black line), and in the presence of an interstitial Na atom (red line), and I atom (blue line). The energy position of the highest occupied electronic state for each system is shown by a vertical dashed line of the corresponding color. An inset of the electronic band gap region is also present, showcasing how in the presence of I interstitial atoms new states emerge in the band gap.
• Figure 2: Mollweide projection of the TDE, in case of Na atom as the PKA (top), and the I atom (bottom). Lighter regions correspond to high TDE values, while darker ones to lower TDE values. Due to the larger mass, the TDE is larger when the PKA is an I atom.
• Figure 3: Ratio of events with a signal loss due to the formation of Frenkel pairs, as a function of the DM mass and depending on the PKA. The red (blue) line shows the result obtained using the calculated TDE for Na (I), while the dashed lines correspond to a $\pm$5 eV uncertainty on the corresponding TDE. The black line represents the ratio between the total rates $R_{\text{Def}}/R$. The inset shows a zoom of the plot at lower masses.
• Figure 4: Experimental reach as a function of the DM particle mass, assuming a 1 kg$\cdot$yr exposure, and a background-free experiment. In black the total cross section is plotted assuming a sensitivity threshold of 3 eV; in green the defects cross section for both Na and I is shown, the shaded region corresponds to the uncertainty window on the TDE estimate. In blue and red, dash-dotted lines, the defects cross section for I and Na individually, respectively. In yellow-orange the lower estimate for the electronic channel cross section is reported.
• Figure 5: (a-b) Sodium interstitial atom and its corresponding vacancy. Na atoms are shown in red while I atoms are in blue. The yellow surfaces indicate the charge density associated to the states present in the energy range [-3.4,-2.8] eV for panel (a) and [-0.6,0.0] eV for panel (b), relative to the corresponding Fermi energy (red dashed line in Fig. \ref{['fig:defect-dos']} (c)). (c-d) Snapshots of the molecular dynamics simulation of a 26 eV DM collision along the [110] direction on an Na PKA. Panel (c) is taken after 1 ps from the collision, while panel (d) after 20 ps. The color coding refers to the atom's kinetic energy, going from blue (lowest energy) to red (highest energy).