⚛️ phenomenology

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

This study utilizes molecular dynamics and density functional theory to investigate defect formation in NaI crystals induced by dark matter collisions, proposing that the resulting new electronic states within the band gap could serve as a novel detection channel for dark matter searches.

Original authors: G. Angloher, M. R. Bharadwaj, A. Böhmer, M. Cababie, I. Colantoni, I. Dafinei, N. Di Marco, C. Dittmar, F. Ferella, F. Ferroni, S. Fichtinger, A. Filipponi, T. Frank, M. Friedl, D. Fuchs, L. Gai, M. G

Published 2026-02-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: G. Angloher, M. R. Bharadwaj, A. Böhmer, M. Cababie, I. Colantoni, I. Dafinei, N. Di Marco, C. Dittmar, F. Ferella, F. Ferroni, S. Fichtinger, A. Filipponi, T. Frank, M. Friedl, D. Fuchs, L. Gai, M. Gapp, M. Heikinheimo, M. N. Hughes, K. Huitu, M. Kellermann, R. Maji, M. Mancuso, L. Pagnanini, F. Petricca, S. Pirro, F. Pröbst, G. Profeta, A. Puiu, F. Reindl, K. Schäffner, J. Schieck, P. Schreiner, C. Schwertner, P. Settembri, K. Shera, M. Stahlberg, A. Stendahl, M. Stukel, C. Tresca, S. Yue, V. Zema, Y. Zhu, N. Zimmermann, M. Di Giambattista, F. Giannessi, R. Rollo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to hear a whisper in a very noisy room. That is essentially what scientists are doing when they search for Dark Matter. Dark Matter is the invisible "ghost" stuff that makes up most of the universe, but it rarely talks to us. It passes right through our bodies and the Earth without a scratch.

For decades, scientists have been using giant, ultra-sensitive crystals made of Sodium Iodide (NaI)—think of them as giant, frozen salt shakers—to listen for these ghosts. When a Dark Matter particle bumps into an atom in the crystal, it's supposed to create a tiny flash of light (scintillation) and a tiny vibration (heat/phonon).

However, there's a problem. The famous DAMA/LIBRA experiment claims to hear this whisper (a signal that changes with the seasons), but other experiments using different materials say, "We hear nothing." It's like one person in the room saying, "I heard a whisper!" while everyone else says, "It's too quiet."

This new paper from the COSINUS collaboration proposes a clever new way to listen: What if we don't just listen for the sound, but look for the damage?

The "Cracked Window" Analogy

Usually, scientists expect a Dark Matter particle to hit an atom and bounce off, creating a tiny ripple of energy. But this paper suggests that sometimes, the hit is hard enough to break the crystal structure.

Imagine the crystal lattice (the orderly arrangement of atoms) as a perfectly stacked tower of Jenga blocks.

The Old Way: You tap a block, and the whole tower wiggles (creating heat and light).
The New Way: You hit a block so hard that it knocks a piece out of the tower and leaves a hole. Now you have a hole (a vacancy) and a loose block sitting on top of another block (an interstitial atom). Together, this pair is called a Frenkel pair.

The paper uses powerful computer simulations to show exactly what happens when a Dark Matter ghost smashes into a Sodium Iodide crystal. They found two main things:

The "Broken Glass" Effect: When these defects (holes and loose blocks) form, they change the rules of the game. The crystal isn't just a perfect grid anymore; it has "scars."
The "Secret Door": This is the most exciting part. In a perfect crystal, electrons (the tiny particles that carry electricity and light) can only jump between specific energy levels, like stairs. You can't stand in between the steps.
- But when a defect forms (specifically involving the heavy Iodine atoms), it creates a new step right in the middle of the gap.
- Think of it like a secret elevator appearing in the middle of a staircase. Now, electrons can jump across the gap using this "elevator state" at much lower energies than before.

Why Does This Matter?

This discovery opens up a new detection channel.

The Signal Loss: When a Dark Matter particle creates these defects, some of its energy gets "stolen" to build the hole and move the loose block. This means the heat and light signal might be weaker than expected. If scientists only looked for the standard "flash and wiggle," they might miss these events or think the particle was lighter than it actually was.
The New Signal: Because of those "secret elevator" states (the new energy levels), the crystal might produce a tiny electrical charge or a specific type of light that wasn't possible before. It's like the crystal is ringing a different bell when it's broken.

The "Elevator" Metaphor

To visualize the electronic change:

Perfect Crystal: Imagine a two-story building. The ground floor is full of people (electrons), and the second floor is empty. There is no way to get to the second floor unless you have a huge jump (high energy).
Defective Crystal: A defect creates a mezzanine level halfway up. Now, people can easily hop up to the mezzanine and then to the second floor with a much smaller jump. This makes it much easier for the crystal to react to low-energy Dark Matter particles.

The Bottom Line

This paper suggests that damage is a feature, not a bug.

Instead of trying to avoid defects or ignoring them, the COSINUS team proposes that we should look for the scars. By understanding how Dark Matter breaks the crystal and creates these "elevator states," we can:

Explain why some experiments see a signal and others don't (maybe they are looking for the wrong type of signal).
Detect Dark Matter particles that are too light to create a big flash but heavy enough to break the crystal lattice.
Use the "broken" parts of the crystal as a new, highly sensitive sensor for the universe's most elusive particles.

In short, they are saying: "If the crystal gets a scratch, that scratch might be the fingerprint of Dark Matter."

1. Problem Statement

Direct detection of Dark Matter (DM), specifically Weakly Interacting Massive Particles (WIMPs), remains a primary goal in particle physics. The DAMA/LIBRA experiment has reported a statistically significant (13.7 $\sigma$ ) annual modulation signal using Thallium-doped Sodium Iodide (NaI(Tl)) crystals. However, other experiments using different target materials have set exclusion limits that conflict with DAMA/LIBRA's results.

To resolve this, the COSINUS experiment aims to test the DAMA/LIBRA signal using NaI crystals as a cryogenic scintillating calorimeter. This approach provides two detection channels: scintillation light and phonons (heat). A critical challenge in these experiments is understanding how DM interactions affect the detector's response. Specifically, high-energy collisions can create lattice defects (Frenkel pairs), which:

Consume energy that would otherwise contribute to the phonon or scintillation signals (signal loss).
Potentially alter the electronic structure of the crystal, creating new detection channels.
Cause long-term degradation of detector performance (aging).

The paper investigates the formation of these defects in NaI crystals induced by DM collisions and explores whether these defects can serve as a novel detection channel rather than just a source of background or signal loss.

2. Methodology

The authors employed a multi-scale computational approach combining Molecular Dynamics (MD) and Density Functional Theory (DFT):

Molecular Dynamics (MD) Simulations:
- Tool: LAMMPS code.
- Setup: A $6\times6\times6$ unit cell of NaI with periodic boundary conditions, thermalized to $\sim1$ K.
- Process: Simulated DM collisions by assigning kinetic energy and momentum to a Primary Knock-on Atom (PKA). The system was divided into an inner region (NVE ensemble) and an outer region (NVT ensemble at 1 K) to simulate energy dissipation.
- Analysis: Used Wigner-Seitz defect analysis (via OVITO) to identify Frenkel pairs (vacancy + interstitial atom).
- Threshold Displacement Energy (TDE): Calculated the minimum energy required to create a defect for various recoil directions (polar and azimuthal angles) for both Na and I PKAs.
Density Functional Theory (DFT) Calculations:
- Tool: VASP code using the PBE exchange-correlation functional.
- Setup: Analyzed a smaller $3\times3\times3$ subset of the simulation cell containing the defects identified by MD.
- Goal: To compute the electronic density of states (DOS), band structure, and charge density distributions to understand how defects modify the electronic properties of NaI.
Dark Matter Rate Calculation:
- Calculated the DM-nucleus scattering rate assuming a spin-independent interaction and the Standard Halo Model.
- Derived the defect formation rate ( $R_{Def}$ ) by integrating the scattering rate over recoil energies above the TDE surface.

3. Key Contributions and Results

A. Defect Formation Energetics and Anisotropy

Formation Energies: The study estimated the formation energy of Frenkel pairs as $\sim4$ eV for Sodium (Na) and $\sim16$ eV for Iodine (I).
Threshold Displacement Energy (TDE): The TDE is highly anisotropic.
- Lowest TDE: Found in the $[110]$ direction ($24$ eV for Na, $51$ eV for I).
- Highest TDE: Found in the $[111]$ direction ($119$ eV for Na, $147$ eV for I).
PKA Behavior:
- When Na is the PKA, an Na interstitial is always formed regardless of direction.
- When I is the PKA, the outcome depends on the recoil direction. Due to the lower formation energy of Na interstitials, momentum transfer often results in an Na interstitial, even if I was the PKA. However, specific directions allow for I interstitials.

B. Electronic Structure Modifications

Na Defects: Do not introduce new states within the band gap but cause localized changes near the valence band maximum.
Iodine Defects (Crucial Finding): The formation of an Iodine Frenkel pair introduces new electronic states within the band gap:
- Occupied states appear at $\sim1$ eV above the valence band.
- Unoccupied states appear at $\sim3$ eV.
- These states are localized around the interstitial atom and the vacancy, respectively.
Implication: These in-gap states allow for electronic transitions at energies lower than the intrinsic band gap, effectively acting as "elevator states" or enabling photodetector-like mechanisms.

C. Impact on Detection Rates

Signal Loss: The study quantified the ratio of events resulting in defect formation ( $R_{Def}/R$ ). For DM masses $>2.5$ GeV/ $c^2$ , up to 90% of Na-induced events and 7.5% of I-induced events result in defect formation. This implies a significant potential loss of phonon/scintillation signal energy.
Novel Detection Channel: The authors propose exploiting the electronic in-gap states created by Iodine defects.
- Mechanisms include charge transfer from in-gap states to the conduction band (via thermal modulation) or luminescence/fluorescence from these states.
- This opens a "charge signal" channel independent of the traditional light/phonon channels.

D. Experimental Reach

The paper projects the sensitivity of a 1 kg $\cdot$ yr exposure experiment.
While the "defect-only" channel (green line in Fig. 4) has a higher threshold than a standard 3 eV threshold detector (black line), it offers a unique signature.
The electronic channel (yellow-orange), relying on Iodine defects, shows promise for detecting lower cross-sections in specific mass ranges, provided the detection of these specific defect-induced states is feasible.

4. Significance and Conclusion

This work provides a critical theoretical foundation for the COSINUS experiment and future NaI-based DM searches by:

Quantifying Signal Loss: Establishing that defect formation is a dominant energy loss mechanism for higher mass WIMPs, which must be accounted for in energy calibration and background discrimination.
Proposing a New Detection Paradigm: Identifying that Iodine-induced defects create in-gap electronic states. This suggests that DM detectors could potentially detect the presence of these defects (via charge or luminescence) rather than just the immediate energy deposition.
Aging Effects: Highlighting that localized vibrational modes (discrete breathers) associated with defects could persist for hundreds of picoseconds, potentially affecting the thermal reset time of the detector and contributing to long-term degradation of light yield.

In conclusion, the paper argues that defect formation in NaI is not merely a nuisance but a complex phenomenon that, if understood and harnessed, could provide a novel, model-independent detection channel for Dark Matter, potentially resolving the tension between DAMA/LIBRA and other experiments.