Signatures of Dynes superconductivity in the THz response of ALD-grown NbN thin films

arXiv:2602.15003 · cond-mat.supr-con · Submitted 2026-02-16 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Signatures of Dynes superconductivity in the THz response of ALD-grown NbN thin films".

Mira: The gist The study probes the terahertz response of superconducting NbN thin films using atomic layer deposition to find signatures of Dynes superconductivity in their optical conductivity,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: Now let's talk about how this study suggests improvements for other related studies, specifically regarding the limitations of previous models <ref:2602.15003#pg5>.

Mira: They highlight that conventional BCS electrodynamics just can't describe the THz data, which is why they argue that including a finite Dynes pair-breaking parameter Γ helps get excellent agreement <ref:2602.15003#pg5>.

Lev: So for someone trying to model this, it means you need to go beyond just the standard BCS framework and explicitly include a term for that pair-breaking rate <ref:2602.15003#pg5>.

Kai: And they show that incorporating a small and temperature-independent pair-breaking rate Γ ∼ zero point zero three six ∆zero leads to the correct description of the optical conductivity, which is what they need to capture that step <ref:2602.15003#pg5>.

Mira: So the improvement is explicitly modeling this in the dynamical conductivity using a model based on Herman and Hlubina five and Equation one <ref:2602.15003#pg5>.

Lev: From an error correction side, if you were trying to run this on real hardware, you'd have to deal with that smearing of the energy gap <ref:2602.15003#pg5>.

Kai: And they show that this modification leads to a "smearing of the energy gap together with the emergence of a distinct absorption step at ∆" <ref:2602.15003#pg5>. That's the key feature they are trying to model correctly.

Mira: So, for our theoretical approach, it means we have to account for this specific feature in the optical conductivity when making predictions <ref:2602.15003#pg5>.

Lev: It means that whatever you're doing, you can't just ignore the pair-breaking term because it shows up in your results <ref:2602.15003#pg5>.

Kai: And they also showed that frequency-domain spectroscopy confirms this in the same way, reproducing the temperature and frequency dependence of the modes <ref:2602.15003#pg5>.

Mira: That means we have a solid experimental benchmark to check our theoretical predictions against when we include these effects <ref:2602.15003#pg5>.

Lev: And if you're aiming for actual hardware, you need to know that the pair-breaking rate is basically constant, which is helpful for designing stable systems <ref:2602.15003#pg5>.

Kai: So the whole point is that this paper gives us a concrete way to model those tricky sub-gap features using the Dynes formalism <ref:2602.15003#pg5>.

Mira: It means we have a better tool to quantify these in-gap states in disordered superconductors like transition-metal nitrides or carbides <ref:2602.15003#pg5>.

Lev: And that's a useful piece of information for designing systems where you need to understand the constraints on those pair-breaking terms <ref:2602.15003#pg5>.

The paper's summary: Kai: So wrapping up the discussion on "Signatures of Dynes superconductivity in the THz response of ALD-grown NbN thin films," it seems like the main point is that we need to include the Dynes formalism when dealing with these types of superconductors <ref:2602.15003#pg5>.

Mira: They show that this formalism successfully reproduces the temperature and frequency dependence of the Fabry-P´erot transmission pattern observed in FDS <ref:2602.15003#pg5>.

Lev: And for us, it means we have a clear path forward for how to interpret these sub-gap features when they appear <ref:2602.15003#pg5>.

Kai: So essentially, the results indicate that Dynes scattering is relevant in the THz regime at zero magnetic field and reveals a constant Γ(T), which contrasts with previous tunneling and point-contact measurements <ref:2602.15003#pg5>.

Mira: This suggests that Dynes formalism might be the appropriate strategy to quantify sub-gap absorption that doesn't comply with Mattis-Bardeen predictions <ref:2602.15003#pg5>.

Lev: And for real hardware, it means we can build systems where we understand the constraints on those pair-breaking terms better <ref:2602.15003#pg5>.

Kai: We've seen some interesting physics here with this paper, and that's what we have for today <ref:2602.15003#pg1>.

The paper's improvements: Kai: So we just looked at how they found that the Dynes formalism helps us describe these sub-gap features in NbN films, and now we're going to talk about what this work suggests for improving other research <ref:2602.15003#pg5>.

Mira: They suggest that because conventional BCS electrodynamics just can't handle the THz data, you absolutely have to include that finite pair-breaking parameter Γ in your models <ref:2602.15003#pg5>.

Lev: From an engineering side, incorporating that requires you to model how the energy gap gets smeared out and how those absorption steps actually emerge when you try to run it on real hardware <ref:2602.15003#pg5>.

Kai: They show that this specific parameter, Γ ∼ zero point zero three six ∆zero is temperature-independent across both time-domain and frequency-domain measurements <ref:2602.15003#pg5>.

Mira: That constancy of the pair-breaking rate is pretty important because it gives us a solid experimental benchmark to check our theoretical predictions against when we include these effects <ref:2602.15003#pg5>.

Lev: If you're aiming for actual hardware, knowing that this rate doesn't change with temperature is helpful for designing stable systems <ref:2602.15003#pg5>.

Kai: So the whole point of their suggestion is that we have a better tool now to quantify those tricky sub-gap states in disordered superconductors like transition-metal nitrides or carbides <ref:2602.15003#pg5>.

Mira: That means for us, it’s a better way to model the dynamical conductivity when you're dealing with things that aren't perfectly clean systems <ref:2602.15003#pg5>.

Lev: And that moves the problem from just fitting data to actually understanding what microscopic processes are driving that constant rate of pair-breaking <ref:2602.15003#pg5>.

Kai: It’s definitely a useful piece of information for designing systems where you need to understand the constraints on those pair-breaking terms <ref:2602.15003#pg5>.

Mira: And we can use this approach to see if there are other similar signatures in different materials or regimes <ref:2602.15003#pg5>.

Lev: The next thing we need to figure out is where the limitations of this Dynes model lie when you try to push it into more complex superconducting scenarios <ref:2602.15003#pg5>.

Conclusion: Kai: So we're wrapping up on "Signatures of Dynes superconductivity in the THz response of ALD-grown NbN thin films," and the main thing is that we’ve shown how including that finite pair-breaking rate Γ helps us model those sub-gap features <ref:2602.15003#pg5>.

Mira: It means for condensed matter theory, we have a better tool now to quantify those in-gap states in disordered superconductors like transition-metal nitrides or carbides <ref:2602.15003#pg5>.

Lev: I think the fact that this rate is temperature-independent across both TDS and FDS measurements is pretty robust, which makes it a good piece of data to work with on real hardware <ref:2602.15003#pg5>.

Kai: Yeah, because if you're building error correction for something like NbN, knowing that the pair-breaking term doesn't drift with temperature simplifies things <ref:2602.15003#pg5>.

Mira: Exactly. It removes one layer of complexity from the fitting process when we try to determine the actual superconducting gap or ns zero <ref:2602.15003#pg5>.

Lev: And that constant rate means the overhead for modeling it in a real system stays predictable, which is crucial for error correction architecture design <ref:2602.15003#pg5>.

Kai: It’s definitely a useful piece of information for designing systems where you need to understand the constraints on those pair-breaking terms <ref:2602.15003#pg5>.

Mira: We can use this approach to see if there are other similar signatures in different materials or regimes where standard BCS theory falls short <ref:2602.15003#pg5>.

Lev: The next thing we need to figure out is where the limitations of this Dynes model lie when you try to push it into more complex superconducting scenarios <ref:2602.15003#pg5>.

Physikalisches Institut, Universität Stuttgart · Center for Integrated Quantum Science and Technology (IQST), Universität Stuttgart · Institute for Complex Quantum Systems and IQST, Universität Ulm · Leibniz Institute of Photonic Technology, Jena · Institute for Solid State Physics, Friedrich-Schiller Universität Jena

cond-mat.supr-con

Submitted: 2026-02-16

Updated: 2026-10-15

DOI: 10.1103/q3yw-r68s

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 83/100

The gist: The gist The study probes the terahertz response of superconducting NbN thin films using atomic layer deposition to find signatures of Dynes superconductivity in their optical conductivity, which

Key concepts

Optical Conductivity
This measures how much light (electromagnetic radiation) can be absorbed by a material at different frequencies. In superconductors, it reveals properties like the energy gap and superfluid density, which are crucial for understanding their behavior in the THz range.
BCS Theory
Bardeen-Cooper-Schrieffer theory is the standard model used to describe conventional superconductivity. The paper shows that this model fails to fully explain the observed absorption features in these disordered NbN films, necessitating a more complex approach.
Dynes Electrodynamics
This is a phenomenological model used to describe superconductors with disorder, introducing an extra pair-breaking rate ($\Gamma$). This modification allows the theory to accurately capture sub-gap absorption features, such as the characteristic step observed at half the energy gap.

Terminology

Summary

The gist The study probes the terahertz response of superconducting NbN thin films using atomic layer deposition to find signatures of Dynes superconductivity in their optical conductivity, which reveals an absorption step at half the zero-temperature spectral gap.

Experimental Setup and Material Properties

NbN films with thicknesses ranging from 4.5 to 20 nm were deposited on sapphire using atomic layer deposition (ALD) <ref:2602.15003#pg2> The frequency range studied was from 0.3 to 2.1 THz <ref:2602.15003#pg2>. Transport measurements revealed critical temperatures ranging from 8.5 to 13.3 K, with the normal-state resistivity increasing and the critical temperature being suppressed with decreasing film thickness <ref:2602.15003#pg3>. Table I summarizes characteristic material properties such as thickness, sheet resistance Rs DC, and spectral gap 2∆0 for five samples <ref:2602.15003#pg4>.

Signatures of Dynes Superconductivity in Optical Conductivity

The complex optical conductivity of the 20 nm NbN film showed a step-like characteristic in the absorption at ∆0, i.e. half the zero-temperature spectral gap <ref:2602.15003#pg5>. This feature was fully captured by Dynes electrodynamics with a small and temperature-independent pair-breaking rate Γ ∼ 0.036 ∆0 <ref:2602.15003#pg5>. The inset in Figure 2(b) showed that in the Dynes case (here: Γ = 0.1∆), excitations at lower energies are possible, and the transitions indicated by light blue arrows, with hf = ∆, lead to the step near ∆ in σ1(f) <ref:2602.15003#pg5>.

Modeling and Validation of Dynes Formalism

The Zimmermann fit did not fully describe the data for the lowest temperature T = 3.1 K, leading researchers to use a model based on Herman and Hlubina [5] and Equation 1 <ref:2602.15003#pg5>. This modification leads to a smearing of the energy gap together with the emergence of a distinct absorption step at ∆ <ref:2602.15003#pg5>. A two-parametric fit for all temperatures allowed them to obtain the temperature-dependent energy gap ∆(T) and the pair-breaking rate Γ(T), which was found to be basically constant Γ = 0.036 ∆0 <ref:2602.15003#pg5>. This model achieved a near-perfect description of the dynamical conductivity in Figure 2, capturing the steplike feature observed at 3.1 K <ref:2602.15003#pg5>.

Frequency-Domain Spectroscopy (FDS) Confirmation

Frequency-domain spectroscopy (FDS) studies confirmed the in-gap absorption seen previously in TDS, showing a very convincing match between theory and experiment, fully reproducing the temperature and frequency dependence of the modes <ref:2602.15003#pg5>. The magnitude of the pair-breaking rate determined from this FDS investigation was found to be Γ = 0.036 ∆0, which matches TDS on the same film <ref:2602.15003#pg5>. This result confirms the temperature-independence of the pair-breaking rate <ref:2602.15003#pg5>.

Superconducting Properties and Microscopic Origin

The analysis of optical conductivity allowed for the calculation of superfluid density ns = 2πm∗e2 lim f→0 fσ2(f) <ref:2602.15003#pg5>. The gap ratio 2∆0/(kBTc) for thicker films was significantly higher (≈ 4.0) than the weak coupling limit of 3.528, indicating strong electron-phonon coupling <ref:2602.15003#pg5>. The discussion suggests that magnetic scattering at a localized impurity can lead to an in-gap density of states consistent with the Dynes formula <ref:2602.15003#pg5>. Furthermore, the paper concludes that the pair-breaking rate remains small in its magnitude (only few percent of the energy gap) and does not show a systematic dependence on film thickness <ref:2602.15003#pg5>.

Conclusion on Dynes Relevance

Conventional BCS electrodynamics cannot describe the THz data, whereas inclusion of a finite Dynes pair-breaking parameter Γ leads to excellent agreement <ref:2602.15003#pg5>. The results indicate that Dynes scattering is relevant in the THz regime at zero magnetic field, revealing a constant Γ(T), in contrast to previous tunneling and point-contact measurements <ref:2602.15003#pg5>. This suggests that the Dynes formalism might be the appropriate strategy to quantify sub-gap absorption that does not comply with Mattis-Bardeen predictions <ref:2602.15003#pg5>.

How it works

The key mechanism involves modifying the single-particle density of states (DOS) using the phenomenological Dynes formula, which introduces a phenomenological scattering rate Γ that quantifies additional pair-breaking mechanisms <ref:2602.15003#pg2>. This modification to the DOS has direct consequences for the dynamical conductivity [5] <ref:2602.15003#pg2>.

The Dynes model is used to describe the in-gap states observed experimentally, where N(E) = N0 Re (E + iΓq (E + iΓ)2 − ∆2) <ref:2602.15003#pg2>. This modification leads to a characteristic step-like absorption feature at half of the spectral gap ∆ <ref:2602.15003#pg2>.

Key Findings Enumerated

  1. Distinct deviations from the BCS model were observed in the 20 nm NbN film, including a step-like characteristic in absorption at ∆0 <ref:2602.15003#pg5>.

  2. The observations for other films also showed signs of Dynes electrodynamics, allowing discussion of the evolution of 2∆0, ns 0, and Γ as function of film thickness <ref:2602.15003#pg5>.

  3. The pair-breaking rate was found to be temperature-independent across both TDS and FDS measurements, with a value of Γ = 0.036 ∆0 <ref:2602.15003#pg5>.

  4. The Dynes formalism successfully reproduced the temperature and frequency dependence of the Fabry-P´erot (FP) transmission pattern observed in FDS <ref:2602.15003#pg5>.

  5. The study concluded that Dynes scattering is relevant in the THz regime at zero magnetic field, revealing a constant Γ(T) <ref:2602.15003#pg5>.

Summary of Superconducting Properties

The temperature dependence of the energy gap was modeled using a BCS approximation ∆(T) = ∆(0) tanh(1.74pTc/T − 1) <ref:2602.15003#pg5>. The superfluid density ns(T) was modeled using the procedure described in [31] <ref:2602.15003#pg5>. The suppression of superconducting properties due to increased electron-electron repulsion was noted as disorder increased <ref:2602.15003#pg5>. This suggests that the suppression of superconductivity within the disorder regime is mainly governed by electronic interactions <ref:2602.15003#pg5>.

The paper demonstrates that Dynes formalism is a relevant strategy to quantify sub-gap absorption in disordered superconductors like transition-metal nitrides or carbides <ref:2602.15003#pg5>. This work confirms the necessity of describing the dynamical conductivity of NbN film using the Dynes formalism <ref:2602.15003#pg5>. The results indicate that microscopic processes underlying the Dynes scattering parameter Γ are more complex than previously thought <ref:2602.15003#pg5>.

The research is supported by funding from the Carl-ZeissStiftung as part of CZS Center QPhoton and by the German Federal Ministry of Research, Technology and Space (BMFTR) within project QSolid <ref:2602.15003#pg5>. The acknowledgments include M. Ziegler for supporting the sample growth <ref:2602.15003#pg5>.

The paper is published on arXiv as 2602.15003v1 <ref:2602.15003#pg5>. The work is presented by Frederik Bolle, Yayi Lin, Ozan Saritas, Martin Dressel, Ciprian Padurariu, Sahitya Varma Vegesna, Nitesh Yerra, Heidemarie Kr¨uger and Marc Scheffler <ref:2602.15003#pg5>. The research is supported by the German Federal Ministry of Research, Technology and Space (BMFTR)

Improvements for AI systems

  1. In-gap State Modeling for Disordered Superconductors: The improved AI system can accurately model deviations in the observed DOS typically require modelling by the phenomenological Dynes formula by incorporating a small and temperature-independent pair-breaking rate Γ ∼ 0.036 ∆0 into its predictions for optical conductivity, moving beyond standard BCS theory.

  2. THz Spectroscopy Data Interpretation: The system can now perform direct validation of theoretical models by matching experimental data, specifically reproducing the steplike feature observed at 3.1 K in the real part of the optical conductivity using the model for the optical conductivity of superconductors with pair-breaking processes as described by Herman and Hlubina [5] and based on the Dynes DOS.

  3. Temperature-Independent Parameter Extraction: The AI can reliably extract fundamental material parameters, such as a temperature-independent pair-breaking rate Γ = 0.036 ∆0, from both time-domain spectroscopy (TDS) and frequency-domain spectroscopy (FDS) measurements, providing a robust measure of the underlying microscopic physics.

  4. Superfluid Density Calculation: The improved system can calculate the superfluid density ns(T) using the Kramers-Kronig relations, relating it to the imaginary part of the optical conductivity as defined by ns = 2πm∗ e2 lim f→0 fσ2(f).

  5. Phase Diagram Analysis for Disorder: The AI can analyze the complex phase diagram of NbN films, distinguishing between different regimes—such as the intermediate disorder regime governed by the suppression of the superfluid stiffness J—to predict when superconductivity is suppressed due to electronic interactions versus other mechanisms.

Abstract

The frequency-dependent complex optical conductivity reflects key properties of superconductors, such as the energy gap in the density of states (DOS) and the superfluid density. For disordered superconductors, the optical conductivity often can be described within Bardeen-Cooper-Schrieffer (BCS) theory, while in corresponding tunneling experiments, deviations in the observed DOS typically require modelling by the phenomenological Dynes formula. The implications of such Dynes DOS for optics were rarely discussed so far. Here we probe the terahertz conductivity of superconducting NbN thin films with thicknesses ranging from 4.5 to 20nm, which were grown by atomic layer deposition (ALD). Our frequency range from 0.3 to 2.1 THz covers energies below and above the spectral gap. For 20nm thick NbN, we find in the optical conductivity distinct deviations from the BCS model, including a step-like characteristic in the absorption at half the zero-temperature spectral gap. These observations can be fully captured by Dynes electrodynamics with a small and temperature-independent pair-breaking rate. For the other films, we also observe signs of Dynes electrodynamics, and we discuss the evolution of the energy gap, the superfluid density, and the pair-breaking rate as function of film thickness.

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