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Signatures of Dynes density of states in the terahertz response of atomic layer deposition grown superconducting NbN thin films

Frederik Bolle1, Yayi Lin1, Ozan Saritas1, Martin Dressel1,2, Ciprian Padurariu3, Sahitya Varma Vegesna4,5, Nitesh Yerra4, Heidemarie Krüger4,5, and Marc Scheffler1,2

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Phys. Rev. B 114, 144505 – Published 9 September, 2026

DOI: https://doi.org/10.1103/q3yw-r68s

Abstract

The frequency-dependent complex optical conductivity σ̂(f) reflects key properties of superconductors, such as the energy gap 2Δ in the density of states (DOS) and the superfluid density ns. For disordered superconductors, σ̂(f) often can be described within Bardeen-Cooper-Schrieffer (BCS) theory, while in corresponding tunneling experiments, deviations in the observed DOS typically require modeling by the phenomenological Dynes formula. The implications of such Dynes DOS for optics have been rarely discussed so far. Here we probe the terahertz σ̂(f) of superconducting NbN thin films with thicknesses ranging from 4.5 to 20 nm, which were grown by atomic layer deposition. Our frequency range from 0.3 to 2.1 THz covers energies below and above 2Δ. For 20-nm-thick NbN, we find in σ̂(f) distinct deviations from the BCS model, including a steplike characteristic in the absorption at Δ0, i.e., half the zero-temperature spectral gap. These observations can be fully captured by introducing a small and temperature-independent Dynes pair-breaking rate Γ∼0.036Δ0. For the other films, we also observe signs of Dynes-type DOS and we discuss the evolution of 2Δ0, ns,0, and Γ as a function of film thickness.

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Phys. Rev. B 114, 144505– Published 9 September, 2026
  • Received 20 February 2026
  • Revised 24 June 2026
  • Accepted 17 July 2026
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