Terahertz Conductivity Models Density of States above 0.3THz

Scientists investigate the optical properties of superconducting materials to understand fundamental characteristics like energy gaps and superfluid density. Frederik Bolle, Yayi Lin, and Ozan Saritas, working at the 11. Physikalisches Institut, Universität Stuttgart, in collaboration with Ciprian Padurariu and colleagues at the Institute for Complex Quantum Systems and IQST, Universität Ulm, and Sahitya Varma Vegesna, Nitesh Yerra, and Heidemarie Krüger at the Leibniz Institute of Photonic Technology, have explored the terahertz conductivity of niobium nitride (NbN) thin films grown using atomic layer deposition. This research is significant because it connects observations from tunneling experiments, which often require the Dynes formula to model deviations in the density of states, with optical conductivity measurements, revealing distinct Dynes-like behaviour in the films’ response and providing insights into the evolution of the superconducting gap and pair-breaking rate with varying film thickness, alongside contributions from Marc Scheffler from both the 11. Physikalisches Institut, Universität Stuttgart, and the Center for Integrated Quantum Science and Technology (IQST), Universität Stuttgart.

Scientists are edging closer to fully understanding superconductivity, a phenomenon with the potential to revolutionise energy transmission and computing. New work examining ultra-thin films reveals subtle but significant deviations from established theory, hinting at previously unobserved mechanisms at play within these materials. These findings could unlock pathways to more efficient and robust superconducting devices.

Recent work focusing on niobium nitride (NbN) thin films, created using a precise atomic layer deposition technique, reveals deviations from conventional superconductivity theory. These findings centre on the terahertz conductivity, how efficiently these films transmit energy at frequencies between 0.3 and 2.1THz, and demonstrate a step-like absorption feature not predicted by the standard Bardeen-Cooper-Schrieffer (BCS) model.

The BCS theory describes how electrons pair up to form a superconducting state, but struggles to fully explain behaviour in disordered or ultra-thin materials. Researchers probed the electrical response of NbN films with varying thicknesses, ranging from 4.5 to 20 nanometres, at extremely low temperatures. The study highlights that the observed conductivity deviates from the predictions of the BCS model, particularly in the 20nm thick film.

This deviation manifests as a distinct, step-like increase in absorption at half the energy gap, a crucial parameter defining the superconducting state, suggesting the presence of additional factors influencing electron behaviour. These observations are fully explained by employing the Dynes model, a phenomenological approach that accounts for pair-breaking mechanisms within the superconductor.

The team’s analysis indicates a small, temperature-independent rate at which these Cooper pairs are broken, approximately 0.036times the zero-temperature energy gap. This suggests that imperfections or disorder within the NbN films are playing a role in disrupting the perfect superconducting state. Furthermore, the research demonstrates that the energy gap, superfluid density, and the pair-breaking rate all evolve predictably as the film thickness changes. This work provides direct optical evidence supporting the Dynes model and opens new avenues for tailoring the properties of superconducting thin films for advanced technological applications.

Superconducting properties and spectral gap analysis of niobium nitride thin films

Critical temperatures ranging from 8.5 to 13.3 K were observed in five NbN thin films during transport measurements. Normal-state resistivity increased and critical temperature decreased with decreasing film thickness, alongside an increase in the width of the superconducting transition. The complex optical conductivity of a 20nm NbN film, measured using terahertz time-domain spectroscopy, exhibited a frequency-independent real part of 4460 Ω−1cm−1 above 13.3 K, consistent with Drude-type scattering.

Below the critical temperature, low-frequency σ1 was significantly suppressed, indicating Cooper pair formation and defining a spectral gap. A distinct step-like characteristic in the absorption spectrum was identified at half the zero-temperature spectral gap for the 20nm film. This deviation from the standard Bardeen-Cooper-Schrieffer (BCS) model is fully captured by employing a Dynes electrodynamics model with a temperature-independent pair-breaking rate of 0.036∆0.

The spectral gap, 2∆0, varied between 0.605THz for the 4.5nm film and 1.124THz for the 10nm film, while the coupling ratio 2∆0/(kBTc,DC) ranged from 2.50 to 4.65. Superfluid density, ns,0, was determined to be between 3.04x 1025m−3 and 16.87x 1025m−3, and the London penetration depth, λL,0, ranged from 848nm to 493nm. Sheet kinetic inductance, L□ kin,0, varied from 259 pH/sq for the 4.5nm film to 10.5 pH/sq for the 20nm film, and the pair-breaking rate, Γ/∆0, was found to be between 0.017 and 0.036. The observation of an absorption onset at half the spectral gap in the 20nm film confirms the presence of Dynes superconductivity, characterised by a smearing of the energy gap and additional absorption mechanisms.

Niobium nitride film characterisation using terahertz time and frequency domain spectroscopy

Terahertz spectroscopy underpinned this work, employing both time-domain and frequency-domain techniques to probe the complex optical conductivity of niobium nitride films. Films of varying thicknesses, ranging from 4.5 to 20 nanometres, were grown via atomic layer deposition on R-plane sapphire substrates measuring 10 × 10 millimetres and 530 micrometres thick.

This deposition method ensures precise control over film stoichiometry and uniformity, critical for reliable optical measurements. Initial characterisation involved van der Pauw measurements, a standard four-point probe technique used to determine the transition temperature and normal-state resistivity of each film. Frequency-domain spectroscopy utilised backward wave oscillators to generate monochromatic terahertz radiation, subsequently transmitted through the samples and detected by a Golay cell or a helium-cooled bolometer.

This transmission geometry allows for direct measurement of the complex conductivity as a function of frequency and temperature. The frequency range, spanning 0.3 to 2.1 terahertz, was strategically chosen to encompass energies both below and above the superconducting spectral gap, enabling detailed investigation of the electronic structure. To complement the frequency-domain data, a commercial terahertz time-domain spectrometer was also employed.

This technique generates broadband terahertz pulses, providing a comprehensive view of the material’s optical response. By analysing the transmitted pulses, the real and imaginary components of the complex conductivity were extracted. The use of both frequency-domain and time-domain spectroscopy provides a robust and cross-validated dataset, enhancing the reliability of the findings and allowing for a more complete understanding of the superconducting behaviour.

Terahertz conductivity reveals nanoscale disorder in niobium nitride superconductors

Scientists have long sought to understand the subtle imperfections within superconducting materials, and how these flaws impact their ability to conduct electricity with zero resistance. This work offers a crucial link between microscopic disorder and the macroscopic optical properties of thin films of niobium nitride. For years, the standard Bardeen-Cooper-Schrieffer (BCS) theory has provided a solid foundation, but it often fails to fully explain experimental observations, necessitating the use of more complex, phenomenological models like the Dynes formula.

What distinguishes this research is the direct observation of features predicted by the Dynes formula in the terahertz conductivity of these films. The team’s ability to correlate film thickness with the emergence of these characteristics is particularly compelling, suggesting a systematic relationship between nanoscale structure and superconducting behaviour.

This is not merely an academic exercise; understanding these effects is vital for optimising materials used in sensitive detectors and potentially, future quantum technologies. However, the precise nature of the disorder remains somewhat elusive. While the Dynes formula provides a good fit to the data, it doesn’t reveal the underlying cause of the pair-breaking.

Is it due to impurities, structural defects, or inherent fluctuations within the material itself. Future work should focus on directly imaging these imperfections to establish a clearer connection. Moreover, extending these measurements to other superconducting materials and exploring the impact of different fabrication techniques will be essential to determine the generality of these findings and unlock the full potential of tailored superconducting films.