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arXiv:2607.20096

Power-Law Suppression of Superfluid Stiffness in High-Kinetic-Inductance NbN Films

Meenakshi Sharma, Hrishikesh Borah, Sandeep Singh, Berit Hansen Goodge, Edouard Lesne, Sandra Nestler, S. Singh, Haolin Jin, Yejin Lee, Bernd Büchner, Uri Vool

Published Jul 22, 2026• 0 citations
arXivHTMLPDF

Abstract

Disorder is a powerful route to high kinetic inductance in superconducting ultrathin films, enabling compact high-impedance quantum circuits. This functionality, however, comes at the cost of reduced phase rigidity and potentially anomalous electrodynamics. Here, we use NbN microwave resonators with thicknesses down to 2.8 nm and sheet kinetic inductance up to 300 pH per square to probe how this trade-off reshapes the superconducting response. In the thinnest films, transport shows signatures of a Berezinskii-Kosterlitz-Thouless transition, while the microwave response reveals a pronounced low-temperature power-law suppression of the superfluid stiffness, inconsistent with Mattis-Bardeen theory. With increasing thickness, this anomalous regime is progressively suppressed, marking a continuous crossover toward conventional, gap-dominated electrodynamics. Cross-sectional transmission electron microscopy reveals a nanocrystalline twin-domain structure, pointing to oriented microstructural disorder as a crucial factor in the observed response. Overall, the crossover is governed by the ratio of superfluid stiffness to pairing energy, Theta(0)/Tc, identifying this ratio as a parameter governing the boundary between phase-fluctuation-dominated and gap-dominated superconducting electrodynamics in disordered nanofilms.

DOI
10.48550/arxiv.2607.20096

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Applied Physics Letters•Aug 1, 2022•19 citations
Disorder is a powerful route to high kinetic inductance in superconducting ultrathin films, enabling compact high-impedance quantum circuits. This functionality, however, comes at the cost of reduced phase rigidity and potentially anomalous electrodynamics. Here, we use NbN microwave resonators with thicknesses down to 2.8 nm and sheet kinetic inductance up to 300 pH per square to probe how this trade-off reshapes the superconducting response. In the thinnest films, transport shows signatures of a Berezinskii-Kosterlitz-Thouless transition, while the microwave response reveals a pronounced low-temperature power-law suppression of the superfluid stiffness, inconsistent with Mattis-Bardeen theory. With increasing thickness, this anomalous regime is progressively suppressed, marking a continuous crossover toward conventional, gap-dominated electrodynamics. Cross-sectional transmission electron microscopy reveals a nanocrystalline twin-domain structure, pointing to oriented microstructural disorder as a crucial factor in the observed response. Overall, the crossover is governed by the ratio of superfluid stiffness to pairing energy, Theta(0)/Tc, identifying this ratio as a parameter governing the boundary between phase-fluctuation-dominated and gap-dominated superconducting electrodynamics in disordered nanofilms.
In this thesis, we first demonstrate that a disordered superconductor with high kinetic inductance can realise a microwave low-loss, non-dissipative circuit element with impedance greater than the quantum resistance. This element, known as a superinductor, can suppress the fluctuations of charge in a quantum circuit.For this purpose, we fabricated and characterised 20 nm thick, 40 nm wide niobium-nitride nanowires and determined the impedance to 6.795 kΩ. We demonstrate internal quality factors Qi = 2.5e4 in nanowire resonators at single photon excitation, which is significantly higher than values reported in devices with similar materials and geometries. Moreover, we show that the dominant dissipation in our nanowires is not an intrinsic property of the disordered films, but can instead be fully understood within the framework of two-level systems.To further characterise these losses, we then explore the geometrical scaling, toward nanowire dimensions, of dielectric losses in superconducting microwave resonators fabricated with the same techniques and from the same NbN thin-film as the nanowire superinductors. For this purpose, we perform an experimental and numerical study of dielectric loss at low temperatures. Using 3D finite-element simulation of the Maxwell--London equations, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. Finally, we study the effect of two-level systems on the performance of various superconducting quantum circuits. For this purpose, we measure coherence-time fluctuations in qubits and frequency fluctuations in resonators. In all devices, through statistical analysis, we identify the signature of individual Lorentzian fluctuators in the noise. We find that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems. Furthermore, when examining the low-frequency noise of three different types of superconducting resonator - one NbN nanowire, one Al coplanar waveguide, and one Al 3D cavity - we observe a similar power-law dependence of the Lorentzian switching time and amplitude on the circulating power in the resonators, suggesting a common noise mechanism in the three different types of devices.
We have measured the rf impedance of 10-nm thick superconducting granular NbN meander lines between 5 /spl mu/m and 20 /spl mu/m wide. The complex reflection coefficient was obtained directly using a vector network analyzer. The impedance (at 10 MHz for a 5 /spl mu/m wide line) is dominated by the large kinetic Inductance of the film, with a sheet inductance of order 1 nH, giving a total inductance of 400 nH for a 5 /spl mu/m/spl times/2 mm line. The kinetic inductance diverges as T/spl rarr/T/sub c/=6.5 K, as expected from Ginzburg-Landau theory (GL). Of particular interest is a substantial decrease of measured inductance with increasing dc current, contrary to the dependence expected from GL. This anomalous current dependence is not well understood, but may be related to vortex dynamics and Josephson effects in these granular films, as supported by preliminary Josephson array simulations. These results have important implications for potential devices such as tunable rf phase shifters and kinetic inductance photodetectors.
Abstract Superconducting microwave metamaterials offer enormous potential for quantum optics and information science, enabling the development of advanced quantum technologies for sensing and amplification. In the context of circuit quantum electrodynamics, such metamaterials can be implemented as coupled cavity arrays (CCAs). In the continuous effort to miniaturize quantum devices for increasing scalability, minimizing the footprint of CCAs while preserving low disorder becomes paramount. In this work, we present a compact CCA architecture using superconducting NbN thin films manifesting high kinetic inductance. The latter enables high-impedance CCA (~1.5 kΩ), while reducing the resonator footprint. We demonstrate its versatility and scalability by engineering one-dimensional CCAs with up to 100 resonators and with structures that exhibit multiple bandgaps. Additionally, we quantitatively investigate disorder in the CCAs using symmetry-protected topological SSH edge modes, from which we extract a resonator frequency scattering of 0.22−0.03+0.04%0.2{2}_{-0.03}^{+0.04}\%0.22−0.03+0.04​% 0.2 2 − 0.03 + 0.04 % . Our platform opens up exciting prospects for analog quantum simulations of many-body physics with ultrastrongly coupled emitters.
Coupling quantum materials to electromagnetic cavities or resonators without external driving has gained prominence as a new control mechanism. Here we develop an equilibrium theory of a mesoscopic, disordered two-dimensional superconductor coupled to a subwavelength terahertz resonator, focusing on the interplay between superconducting phase fluctuations in the sample and electromagnetic fluctuations of the resonator. Modeling the resonator as a lumped-element circuit, we show that the coupling enhances, rather than suppresses, the superconducting transition temperature TcT_cTc​. When the sample is smaller than the Pearl length, phase fluctuations near the Berezinskii--Kosterlitz--Thouless (BKT) transition strongly amplify this enhancement. Crucially, the resistive quasiparticle response of the sample must be included in the analysis: at low frequencies the superfluid shunts the normal-fluid channel, reducing the total sample impedance. For representative parameters, a 1 μm×1 μm1 \,μ\mathrm{m} \times 1 \,μ\mathrm{m}1μm×1μm, $8 $nm-thick disordered film, we find a relative TcT_cTc​ enhancement of about 1%1\%1%, an order of magnitude larger than the $0.1\% $ obtained when phase fluctuations are neglected. These results identify superconductors with soft phase fluctuations as promising platforms for equilibrium control with terahertz resonators.
Disordered superconducting materials with high kinetic inductance are an important resource for generating nonlinearity in quantum circuits and creating high-impedance environments. In thin films fabricated from these materials, the combination of disorder and low effective dimensionality leads to increased order parameter fluctuations and enhanced kinetic inductance values. Among the challenges of harnessing these compounds in coherent devices are their proximity to the superconductor-insulator phase transition and the two-level systems located in the disordered structure. Here, we fabricate tungsten silicide wires from quasi-two-dimensional films and embed them into microwave resonators and fluxonium qubits, where the kinetic inductance provides the inductive part of the circuits. In this work, we study the dependence of loss on the frequency, disorder, and geometry of the devices, and find that the loss increases with the level of disorder and is dominated by the localized quasiparticles trapped in the spatial variations of the superconducting gap. High kinetic inductance materials are widely used in superconducting circuits, yet their loss mechanisms are not fully understood. Here the authors study quantum circuits incorporating nanowires made of quasi-2D disordered superconductor WSi and identify localized quasiparticles as the dominant source of loss.
We examine the DC and radio frequency (RF) response of superconducting transmission line resonators comprised of very thin NbTiN films, <12 nm in thickness, in the high-temperature limit, where the photon energy is less than the thermal energy. The resonant frequencies of these superconducting resonators show a significant nonlinear response as a function of RF input power, which can approach a frequency shift of Δf=−0.15% in a −20 dB span in the thinnest film. The strong nonlinear response allows these very thin film resonators to serve as high kinetic inductance parametric amplifiers.