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Physical review. B./Physical review. B

Effect of temperature oscillations on kinetic inductance and depairing in thin and narrow superconducting nanowire resonators

Jason P. Allmaras, Alexander G. Kozorezov, Marco Colangelo, Boris A. Korzh, Matthew D. Shaw, Karl K. Berggren

Published Mar 30, 2023• 2 citations
Publisher

Abstract

Recent experiments have demonstrated a method for extracting the depairing current of nanowires fabricated from thin-film dirty superconductors using the AC response of DC-current biased resonators. While the existing theoretical model for understanding this response, developed by Clem and Kogan, provides agreement with Eilenberger-Usadel theory at low temperatures, there is a systematic and substantial deviation from theory at elevated temperatures. We propose that the DC bias in the presence of electromagnetic oscillations leads to Joule heating in the superconductor. This heating, combined with the strong electron-electron scattering in these heavily disordered materials, leads to oscillations in the effective temperature of the superconductor which alter the kinetic inductance. In this work, we derive the expression for the shift in kinetic inductance in the presence of a bias current and demonstrate that this model provides a significantly improved agreement between experiment and theory.

DOI
10.1103/physrevb.107.104520

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Recent experiments have demonstrated a method for extracting the depairing current of nanowires fabricated from thin-film dirty superconductors using the AC response of DC-current biased resonators. While the existing theoretical model for understanding this response, developed by Clem and Kogan, provides agreement with Eilenberger-Usadel theory at low temperatures, there is a systematic and substantial deviation from theory at elevated temperatures. We propose that the DC bias in the presence of electromagnetic oscillations leads to Joule heating in the superconductor. This heating, combined with the strong electron-electron scattering in these heavily disordered materials, leads to oscillations in the effective temperature of the superconductor which alter the kinetic inductance. In this work, we derive the expression for the shift in kinetic inductance in the presence of a bias current and demonstrate that this model provides a significantly improved agreement between experiment and theory.
This work presents a method to estimate experimentally the superconducting depairing current of ultrathin films by means of nanowire-style resonators. Measuring the depairing current allows for a better determination of the figure of merit for the quality of superconducting nanowires. The resonance is set by impedance mismatch between the nanowire and the transmission line. Bias current dependent shifts in the measured resonant frequency correspond to the change in the kinetic inductance, which can be compared with theoretical predictions to estimate the resonator superconducting depairing current. The experiments lead to an unexpected and original result - a decrease of the switching-to-depairing current ratio with increasing temperature.
Superconducting nanowire single-photon detectors are central to applications across quantum information science. Yet, their performance is limited by the effects of disorder and electrodynamic inhomogeneities that are not well understood. By combining DC transport, dark-count measurements, and bias-dependent microwave transmission spectroscopy in the presence of controlled nanoscale disorder introduced through helium-ion irradiation, we distinguish local instability-driven processes from intrinsic superconducting depairing and kinetic inductance nonlinearities. This approach enables systematic tuning of kinetic inductance, depairing currents, microwave dissipation, and mode structure within a single device. Bias- and temperature-dependent resonance shifts quantify disorder-induced modifications of the superconducting density of states through the nonlinear kinetic inductance, while the emergence of multiple resonant modes reveals the formation of electrodynamically distinct superconducting regions. Comparing depairing under current, field, and temperature isolates the dominant microwave loss mechanisms, separating vortex, quasiparticle, and two-level-system contributions, thus providing a robust multifunctional foundation for disorder engineering of superconducting nanowire detectors and resonators.
Inductance plays a crucial role in the design and optimization of superconducting quantum interference devices (SQUIDs) for quantum sensing applications, since it dictates the sensitivity and coupling ratio with other circuit elements. In high-temperature superconductors the kinetic inductance, which depends on both geometry and temperature, becomes a dominant part of the device's total self-inductance, since their London penetration depth is considerably larger compared to low-temperature superconductors. In this work, we use an asymmetric SQUID to investigate the kinetic self-inductance ratio and voltage modulation depth at different operating temperatures, device geometries and bias currents. We first validate our approach by comparing our modelled data with experimental measurements. Then, through numerical simulations, we show: (i) kinetic inductance dominates for thin superconducting films, while for thicker films the inductance is less sensitive to temperature changes; (ii) the voltage modulation depth decreases exponentially with the total inductance independent of the asymmetry ratio; (iii) narrower superconducting tracks lead to a broader temperature operation range, ΔT∼30KΔT \sim 30 KΔT∼30K, while wider tracks operate in a smaller temperature range, ΔT∼10KΔT \sim 10 KΔT∼10K, but are more sensitive to temperature changes; and (iv) the device performance versus temperature strongly depends on the bias current used.
Superconducting planar resonators of thin molybdenum carbide (MoC) films were fabricated by optical lithography. The films were deposited via reactive magnetron sputtering and by changing the deposition parameters, the sheet resistance of the films was varied. The microwave properties of the resonators were studied by broadband coplanar waveguide spectroscopy in flip-chip configuration. The kinetic inductance of MoC films governs the high frequency response of the resonators and is determined by the complex conductivity of the superconducting film. Well below the critical temperature of transition, kinetic inductance is proportional to film sheet resistance in normal state. The temperature-dependent resonances in the broadband spectra below critical temperature are described by a lumped LC model, where the inductance consists of geometric and kinetic inductance of the resonator. The temperature and frequency dependent complex conductivity of the superconducting film is calculated by the Dynes model for dirty superconductors. Furthermore, a numerical model of the kinetic planar resonator in Sonnet software is presented, which can be utilized to design resonators with desired properties, based on highly disordered superconductors. An on-chip design of a kinetic planar resonator filter is presented. The high kinetic inductance of the superconducting films allows us to minimize microwave filter dimensions.
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.
Superconducting boron-doped silicon is a promising material for integrated silicon quantum devices. In particular, its low electronic density and moderate disorder make it a suitable candidate for the fabrication of large inductances with low losses at microwave frequencies. We study experimentally the electrodynamics of superconducting silicon thin layers using coplanar waveguide resonators, focusing on the kinetic inductance, the internal losses, and the variation of these quantities with the resonator readout power. We report the observation in a doped semiconductor of microwave resonances with internal quality factors of a few thousand. As expected in the BCS framework, superconducting silicon presents a large sheet kinetic inductance in the 50--500-pH range, comparable to that of strongly disordered superconductors. The temperature dependence of the kinetic inductance is well described by the Mattis-Bardeen theory. However, we find an unexpectedly strong nonlinearity in the complex surface impedance that cannot be satisfactorily explained either by depairing or by quasiparticle heating.