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arXiv:2610.05903

Giant nonlinearity of kinetic inductance in superconducting hybrid strip

Denis Yu. Vodolazov, Yu. P. Korneeva, Mikhail Dryazgov, S. S. Ustavschikov, N. V. Porokhov, N. N. Osipov, Igor Yu. Pashen’kin, Alexander A. Korneev, Michael A. Tarkhov

Published Oct 5, 2026• 0 citations
arXivHTMLPDF

Abstract

We demonstrate giant nonlinearity of the kinetic inductance $L_k$ in a superconducting NbN/Al hybrid strip. In contrast to ordinary superconductors, where the maximum observed current-induced variation of $L_k$ does not exceed tens of percent, we observe a 50-fold change in $L_k$. Physically, this effect is connected with the proximity-induced superconductivity in the Al layer and the specific choice of parameters for which the dependence of the superconducting current $I$ on the Cooper pair momentum $\hbar q$ exhibits a plateau at a current $I^*$ {\it well below} the depairing current. Formally, this leads to $L_k \sim dq/dI \to \infty$ as $I \to I^*$. We believe that our results open a new route for creating the next generation of highly sensitive detectors of electromagnetic radiation, calorimeters, parametric amplifiers, and magnetometers.

DOI
10.48550/arxiv.2610.05903

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We describe a novel class of devices based on the nonlinearity of the kinetic inductance of a superconducting thin film. By placing a current-dependent inductance in a microwave resonator, small currents can be measured through their effect on the resonator’s frequency. By using a high-resistivity material for the film and nanowires as kinetic inductors, we can achieve a large coefficient of nonlinearity to improve device sensitivity. We demonstrate a current sensitivity of 8 pA/√Hz, making this device useful for transition-edge sensor (TES) readout and other cutting-edge applications. An advantage of these devices is their natural ability to be multiplexed in the frequency domain, enabling large detector arrays for TES-based instruments. A traveling-wave version of the device, consisting of a thin-film microwave transmission line, is also sensitive to small currents as they change the phase length of the line due to their effect on its inductance. We demonstrate a current sensitivity of 5 pA/√Hz for this version of the device, making it also suitable for TES readout as well as other current-detection applications. It has the advantage of multi-gigahertz bandwidth and greater dynamic range, offering a different approach to the resonator version of the device. Finally, we also demonstrate a transmission-line resonator version of the device that combines some of the advantages of the nanowire resonator and the traveling-wave device. This version of the device has high dynamic range but can also be easily multiplexed in the frequency domain. A lumped-element resonator similar to the first device can be placed in a loop configuration to make it sensitive to magnetic fields. We demonstrate an example of such a device whose sensitivity could ultimately reach levels similar to those of state-of-the-art DC SQUIDs, making it potentially useful for many magnetometry applications given its ease of multiplexing. Finally, a similar microwave resonator is shown to exhibit parametric gain of up to 29 dB in the presence of a strong pump tone. The noise performance of this parametric amplifier approaches the quantum limit, making it useful for applications in quantum information and metrology.

•Feb 10, 2017•17 citations
We demonstrate giant nonlinearity of the kinetic inductance LkL_kLk​ in a superconducting NbN/Al hybrid strip. In contrast to ordinary superconductors, where the maximum observed current-induced variation of LkL_kLk​ does not exceed tens of percent, we observe a 50-fold change in LkL_kLk​. Physically, this effect is connected with the proximity-induced superconductivity in the Al layer and the specific choice of parameters for which the dependence of the superconducting current III on the Cooper pair momentum ℏq\hbar qℏq exhibits a plateau at a current I∗I^*I∗ {\it well below} the depairing current. Formally, this leads to Lk∼dq/dI→∞L_k \sim dq/dI \to \inftyLk​∼dq/dI→∞ as I→I∗I \to I^*I→I∗. We believe that our results open a new route for creating the next generation of highly sensitive detectors of electromagnetic radiation, calorimeters, parametric amplifiers, and magnetometers.
The concept of nonlinear kinetic inductance sensor (NKIS) of electromagnetic radiation is proposed. The idea is based on divergency of kinetic inductance Lk∼dq/dI{{L}_{k}} \sim dq{\text{/}}dILk​∼dq/dI ( ℏq\hbar qℏq is a momentum of superconducting electrons, I is a supercurrent) of hybrid superconductor/normal metal (SN) bridge at current I*<IdepI{\text{*}} < {{I}_{{{\text{dep}}}}}I*<Idep​ ( Idep{{I}_{{{\text{dep}}}}}Idep​ is a depairing current of the hybrid) and temperature T* much smaller than critical temperature Tc{{T}_{c}}Tc​ . It makes possible to have large change of phase difference δϕ\delta \phi δϕ along SN bridge in current biased regime at I≃I*I \simeq I{\text{*}}I≃I* even for small electron temperature increase. Appearance of δϕ\delta \phi δϕ is accompanied by the change of the current and magnetic flux through the coupled superconducting ring which could be measured with help of superconducting quantum interference device (SQUID). In some respect proposed sensor may be considered as a superconducting counterpart of transition edge sensor (TES) those work is based on large derivative dR/dTdR{\text{/}}dTdR/dT ( RRR is a resistance) near Tc{{T}_{c}}Tc​ . Because at I≃I*I \simeq I{\text{*}}I≃I* SN bridge is in gapless regime there is no low boundary for frequency of detected electromagnetic radiation. Our calculations show that such a sensor can operate in single photon regime and detect single photons with frequency ν≳\nu \gtrsim ν≳ 10 GHz. We argue that the nontrivial dependence I(q)I(q)I(q) of SN bridge could be also used in detectors of continuous electromagnetic radiation, current and magnetic field sensors.
Parametric amplification enables sensitive microwave detection and signal processing by amplifying weak signals with minimal added noise. Here, we demonstrate kinetic inductance mediated parametric amplification in a hybrid magnonic system comprising a nonlinear NbN nanowire resonator strongly coupled to a yttrium iron garnet sphere. The resonator exhibits four wave mixing and nonlinear frequency pulling, enabling parametric amplification both away from and within the magnon-photon strong coupling regime. In the magnon detuned regime, we observe 7 dB gain, while coupling to the YIG magnon shifts the parametric amplification response by ~20 MHz and yields 3.4 dB gain in the hybrid mode. Thus, magnon photon coupling provides a route to magnetically tune the spectral position of kinetic inductance parametric amplification. At higher pump powers, the system transitions to a self oscillatory regime featuring comb-like sidebands and probe activated nonlinear mode mixing. These results establish hybrid magnonics as a platform for tunable nonlinear microwave amplification and dynamics.
We are starting to investigate a novel multiplexable readout method that can be applied to a large class of superconducting pair-breaking detectors.This readout method is completely different from those currently used with STJ and TES detectors, and in principle could deliver large pixel counts, high sensitivity, and Fano-limited spectral resolution.The readout is based on the fact that the kinetic surface inductance L s of a superconductor is a function of the density of quasiparticles n, even at temperatures far below T c .An efficient way to measure changes in the kinetic inductance is to monitor the transmission phase of a resonant circuit.By working at microwave frequencies and using thin films, the kinetic inductance can be a significant part of the total inductance L, and the volume of the inductor can be made quite small, on the order of 1 //m 3 .As is done with other superconducting detectors, trapping could be used to concentrate the quasiparticles into the small volume of the inductor.However, the most intriguing aspect of the concept is that passive frequency multiplexing could be used to read out ~ 10 3 detectors with a single HEMT amplifier. DETECTOR CONCEPTKinetic inductance detectors operate on the principle that a change in the number of quasiparticles in a superconductor will produce a change in the kinetic inductance.This occurs because the quasiparticles block Cooper pairs from occupying some of the electron states.Photons (or particles) are absorbed in the superconductor, producing quasiparticles, and the resulting change in the inductance is measured to produce the detector output.Bolometric detectors using kinetic inductance thermometers have been previously suggested [1, 2, 3, 4, 5, 6].However, such thermometers must be operated close to T c , since the variation of the kinetic inductance with temperature is most rapid near T c , and vanishes exponentially at low temperatures.Although it has been discussed previously [7], it is not widely appreciated that the the variation of the kinetic inductance with energy or quasiparticle number is actually fairly constant down to very low temperatures.The idea, then, is to use the kinetic inductance effect to read out changes in the quasiparticle population produced by the direct absorbtion of pair-breaking photons rather than changes in the temperature of the phonons in a bolometric absorber.How can one measure the change in the kinetic inductance of a superconductor?One way is to make the superconductor act as an inductive element in a resonant circuit.A change in the quasiparticle population will change the inductance of the superconductor, and therefore the resonance frequency of the circuit, which can be monitored by measuring the transmission phase of a constant-frequency microwave probe signal transmitted through (or reflected from) the resonator.This method is extremely attractive, due both to CP605, Low Temperature Detectors, edited by F. S. Porter et al.
We characterize inductors fabricated from ultra-thin, approximately 100 nm wide strips of niobium (Nb) and niobium nitride (NbN). These nanowires have a large kinetic inductance in the superconducting state. The kinetic inductance scales linearly with the nanowire length, with a typical value of 1 nH µm(-1) for NbN and 44 pH µm(-1) for Nb at a temperature of 2.5 K. We measure the temperature and current dependence of the kinetic inductance and compare our results to theoretical predictions. We also simulate the self-resonant frequencies of these nanowires in a compact meander geometry. These nanowire inductive elements have applications in a variety of microwave frequency superconducting circuits.
We describe a novel class of devices based on the nonlinearity of the kinetic inductance of a superconducting thin film. By placing a current-dependent inductance in a microwave resonator, small currents can be measured through their effect on the resonator’s frequency. By using a high-resistivity material for the film and nanowires as kinetic inductors, we can achieve a large coefficient of nonlinearity to improve device sensitivity. We demonstrate a current sensitivity of 8 pA/√Hz, making this device useful for transition-edge sensor (TES) readout and other cutting-edge applications. An advantage of these devices is their natural ability to be multiplexed in the frequency domain, enabling large detector arrays for TES-based instruments. A traveling-wave version of the device, consisting of a thin-film microwave transmission line, is also sensitive to small currents as they change the phase length of the line due to their effect on its inductance. We demonstrate a current sensitivity of 5 pA/√Hz for this version of the device, making it also suitable for TES readout as well as other current-detection applications. It has the advantage of multi-gigahertz bandwidth and greater dynamic range, offering a different approach to the resonator version of the device. Finally, we also demonstrate a transmission-line resonator version of the device that combines some of the advantages of the nanowire resonator and the traveling-wave device. This version of the device has high dynamic range but can also be easily multiplexed in the frequency domain. A lumped-element resonator similar to the first device can be placed in a loop configuration to make it sensitive to magnetic fields. We demonstrate an example of such a device whose sensitivity could ultimately reach levels similar to those of state-of-the-art DC SQUIDs, making it potentially useful for many magnetometry applications given its ease of multiplexing. Finally, a similar microwave resonator is shown to exhibit parametric gain of up to 29 dB in the presence of a strong pump tone. The noise performance of this parametric amplifier approaches the quantum limit, making it useful for applications in quantum information and metrology.