A theory of dissipative nonlinear conductivity, σ(1)(ω,H), of s-wave superconductors under strong electromagnetic fields at low temperatures is proposed. Closed-form expressions for σ(1)(H) and the surface resistance R(s)(ω,H) are obtained in the nonequilibrium dirty limit for which σ(1)(H) has a significant minimum as a function of a low-frequency (ħω ≪ k(B)T) magnetic field H. The calculated microwave suppression of R(s)(H) is in good agreement with recent experiments on alloyed Nb resonator cavities. It is shown that superimposed dc and ac fields, H = H(0) + H(a)cosωt, can be used to reduce ac dissipation in thin film nanostructures by tuning σ(1)(H(0)) with the dc field.

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Reduction of dissipative nonlinear conductivity of superconductors by static and microwave magnetic fields

We report on atomic-scale analyses using high-resolution scanning transmission electron microscopy (HR-STEM), atom-probe tomography (APT), and first-principles calculations to study grain-boundary (GB) segregation behavior of Nb3Sn coatings on Nb, prepared by a vapor-diffusion process for superconducting radiofrequency (SRF) cavity applications. The results reveal Sn segregation at GBs of some Nb3Sn coatings, with a Gibbsian interfacial excess of ~10-20 Sn atoms/nm2. The interfacial width of Sn segregation at a GB is ~3 nm, with a maximum concentration of ~35 at.%. HR-STEM imaging of a selected [1-20] tilt GB displays a periodic array of the structural unit at the core of the GB, and first-principle calculations for the GB implies that excess Sn in bulk Nb3Sn may segregate preferentially at GBs to reduce total internal energy. The amount of Sn segregation is correlated with two factors: (i) Sn supply; and (ii) the temperatures of the Nb substrate and Sn source, which may affect the overall kinetics including GB diffusion of Sn and Nb, and the interfacial reaction at Nb3Sn/Nb interfaces. An investigation of the correlation between the chemistry of GBs and Nb3Sn SRF cavity performance reveals no significant Sn segregation at GBs of high-performance Nb3Sn SRF cavities, indicating possible effects of GB segregation on the quality (Q0) factor of Nb3Sn SRF cavities. Our results suggest that the chemistry of GBs of Nb3Sn coatings for SRF cavities can be controlled by grain-boundary engineering, and can be used to direct fabrication of high-quality Nb3Sn coatings for SRF cavities.

Grain-boundary segregation behavior in Nb3Sn coatings on Nb for superconducting radiofrequency cavity applications

Recently, Nb superconducting radio frequency cavities vacuum heat treated between 300 and 400 °C for a few hours have exhibited very high quality factors (∼5 × 1010 at 2.0 K). Secondary ion mass spectrometry measurements of O, N, and C show that this enhancement in RF surface conductivity is primarily associated with interstitial O alloying via dissolution and diffusion of the native oxide. We use a theory of oxide decomposition and O diffusion to quantify previously unknown parameters crucial in modeling this process. RF measurements of a vacuum heat-treated Nb superconducting radio frequency cavity confirm the minimized surface resistance (higher Q0) previously expected only from 800 °C diffusive alloying with N.

RF surface resistance tuning of superconducting niobium via thermal diffusion of native oxide

It is shown that a multilayer comprised of alternating thin superconducting and insulating layers on a thick substrate can fully screen the applied magnetic field exceeding the superheating fields $H_s$ of both the superconducting layers and the substrate, the maximum Meissner field is achieved at an optimum multilayer thickness. For instance, a dirty layer of thickness $\sim 0.1\; \mu$m at the Nb surface could increase $H_s\simeq 240$ mT of a clean Nb up to $H_s\simeq 290$ mT. Optimized multilayers of Nb$_3$Sn, NbN, some of the iron pnictides, or alloyed Nb deposited onto the surface of the Nb resonator cavities could potentially double the rf breakdown field, pushing the peak accelerating electric fields above 100 MV/m while protecting the cavity from dendritic thermomagnetic avalanches caused by local penetration of vortices.

Maximum screening fields of superconducting multilayer structures

Advances in SRF technology over the last 40 years allowed achieving accelerating gradients ~ 50 MV/m corresponding to peak surface magnetic field close to the theoretical limit of niobium. However, the quality factor decreases significantly with increasing accelerating gradient. This decrease is expected since increasing the rf field increases the number of quasiparticles and therefore the rf losses. Recently, a new phenomenon of increase in quality factor with the accelerating gradient has been observed when SRF cavities are doped with certain non-magnetic impurities. In particular, the diffusion of nitrogen into the niobium cavities inner surface has been has been successfully implemented into the commercialization of SRF technology. The quest is still ongoing towards process development to achieve high accelerating gradient SRF structures with high quality factors for future high power accelerators. Here, we present the review of the research and development via nitrogen diffusion, materials analysis and current theoretical understanding in high Q0 SRF cavities.

Nitrogen Doping and Infusion in SRF Cavities: A Review

We use scanning tunneling microscopy (STM) and spectroscopy (STS), and x-ray photoelectron spectroscopy (XPS) to investigate the effect of nitrogen doping on the surface electronic and chemical structures of cutouts from superconducting $\mathrm{Nb}$ radio-frequency cavities. The goal of this work is to get insights into the fundamental physics and materials mechanisms behind the striking decrease of the surface resistance with the radio-frequency magnetic field, which has been observed on $N$-doped $\mathrm{Nb}$ cavities. Our XPS measurements reveal significantly more oxidized $\mathrm{Nb}$ $3d$ states and a thinner metallic suboxide layer on the $N$-doped $\mathrm{Nb}$ surfaces, which is also confirmed by tunneling spectroscopy measurements. In turn, tunneling measurements performed on native surfaces as well as on $\mathrm{Ar}$-ion sputtered surfaces allow us to separate the effect of $N$ doping on the surface-oxide layer from that on the density of states in the bulk. Analysis of our tunneling spectra in the framework of a model of a proximity-coupled normal layer at the surface [A. Gurevich and T. Kubo, Phys. Rev. B 96, 184515 (2017)] is consistent with the hypothesis that $N$-doping ameliorates lateral inhomogeneities of superconducting properties on the surface and shrinks the metallic suboxide layer. For the $\mathrm{Ar}$ sputtered surfaces, we also find evidence that $N$ doping changes the contact resistance between the metallic suboxide and the bulk niobium toward an optimum value corresponding to a minimum surface resistance. The totality of our experimental data suggests that the $N$ doping provides an effective tuning of the density of states in such a way that it can result in a decrease of the surface resistance with the radio-frequency field, as predicted by calculations of the nonlinear low-frequency electromagnetic response of dirty superconductors. Furthermore, STM imaging of vortex cores shows a slightly reduced average superconducting gap and a shorter coherence length in the $N$-doped $\mathrm{Nb}$ samples as compared to typically prepared $\mathrm{Nb}$ samples, indicating a stronger impurity scattering caused by nitrogen doping in a moderately disordered material.

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Electron Tunneling and X-Ray Photoelectron Spectroscopy Studies of the Superconducting Properties of Nitrogen-Doped Niobium Resonator Cavities

Superconducting radio-frequency (SRF) resonator cavities provide extremely high quality factors > 1010 at 1-2 GHz and 2 K in large linear accelerators of high-energy particles. The maximum accelerating field of SRF cavities is limited by penetration of vortices into the superconductor. Present state-of-the-art Nb cavities can withstand up to 50 MV/m accelerating gradients and magnetic fields of 200-240 mT which destroy the low-dissipative Meissner state. Achieving higher accelerating gradients requires superconductors with higher thermodynamic critical fields, of which Nb3Sn has emerged as a leading material for the next generation accelerators. To overcome the problem of low vortex penetration field in Nb3Sn, it has been proposed to coat Nb cavities with thin film Nb3Sn multilayers with dielectric interlayers. Here, we report the growth and multi-technique characterization of stoichiometric Nb3Sn/Al2O3 multilayers with good superconducting and RF properties. We developed an adsorption-controlled growth process by co-sputtering Nb and Sn at high temperatures with a high overpressure of Sn. The cross-sectional scanning electron transmission microscope images show no interdiffusion between Al2O3 and Nb3Sn. Low-field RF measurements suggest that our multilayers have quality factor comparable with cavity-grade Nb at 4.2 K. These results provide a materials platform for the development and optimization of high-performance SIS multilayers which could overcome the intrinsic limits of the Nb cavity technology.

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Development and characterization of Nb3Sn/Al2O3 superconducting multilayers for particle accelerators.

It was recently shown that diffusing nitrogen on the inner surface of superconducting radiofrequency (SRF) cavities at high temperature can improve the quality factor of the niobium cavity. However, a reduction of the quench field is also typically found. To better understand the location of rf losses and quench, we used a thermometry system to map the temperature of the outer surface of ingot Nb cavities after nitrogen doping and electropolishing. Surface temperature of the cavities was recorded while increasing the rf power and also during the quenching. The results of thermal mapping showed no precursor heating on the cavities and quenching to be ignited near the equator where the surface magnetic field is maximum. Hot-spots at the equator area during multipacting were also detected by thermal mapping.

Temperature Mapping of Nitrogen-doped Niobium Superconducting Radiofrequency Cavities

Thermal diffusion of nitrogen in niobium superconducting radio frequency cavities at temperature ~800 °C has resulted in the increase in quality factor with a low-field Q-rise extending to Bp > 90 mT. However, the maximum accelerating gradient of these doped cavities often deteriorates below the values achieved by standard treatments prior to doping. Here, we present the results of the measurements on ingot niobium cavities doped with nitrogen at 800 °C. The rf measurements were carried out after the successive electropolishing to remove small amount of material from the inner surface layer. The result showed higher breakdown field with lower quality factor as material removal increases.

Nitrogen doping study in ingot niobium cavities

Superconducting radio-frequency (SRF) resonator cavities provide extremely high quality factors > 10 at 1-2 GHz and 2K in large linear accelerators of high-energy particles. The maximum accelerating field of SRF cavities is limited by penetration of vortices into the superconductor. Present state-of-the-art Nb cavities can withstand up to 50 MV/m accelerating gradients and magnetic fields of 200-240 mT which destroy the low-dissipative Meissner state. Achieving higher accelerating gradients requires superconductors with higher thermodynamic critical fields, of which Nb3Sn has emerged as a leading material for the next generation accelerators. To overcome the problem of low vortex penetration field in Nb3Sn, it has been proposed to coat Nb cavities with thin film Nb3Sn multilayers with dielectric interlayers. Here, we report the growth and multi-technique characterization of stoichiometric Nb3Sn/Al2O3 multilayers with good superconducting and RF properties. We developed an adsorption-controlled growth process by co-sputtering Nb and Sn at high temperatures with a high overpressure of Sn. The cross-sectional scanning electron transmission microscope images show no interdiffusion between Al2O3 and Nb3Sn. Low-field RF measurements suggest that our multilayers have quality factor comparable with cavitygrade Nb at 4.2 K. These results provide a materials platform for the development and optimization of high-performance SIS multilayers which could overcome the intrinsic limits of the Nb cavity technology.

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Junki Makita

Papers

Electron Tunneling and X-Ray Photoelectron Spectroscopy Studies of the Superconducting Properties of Nitrogen-Doped Niobium Resonator Cavities

Development and characterization of Nb3Sn/Al2O3 superconducting multilayers for particle accelerators.

Temperature Mapping of Nitrogen-doped Niobium Superconducting Radiofrequency Cavities

Nitrogen doping study in ingot niobium cavities

Development and Characterization of Nb3Sn/Al2O3 Superconducting Multilayers for High-performance Radio-Frequency Applications