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arXiv:1803.04222 · Superconductor Science and Technology

Electromagnetic models for multilayer superconducting transmission lines

Songyuan Zhao, S Withington, D J Goldie, C N Thomas

Published Jun 15, 2018• 13 citations
arXivHTMLPDF

Abstract

Abstract Thin-film superconducting transmission lines play important roles in many signal transmission and detection systems, including qubit coupling and read-out schemes, electron spin resonance systems, parametric amplifiers, and various ultra high sensitivity detectors. Here we present a rigorous method for computing the electromagnetic behaviour of superconducting microstrip transmission lines and coplanar waveguides. Our method is based on conformal mapping, and is suitable for both homogeneous superconductors and proximity-coupled multilayers. We also present an effective conductivity approximation of multilayers, thereby allowing the multilayers to be analysed using existing electromagnetic design software. We compute the numerical results for Al–Ti bilayers and discuss the validity of our full computation and homogeneous approximation.

DOI
10.1088/1361-6668/aacc53

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Abstract Thin-film superconducting transmission lines play important roles in many signal transmission and detection systems, including qubit coupling and read-out schemes, electron spin resonance systems, parametric amplifiers, and various ultra high sensitivity detectors. Here we present a rigorous method for computing the electromagnetic behaviour of superconducting microstrip transmission lines and coplanar waveguides. Our method is based on conformal mapping, and is suitable for both homogeneous superconductors and proximity-coupled multilayers. We also present an effective conductivity approximation of multilayers, thereby allowing the multilayers to be analysed using existing electromagnetic design software. We compute the numerical results for Al–Ti bilayers and discuss the validity of our full computation and homogeneous approximation.
Strategies are explored to reduce the electromagnetic simulation time of electrically large superconducting transmission line structures while retaining model accuracy. The complex surface reactance of an infinite thin-film superconducting sheet is evaluated with the BCS (Bardeen-Cooper-Schrieffer) theory and used as an input to model the phase velocity and characteristic impedance of finite width transmission line structures. Commercially available electromagnetic simulation software are employed for the calculations and the results are compared with limiting analytic forms from the literature. The influences of line width, metallization thickness, and substrate height on microstrip transmission line propagation are considered in detail and a scaling approach is presented to compensate for the leading order effect in numerical simulations. These findings are particularly important near the energy gap of the superconductor due to the influence of the kinetic inductance on the transmission line dispersion.
In this work, we present a numerical model specifically designed for 3D multilayer devices, with a focus on nanobridge junctions and coplanar waveguides. Unlike existing numerical models, ours does not approximate the physical layout or limit the number of constituent materials, providing a more accurate and flexible design tool. We calculate critical currents, current–phase relationships, and the energy gap where relevant. We validate our model by comparing it with published data. Through our analysis, we found that using multilayer films significantly enhances control over these quantities. For nanobridge junctions in particular, multilayer structures improve qubit anharmonicity compared to monolayer junctions, offering a substantial advantage for qubit performance. For coated multilayer microwave circuits, it allows for better studies of the proximity effect, including their effective kinetic inductance.
Abstract We present a theoretical and experimental study of superconducting ring resonators as an initial step toward their implementation in superconducting electronics and quantum technologies, with promising applications including superconducting parametric amplifiers with pump-signal isolation, flux-controlled quantum circuits, ultra-sensitive measurements in quantum sensing, and THz instrumentations. These devices have the potentially valuable property of supporting two orthogonal electromagnetic modes that couple to a common Cooper pair, quasiparticle, and phonon system. We present here a comprehensive theoretical and experimental analysis of the superconducting ring resonator system. We have developed superconducting ring resonator models that describe the key features of microwave behaviour to first order, providing insights into how transmission line inhomogeneities give rise to frequency splitting and mode rotation. Furthermore, we constructed signal flow graphs for a four-port ring resonator to numerically validate the behaviour predicted by our theoretical analysis. Superconducting ring resonators were fabricated in both coplanar waveguide and microstrip geometries using Al and Nb thin films. Microwave characterisation of these devices demonstrates close agreement with theoretical predictions. Our study reveals that frequency splitting and mode rotation are prevalent in ring systems with coupled degenerate modes, and these phenomena become distinctly resolved in high quality factor superconducting ring resonators.
In this work, we present a numerical model specifically designed for 3D multilayer devices, with a focus on nanobridge junctions and coplanar waveguides. Unlike existing numerical models, ours does not approximate the physical layout or limit the number of constituent materials, providing a more accurate and flexible design tool. We calculate critical currents, current phase relationships, and the energy gap where relevant. We validate our model by comparing it with published data. Through our analysis, we found that using multilayer films significantly enhances control over these quantities. For nanobridge junctions in particular, multilayer structures improve qubit anharmonicity compared to monolayer junctions, offering a substantial advantage for qubit performance. For coated multilayer microwave circuits it allows for better studies of the proximity effect, including their effective kinetic inductance.
Transmission losses in Nb superconducting coplanar waveguide (CPW) and microstrip lines were quantified at 2-mm wavelength and 3.3 K using a network analyzer. The loss measurement utilized both half-wavelength resonators and electrically long transmission lines. Validation of the measurement was achieved using a silicon membrane-based waveguide-to-CPW transition with low return loss across a broad bandwidth. Intrinsic losses were measured within a parametric space defined by frequency, temperature, signal power, and magnetic field. The multidimensional information allowed the breakdown of overall losses into major components, including quasiparticle loss, two-level system dielectric loss, vortex flow loss, and radiation loss. The performance of these transmission lines was extrapolated into the terahertz range based on these findings.
We present calculations of the properties of the first coplanar waveguide transmission line resonators patterned from high-Tc superconducting films at 8.8 and 6.5 GHz [1, 2]. Based on field calculations of the corresponding coplanar waveguides with infinite conductivity, performed by a partial wave synthesis (mode-matching method) [3], we obtain the superconductor losses subsequently using London's theory. Due to the high conductivity of the superconductive material both the electric and magnetic fields within the superconductor may be assumed to be parallel to the surface planes. For the small conductor thickness the tangential electrical field on each surface plane depends on the tangential magnetic fields on both surface planes. This relation is modelled by the surface impedance matrix Zs. The substrate losses are treated in the field calculations and are also taken into account. The calculated overall Q values are compared with the measured values and it has to be pointed out, that the superconducting thin films are due to the available material datas of the YBaCuO superconductor and the used substrate materials of a very good quality, because they reach nearly their upper limit given by the known material datas.