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Applied Physics Letters

Magnetic field dependence of the coupling efficiency of a superconducting transmission line due to the proximity effect

S. Zhu, T. Zijlstra, Alexander A. Golubov, M. van den Bemt, Andrey M. Baryshev, T. M. Klapwijk

Published Dec 21, 2009• 6 citations
Publisher

Abstract

The coupling efficiency of a Nb superconducting transmission line has been measured using a Fourier transform spectrometer for different magnetic fields. It is found that the coupling decreases with increasing magnetic field when the frequency is close to the gap of the Nb superconductor. This is attributed to the changes of the surface impedance of the proximity-coupled superconductor/normal-metal bilayers in the transmission line.

DOI
10.1063/1.3276076

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The coupling efficiency of a Nb superconducting transmission line has been measured using a Fourier transform spectrometer for different magnetic fields. It is found that the coupling decreases with increasing magnetic field when the frequency is close to the gap of the Nb superconductor. This is attributed to the changes of the surface impedance of the proximity-coupled superconductor/normal-metal bilayers in the transmission line.
High critical current density tunnel barriers of AlN have two effects on the operation of niobium-based SIS mixers close to the upper frequency limit of superconducting niobium: 1. the bandwidth is no longer limited by the RC time constant of the tunnel-junction, but the physical processes in the superconductors at high frequencies; 2. the devices have smaller lateral dimensions in order to provide impedance matching given the low RnA value, which requires the application of a higher magnetic field to quench the Josephson-effect through the Fraunhofer pattern. Consequently, under operating conditions the superconducting properties are no longer the equilibrium properties as realized by the fabrication conditions, but are deteriorated by the applied magnetic field. We report the measurements of I-V curves and Fourier transmission spectrum to determine and correlate the evolution of the superconducting properties in a high magnetic field. The results are compared with a calculation of the proximity effect based on the Keldysh Greens' function technique, leading to a magnetic field dependent density of states in the Al toplayer of the commonly used Nb-Al bilayer to fabricate tunnel barriers as well as forming one part of the superconducting stripline.
The frequency dependence of the coupling of niobium superconducting transmission lines is measured for frequencies up to and above the superconducting gap frequency. For this purpose superconducting microstrips are integrated in log-periodic planar antennas and the spectral response is measured by means of a Fourier transform spectrometer with 1 μm2 Nb/Al2O3/Nb SIS junctions as detectors. Resonances of microstrips are observed up to 650 GHz, the superconducting gap frequency of niobium, but above that frequency no resonances have been detected. The measured resonance frequencies are in good agreement with a dispersive model for superconducting transmission lines based on the Mattis–Bardeen theory. The radiation coupling is lower than calculated, indicating significant dielectric losses.
The standard mean-field treatment of low-temperature superconductors leads to a square-root divergent density of states at the gap value. This feature can lead to unphysical logarithmic divergences in various quantities, such as currents and qubit transition rates. We revisit their possible regularization based on the proximity effect between two superconducting films with different gaps. We derive analytical approximations for the density of states in each superconducting film. We find that the smearing of the density of states grows with the gap asymmetry. As a concrete example, we discuss the regularization of transition rates in qubits with frequency close to resonance with the gap asymmetry between the two films, and the consequent smoothening of the jump discontinuity in the qubit frequency shift. Our results could also aid the development of superconducting detectors and related devices based on superconducting bilayers.
In this letter, we have studied the effects of proximity of a superconductor to a normal metal. The system, represented by a bilayer attractive Hubbard model, is investigated using layer-dynamical mean field theory and iterated perturbation theory for superconductivity as an impurity solver. The bilayer system comprises a superconducting and a normal metallic layer, connected by an inter-planar hopping (t⊥t_\perpt⊥​). It is found that superconductivity is induced in the normal layer for small t⊥t_\perpt⊥​. With increasing inter-layer hopping, the bilayer system undergoes two transitions: a first order transition to a normal metallic phase, and subsequently a continuous crossover to a band insulator.
The proximity effect in hybrid superconducting--normal-metal structures is shown to affect strongly the coherent oscillations of the superconducting order parameter $\mathrm{\ensuremath{\Delta}}$ known as the Higgs modes. The standard Higgs mode at frequency $2\mathrm{\ensuremath{\Delta}}$ is damped exponentially by the quasiparticle leakage from the primary superconductor. Two new Higgs modes with the frequencies depending on both the primary and induced gaps in the hybrid structure are shown to appear due to the coherent electron transfer between the superconductor and the normal metal. Altogether, these three modes determine the long-time asymptotic behavior of the superconducting order parameter disturbed either by the electromagnetic pulse or the quench of the system parameters and thus are of crucial importance for the dynamical properties and restrictions on the operating frequencies for superconducting devices based on the proximity effect used, e.g., in quantum computing, in particular, with topological low-energy excitations.
The bandwidth and noise temperature of superconducting-insulating-superconducting (SIS) mixers are strongly determined by the matching between antenna and tunnel-junction. Optimal scientific benefit from Band 9 (600 to 720 GHz) of the Atacama large millimeter array requires a proper design of the matching circuit by taking into account the energy gap of the niobium (680 GHz). In preliminary experiments we have found that tapered structures lead to significant improvements, which suggests that a systematic analysis of optimized geometrical shapes might be beneficial. The tuning circuits are analysed using a model, which includes the Mattis-Bardeen theory for the surface impedance of Nb and which allows arbitrary shapes. We will present simulations and experimental results focusing on the transmission efficiency, which can conveniently be evaluated experimentally by using a Fourier transform spectrometer. We will show how the shape influences the transmission efficiency and relate it to observed noise temperatures of the mixers.