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arXiv:1812.03227

Magnetic hysteresis of a superconducting microstrip resonator with a high edge barrier

Sangil Kwon, Yongchao Tang, Hamid Reza Mohebbi, David G. Cory, Guo‐Xing Miao

Published Dec 7, 2018• 0 citations
arXivHTMLPDF

Abstract

We investigate the magnetic hysteresis of a superconducting microstrip resonator with a high edge barrier. We measure the magnetic hysteresis while either sweeping a magnetic field or tuning the edge barrier by high microwave current. We show that the magnetic hysteresis of such a device is qualitatively different from that of one without an edge barrier and can be understood based on the generalized critical-state model. In particular, we propose and demonstrate a simple and intuitive method that relies on a plot of the quality factor versus the resonance frequency for revealing the physical processes behind those hysteretic behaviors. Based on this, we find that the interplay between the Meisser current and vortex pinning is essential for understanding the magnetic hysteresis of such a device.

DOI
10.48550/arxiv.1812.03227

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We investigate the magnetic hysteresis of a superconducting microstrip resonator with a high edge barrier. We measure the magnetic hysteresis while either sweeping a magnetic field or tuning the edge barrier by high microwave current. We show that the magnetic hysteresis of such a device is qualitatively different from that of one without an edge barrier and can be understood based on the generalized critical-state model. In particular, we propose and demonstrate a simple and intuitive method that relies on a plot of the quality factor versus the resonance frequency for revealing the physical processes behind those hysteretic behaviors. Based on this, we find that the interplay between the Meisser current and vortex pinning is essential for understanding the magnetic hysteresis of such a device.
We performed transmission spectroscopy experiments on coplanar half-wavelength niobium resonators at temperature T=4.2T=4.2\phantom{\rule{0.16em}{0ex}}T=4.2K. We observe not only a strong dependence of the quality factor QQQ and the resonance frequency fres{f}_{\mathrm{res}}fres​ on an externally applied magnetic field but also on the magnetic history of our resonators, i.e., on the spatial distribution of trapped Abrikosov vortices in the device. This is valid for a broad range of frequencies and angles between the resonator plane and the magnetic field direction and holds for resonators with and without antidots near the edges of the center conductor and the ground planes. In a detailed analysis, we show that characteristic features of the experimental data can only be reproduced by calculations if we assume a highly inhomogeneous rf current density and a flux density gradient with maxima at the edges of the superconductor. We furthermore demonstrate that the hysteretic behavior of the resonator properties can be used to considerably reduce the vortex-induced losses and to fine-tune the resonance frequency by the proper way of cycling to a desired magnetic field value.
Abstract We fabricated a superconducting coplanar waveguide resonator with leads for dc bias, which enables an ac conductivity measurement under dc bias. The current and magnetic field dependences of resonance properties were measured, and hysteretic behavior was observed as a function of the dc driving current. The observed shifts in the inverse of the quality factor, Q −1 , and the center frequency, f 0 , were explained by considering both motion of vortices and suppression of the order parameter by the dc current. Our investigation revealed that the strongly pinned vortices have a small influence on f 0 , while they still affect Q −1 . Our results indicate that the accurate understanding of the dynamics of driven vortices is indispensable for a control of the resonance properties with a high precision.
Vortices in superconductors driven at microwave frequencies exhibit a response related to the interplay between the vortex viscosity, pinning strength, and flux creep effects. At the same time, the trapping of vortices in superconducting microwave resonant circuits contributes excess loss and can result in substantial reductions in the quality factor. Thus, understanding the microwave vortex response in superconducting thin films is important for the design of such circuits, including superconducting qubits and photon detectors, which are typically operated in small, but nonzero, magnetic fields. By cooling in fields on the order of $100\text{ }\ensuremath{\mu}\text{T}$ and below, we have characterized the magnetic field and frequency dependence of the microwave response of a small density of vortices in resonators fabricated from thin films of Re and Al, which are common materials used in superconducting microwave circuits. Above a certain threshold cooling field, which is different for the Re and Al films, vortices become trapped in the resonators. Vortices in the Al resonators contribute greater loss and are influenced more strongly by flux creep effects than in the Re resonators. This different behavior can be described in the framework of a general vortex dynamics model.
Microwave resonators fabricated from superconducting thin films are playing a critical role with recent advances in superconducting quantum computing technology and photon detectors. There has been an intensive worldwide effort to study the sources of loss that limit the quality factors of these resonators. In this thesis, I have focused on the measurements of the microwave response of vortices in Al and Re superconducting thin film resonators cooled in magnetic fields comparable to or less than that of the Earth. Previous work on vortex dynamics at microwave frequencies has involved large magnetic fields, orders of magnitude larger than the Earth's fields. Al and Re are common materials used in superconducting resonant circuits for qubits and detectors. Despite the similarities of Al and Re superconductors, the microwave vortex response is strikingly different in the two materials from my resonator measurements. I present a quantitative model for the dissipation and reactance contributed by the vortices in terms of the elastic pinning forces and the viscous damping from the vortex cores. The differences in the vortex response in Al and Re were due to the vortex pinning strength in the two films The critical role played by pinning in determining the microwave response motivated us to try to modify the pinning in our Al films by nanostructuring the film surface. A single narrow slot along the center line of a resonator was used to increase the pinning in the resonator traces and resulted in a reduction of the loss from vortices by over an order of magnitude. Such patterned pinning techniques could be used on resonators in systems with insufficient shielding or pulsed control fields to reduce the loss from unwanted trapped vortices. Finally, we explored the possibility for using measurements of the power dependence of the resonators to determine if trapped vortices are present.
We demonstrate the microwave signatures of individual Abrikosov-vortex penetration events in superconducting microwave resonators. λ/4λ/4λ/4 resonators with a narrowed region near the grounded end acting as a vortex trap were fabricated and studied using microwave transmission spectroscopy at millikelvin temperatures. Sharp stepwise drops in resonance frequency are detected as a function of increasing external magnetic field, attributed to the entry of individual Abrikosov vortices in the narrow region. This interpretation is confirmed by NV center magnetometry revealing discrete vortex entry events on increasing field and the absence of such drops in a device with a wider narrowed region. Our results establish a method to investigate and manipulate the states of Abrikosov vortices with microwaves access and readout vortex configurations using magnetic-field sweeps and microwave drive.
Characterizing superconducting microwave resonators with highly dissipative elements is a technical challenge, but a requirement for implementing and understanding the operation of hybrid quantum devices involving dissipative elements, e.g., for thermal engineering and detection. We present experiments on λ/4 superconducting niobium coplanar waveguide resonators, terminating at the antinode by a dissipative copper microstrip via aluminum leads, such that the resonator response is difficult to measure in a typical microwave environment. By measuring the transmission both above and below the superconducting transition of aluminum, we are able to isolate the resonance. We then experimentally verify this method with copper microstrips of increasing thicknesses, from 50 nm to 150 nm, and measure quality factors in the range of 10–67 in a consistent way.