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 non-zero, magnetic fields. By cooling in fields of the order of 100 µT 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 with high quality factors have enabled many recent breakthroughs with superconducting qubits and photon detectors, typically operated in shielded environments to reduce the ambient magnetic field. Insufficient shielding or pulsed control fields can introduce vortices, leading to reduced quality factors, although increased pinning can mitigate this effect. A narrow slot etched into the resonator surface provides a straightforward method for pinning enhancement without otherwise affecting the resonator. Resonators patterned with such a slot exhibited over an order of magnitude reduction in the excess loss due to vortices compared with identical resonators from the same film with no slot.Low-loss microwave resonators fabricated from superconducting thin films are playing key roles in many recent low-temperature experiments. Such resonators can be coupled to quantum coherent superconducting devices, or qubits [1], for explorations of QED with circuits [2,3]. Furthermore, high-quality factor resonators have enabled the development of Microwave Kinetic Inductance Detectors (MKIDs), highly sensitive photon detectors for astrophysical measurements [4].A variety of factors determine the quality factor of these resonators, including dielectric loss in the substrates and thin-film surfaces [5]. If the resonators are not cooled in a sufficiently small ambient magnetic field, or if large pulsed fields are present for operating circuits in the vicinity of the resonators, vortices can become trapped in the resonator traces, thus providing another loss channel. The presence of even a few vortices can substantially reduce the resonator quality factor [6].Vortex dynamics at microwave frequencies has been studied for some time both theoretically [7,8] and experimentally in a variety of superconductors [6,9,10,11,12]. The response of vortices to an oscillatory Lorentz force is determined primarily by two forces: the viscous force, due to the motion of the vortex core and characterized by a vortex viscosity η; and the pinning forces in the material that impede the vortex motion and, in the simplest case, can be described by a linear spring constant k p . The ratio of the pinning strength to the vortex viscosity, f d = k p /2πη, determines the crossover frequency separating elastic and viscous response of the vortices.In this letter we demonstrate a technique for patterned pinning on the resonator surface to reduce the excess microwave loss due to trapped vortices. We compare fieldcooled measurements for a series of coplanar waveguide (CPW) resonators patterned from the same thin film of Al, a common material used for qubits and MKIDs. Some of the resonators had a single longitudinal slot partially etched into the surface along the center conductor, while others had no slot. A surface step in a superconductor can pin a vortex because of the line energy variation asso- *
The controlled motion of objects through narrow channels is important in many fields. We have fabricated asymmetric weak-pinning channels in a superconducting thin-film strip for controlling the dynamics of vortices. The lack of pinning allows the vortices to move through the channels with the dominant interaction determined by the shape of the channel walls. We present measurements of vortex dynamics in the channels and compare these with similar measurements on a set of uniformwidth channels. While the uniform-width channels exhibit a symmetric response for both directions through the channel, the vortex motion through the asymmetric channels is quite different, with substantial asymmetries in both the static depinning and dynamic flux flow. This vortex ratchet effect has a rich dependence on magnetic field and driving force amplitude.PACS numbers: 74.25. Qt, 74.25.Sv, 74.25.Op Recently there has been much interest in developing artificial ratchets for generating directed motion using tailored asymmetries [1]. Such ratchets could be used as pathways for producing net transport of matter at the nanoscale. In addition, artificial ratchets can serve as model systems for understanding similar ratchet phenomena in biological systems while allowing for experimental control over many of the ratchet parameters [2]. A variety of ratchets have been considered, but one particular type that has been implemented in several different systems is the rocking ratchet, where a spatial asymmetry is engineered into the potential energy landscape governing particle motion and an external control variable can be adjusted to tilt this potential. The application of an oscillatory drive of the control variable with zero mean can result in the net motion of particles through the potential because of the different rates for overcoming the barriers in the two directions through the ratchet.Implementations of ratchets in solid-state devices include asymmetric structures of electrostatic gates above a two-dimensional electron gas [3], and arrays of Josephson junctions with asymmetric critical currents [4]. Structures have also been developed for producing a ratchet effect with vortices in superconducting thin films involving either asymmetric arrangements of pinning centers [5,6] or asymmetric magnetic pinning structures [7]. In this Communication, we describe a vortex ratchet using two-dimensional guides to generate asymmetric channels for vortex motion. In our structures, the potential asymmetries arise from differences in the interaction strength between vortices and the channel walls, resulting in a substantial ratchet effect for the motion of vortices through the channels. Our design is related to a previous vortex ratchet proposal [8], although our ratchet is in a somewhat different parameter regime.Nanoscale channels for guiding vortices through superconducting films with a minimal influence from pin- ning have been developed for studies of vortex matter in confined geometries, including experiments on melting [9], commensurabili...
We study the dynamics of vortices in an asymmetric (i.e., consisting of triangular cells) ring channel driven by an external ac current I in a Corbino setup. The asymmetric potential rectifies the motion of vortices and induces a net vortex flow without any unbiased external drive, i.e., the ratchet effect. We show that the net flow of vortices strongly depends on vortex density and frequency of the driving current. Depending on the density, we distinguish a "single-vortex" rectification regime (for low density, when each vortex is rectified individually) determined by the potential-energy landscape inside each cell of the channel (i.e., "hard" and "easy" directions) and "multi-vortex", or "collective", rectification (high density case) when the inter-vortex interaction becomes important. We analyze the average angular velocity ω of vortices as a function of I and study commensurability effects between the numbers of vortices and cells in the channel and the role of frequency of the applied ac current. We have shown that the commensurability effect results in a stepwise ω − I curve. Besides the "integer" steps, i.e., the large steps found in the single vortex case, we also found "fractional" steps corresponding to fractional ratios between the numbers of vortices and triangular cells. We have performed preliminary measurements on a device containing a single weak-pinning circular ratchet channel in a Corbino geometry and observed a substantial asymmetric vortex response.
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