We have directly imaged the anisotropic nonlinear Meissner effect in an unconventional superconductor through the nonlinear electrodynamic response of both (bulk) gap nodes and (surface) Andreev bound states. A superconducting thin film is patterned into a compact self-resonant spiral structure, excited near resonance in the radio-frequency range, and scanned with a focused laser beam perturbation. At low temperatures, direction-dependent nonlinearities in the reactive and resistive properties of the resonator create photoresponse that maps out the directions of nodes, or of bound states associated with these nodes, on the Fermi surface of the superconductor. The method is demonstrated on the nodal superconductor YBa2Cu3O 7−δ and the results are consistent with theoretical predictions for the bulk and surface contributions.Introduction -The Meissner effect is the spontaneous exclusion of magnetic flux from the bulk of a superconductor and is one of the hallmarks of superconductivity. In the presence of a magnetic field, a superconductor must invest kinetic energy in a supercurrent flow to screen out the applied field. This reduces the free energy difference between the superconducting and normal states, resulting in a reduction in magnitude of the superconducting order parameter. This in turn leads to a field-and current-dependent magnetic penetration depth, diamagnetic moment, etc. and is referred to as the nonlinear Meissner effect (NLME). Microscopically the NLME arises when Cooper pairs at the leading edge of the current-carrying Fermi surface can de-pair into available quasi-particle states at the back-end and create a quasi-particle backflow current [1]. Conventional (fully gapped) superconductors show the strongest nonlinearities near T c , and have exponentially suppressed nonlinear response at low temperatures, T ≪ T c . Unconventional superconductors with nodes in the superconducting energy gap are expected to have a strong nonlinear Meissner effect at low temperatures, due to the nodal excitations out of the superconducting ground state [2]. In addition this nonlinear response should be anisotropic, reflecting the locations of nodes of the gap on the Fermi surface.

Abstract-A gas will breakdown in a high electric field and the mechanisms of this breakdown at DC and high frequency fields have been an object of study for the past century. This paper describes a method to induce breakdown in a uniform microwave field using a re-entrant sub-quarter wave resonator. Slater's theorem is used to determine the magnitude of the threshold electric field at which breakdown occurs. The breakdown threshold is modeled using the effective electric field concept, showing that breakdown varies withwhere P is the pressure, B and C are fit parameters, and m was found experimentally to equal 1/2. This function exhibits a minimum at P min = ω/B. Breakdown data from the literature for nitrogen at various microwave frequencies were found to exhibit breakdown minima at the pressure predicted by our own determination of B, further validating the model.

This work studies high-temperature superconducting spiral resonators as a viable candidate for realization of RF/microwave metamaterial atoms. The theory of superconducting spiral resonators will be discussed in detail, including the mechanism of resonance, the origin of higher order modes, the analytical framework for their determination, the effects of coupling scheme, and the dependence of the resonance quality factor and insertion loss on the parity of the mode. All the aforementioned models are compared with the experimental data from a micro-fabricated YBa2Cu3O 7−δ (YBCO) spiral resonator. Moreover, the evolution of the resonance characteristics for the fundamental mode with variation of the operating temperature and applied RF power is experimentally examined, and its implications for metamaterial applications are addressed.

We report development and measurement of a micro-fabricated compact high-temperature superconducting (HTS) metamaterial atom operating at a frequency as low as ∼ 53MHz. The device is a planar spiral resonator patterned out of a YBa 2 Cu 3 O 7−δ (YBCO) thin film with the characteristic dimension of ∼ λ 0 /1000, where λ 0 is the free-space wavelength of the fundamental resonance. While deployment of an HTS material enables higher operating temperatures and greater tunability, it has not compromised the quality of our spiral metamaterial atom and a Q as high as ∼ 1000 for the fundamental mode, and ∼ 30000 for higher order modes, are achieved up to 70K. Moreover, we have experimentally studied the effect of the substrate by comparing the performance of similar devices on different substrates.Realization of metamaterials based on sub-wavelength artificial electromagnetic structures has attracted much attention and efforts for a variety of applications 1,2 . This interest applies virtually to the entire span of the electromagnetic spectrum from radio-frequency (RF) up to visible and ultraviolet wavelengths. Nevertheless, at the low-frequency limit, i.e. in the RF regime, where the free-space wavelength of signals ranges from tens of centimeters to meters, the constituent elements of metamaterials, referred to as the metamaterial atoms, are often bulky, which hinders the implementation of scalable RF metamaterials. In addition, RF resonant structures traditionally exhibit low quality factors due to significant dissipation in their bulky structures 3,4 . Since both requirements of scalability/compactness and low dissipation have proved to be challenging to achieve for RF metamaterials, few studies have concerned metamaterials at the low-frequency part of the electromagnetic spectrum 5 . Nonetheless, RF metamaterials have been sought to improve the performance of magnetic resonance imaging (MRI) devices 6,7 , magnetoinductive lenses 8 , microwave antennas 9 , delay-lines 10 , and resonators 11 . Insofar as obtaining RF metamaterials substantially relies on the development of compact and scalable metamaterial atoms that are amenable to conventional microfabrication techniques, many superconducting structures have been recently introduced and tested for metamaterial applications in the RF/microwave regime 12-21 , motivated by their low-losses and deep sub-wavelength sizes.Recently, we have demonstrated superconducting RF metamaterials based on Niobium (Nb) spiral resonators as a viable means to realize efficient metamaterials at low frequencies presenting both a compact physical structure and low loss 22,23 . Given that Nb is a low-temperature superconductor (LTS) whose transition temperature is ∼9.2K, development of analogous superconducting metamaterial atoms capable of functioning at the temperature of liquid nitrogen, 77K, is clearly a technological advantage. Furthermore, accessing a wider range of superconducting temperature allows greater convenience and effectiveness in tuning the properties of the metamaterial ato...

Microwave bandpass filters constructed from materials exhibiting some nonlinearity, such as superconductors, will generate intermodulation distortion (IMD) when subjected to signals at more than one frequency.In commercial applications of superconductive receive filters, it is possible for IMD to be generated when a weak receive signal mixes with very strong out-of-band signals, such as those coming from the transmitter. A measurement procedure was developed and data were taken on several different types of superconducting bandpass filters, all developed for commercial application. It was found that in certain interference situations, the 3-tone mixing can produce a spur that is noticeable by the receiver, but that there are simple preventative design solutions.