Superconductive Ultra-compact Magnetically Coupled Resonator with   Twin-spiral Structure
  We describe a practical design of an ultra-compact on-chip superconductive micro-resonator as a potential magnetic element of metamaterial. The achieved resonator size with respect to the wavelength in our experiment is about {\lambda}/ 14400. The resonator consists of two superconducting Nb spirals, sandwiched face to face, with a small gap filled with dielectric. The spirals are turning in opposite directions: one clockwise, another counter-clockwise. We study the resonator spectral response and its inner modes using numerical simulation in HFSS. In experiment with a Laser Scanning Microscope (LSM) we confirm the predictions for the resonance frequencies of Nb superconductive resonator and its inner modes structures. Small size and the ease of manufacturing make the two-spiral resonator an attractive solution for superconductive filters, coupling circuits, and as a magnetic component of a metamaterial. 
A. S. Averkin, A. P. Zhuravel, A. Karpov, S. M. Anlage, and A.V.   Ustinov
cond-mat.supr-con