Compact, voltage-tunable superconducting microwave resonators on SrTiO₃substrates

Strontium Titanate (SrTiO₃) is a quantum paraelectric material with a large dielectric constant of order 10⁴ at cryogenic temperatures, which is also highly tunable by electric field. This makes SrTiO₃ an attractive material platform to develop compact and voltage tunable superconducting microwave circuits. In this study, we fabricated tunable superconducting co-planar waveguide resonators by patterning Nb thin films sputtered onto SrTiO₃ substrates. Compact resonators as short as 3.5 mm were defined, with tuning bias voltage access to both the resonator and the feedline. We measured fundamental resonance frequencies in the range of 200 to 300 MHz and internal quality factors (Qi) up to 8,000. By varying the gate voltage, we observed resonance frequency shifts of over 20 MHz. This corresponds to tuning the substrate dielectric constant between 40,000 and 45,000 by varying the electric field between the resonator and the ground plane. The combination of compact size and voltage tunability makes these resonators a promising building block for cryogenic microwave applications.