  We demonstrate impedance-matched low-loss transmission lines with a signal
wavelength more than 150 times smaller than the free space wavelength using
superconducting nanowires on high permittivity substrates. A niobium nitride
thin film is patterned in a coplanar waveguide (CPW) transmission line geometry
on a bilayer substrate consisting of 100 nm of epitaxial strontium titanate on
high-resitivity silicon. The use of strontium titanate on silicon enables
wafer-scale fabrication and maximizes process compatibility. It also makes it
possible to realize a $50$ $\Omega$ characteristic impedance across a wide
range of CPW widths, from the nanoscale to the macroscale. We fabricated and
characterized an approximately $50$ $\Omega$ CPW device with two half-wave stub
resonators. Comparing the measured transmission coefficient to numerical
simulations, we determine that the strontium titanate film has a dielectric
constant of $1.1 \times 10^3$ and a loss tangent of not more than 0.009. To
facilitate the design of distributed microwave devices based on this type of
material system, we describe an analytical model of the CPW properties that
gives good agreement with both measurements and simulations.

Superconductivity;Mesoscale and Nanoscale Physics;Applied Physics