  Two-level systems (TLS) are an important, if not dominant, source of loss and
noise for superconducting resonators such as those used in kinetic inductance
detectors and some quantum information science platforms. They are similarly
important for loss in photolithographically fabricated superconducting
mm-wave/THz transmission lines. For both lumped-element and transmission-line
structures, native amorphous surface oxide films are typically the sites of
such TLS in non-microstripline geometries, while loss in the (usually
amorphous) dielectric film itself usually dominates in microstriplines. We
report here on the demonstration of low TLS loss at GHz frequencies in
hydrogenated amorphous silicon (a-Si:H) films deposited by plasma-enhanced
chemical vapor deposition in superconducting lumped-element resonators using
parallel-plate capacitors (PPCs). The values we obtain from two recipes in
different deposition machines, 7$\,\times\,10^{-6}$ and 12$\,\times\,10^{-6}$,
improve on the best achieved in the literature by a factor of 2--4 for a-Si:H
and are comparable to recent measurements of amorphous germanium. Moreover, we
have taken care to extract the true zero-temperature, low-field loss tangent of
these films, accounting for temperature and field saturation effects that can
yield misleading results. Such robustly fabricated and characterized films
render the use of PPCs with deposited amorphous films a viable architecture for
superconducting resonators, and they also promise extremely low loss and high
quality factor for photolithographically fabricated superconducting mm-wave/THz
transmission lines used in planar antennas and resonant filters.
