The main result of this paper is simple: very clean thin films of titanium nitride (TiN), grown by molecular beam epitaxy (MBE) on sapphire, make superconducting microwave resonators with extremely low loss. The authors report internal quality factors Qi above 1,000,000 in the single‑photon limit (average photon number ⟨n⟩ ≈ 1) at 5.8 GHz and a temperature of 10 millikelvin. At high drive powers (⟨n⟩ ≈ 106) Qi rises to more than 20 × 106.

To make the films the team grew 50 nm of TiN on c‑plane sapphire using MBE. Molecular beam epitaxy is a slow, highly controlled way to deposit atoms layer by layer. The growth was done at about 600 °C with a titanium to active nitrogen flux tuned to give roughly 2.5 nm per minute. Structural probes show the films are highly crystalline. High‑resolution X‑ray diffraction (XRD) gives a rocking‑curve full‑width at half‑maximum (FWHM) of 18 arcseconds — the smallest value reported so far for TiN thin films. Scanning transmission electron microscopy (STEM) with multislice electron ptychography shows an atomically sharp interface between TiN and sapphire.

Despite the sharp interface, detailed imaging revealed defects below the sapphire surface that seed dislocations in the TiN layer. The films also show twin domains and columnar growth, features linked to the chosen growth temperature and nitrogen‑rich conditions. The authors note that the exact origin of the substrate subsurface defects is not known; such damage can come from commercial polishing and can be reduced by annealing. The effect of the measured rocking‑curve width and the surface roughness on microwave loss is not yet established.

To test microwave performance the researchers patterned quarter‑wavelength coplanar waveguide (CPW) resonators in a 3 µm/6 µm/3 µm gap/strip/gap geometry and measured them in a dilution refrigerator at 10 mK. Two chips were processed with slightly different photoresist stripping steps. The measurement chain used standard microwave attenuation, filtering, and isolation. Importantly, the high Qi values were obtained without any intentional chemical removal of surface oxides nor deep over‑etch into the substrate.