Phonon heat capacity and disorder: new opportunities for performance enhancement of superconducting devices

We experimentally study for the first time the self-heating normal domain in magnetic field using nanowires made of granular NbTiN films with sub-10~nm thicknesses. Specifically, we found that at temperatures below 10 K, the heat capacity of phonons in such films is reduced with respect to predictions of the Debye model. Moreover, as the temperature decreases, the phonon heat capacity reduces quicker than the Debye prediction. These effects strengthen when the film thickness decreases. We attribute the observed reduction in the heat capacity to the size effect, which arises from the confinement of phonon modes within the grains; a phenomenon that has been predicted but not yet observed. These findings hold great importance in understanding the role of heat transport in superconducting electronic devices and have the potential for practical applications in mid-infrared photon sensing with superconducting nanowire detectors.