Interaction of 9.3-GHz Longitudinal Phonons with Electrons in Superconducting Films

Previous studies of the interaction of longitudinal phonons with superconducting Al-Pb junctions have been extended to include nonuniform strains, arising when the thicknesses of the metal films are not negligible compared to the wavelength of the sound and/or when the wave front makes a small angle $\theta$ with the plane of the junction. It is found that nonuniform strains produce an electric field proportional to the strain gradient inside the "local" superconducting Al film. This result confirms the theories of Dessler et al., Hearing, and Harrison who calculated the gravity-induced electric fields. The strain-induced field in the aluminum excites electromagnetic waves in the junction which are enhanced due to the traveling-wave interaction in the strip line formed by the junction. The electromagnetic field gives rise to an extra tunneling current which exhibits resonant behavior as a function of the angle $\theta$. In the "nonlocal" Pb films, the interaction of the electrons with the strain wave is described by absorption and emission of phonons, and the extra tunneling current due to this process is essentially independent of $\theta$. This behavior enables us to separate the extra current due to the Al film and that due to the Pb film. The agreement between theory and experiment is found satisfactory.