Phonon Damping of Virtual Levels in Thick Superconducting Films

Abstract

By virtue of their sensitivity to incoherent scattering, virtual-state resonances observed by tunneling into thick-film elemental superconductors provide a superior probe of the electron-phonon interaction at low energies where relatively few phonon modes participate. In strong-coupling and intermediate-coupling systems, spontaneous phonon emission progressively limits quasi particle mean-free-paths with increasing energy, causing resonance amplitudes to fall below those predicted for the weak-coupling limit. Accelerated damping of virtual-state oscillations at higher junction biases provides a practical basis for experimental determination of Im{Z(ω)[ ω²−Δ²(ω)]^1/2} which in turn permits α²F(ω), Im{Z(ω)} and Im{Δ(ω)} to be inferred by means of the ELIASHBERG equations. This approach has proven considerably more sensitive than the familiar tunneling method of ROWELL and McMILLAN, and generally tends to augment the latter at low energies. Experimental results obtained with very thick In films exhibit substantial phonon damping compared to those obtained with thick Al films. The coefficinet g₀ appearing in α²F(ω)≐g₀ ω² determined for In by the present method is found to be substantially smaller than that inferred from earlier tunneling studies, as are the quantities Im{Z(ω)} and Im{Δ(ω)}.