Tomasch Oscillations in the Density of States of Superconducting Films

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Abstract
The mechanism which gives rise to the oscillatory structure in the quasiparticle density of states of superconducting films with spatially varying electron-electron interaction is discussed. It is shown that the Tomasch effect results from processes in which a quasiparticle is condensed into the sea of Cooper pairs, leaving behind a different but degenerate quasiparticle. The tunneling density of states is obtained for a composite two-region superconductor. The nature of the density-of-states structure depends strongly upon the ratio of the energy gaps of the two regions. In the low-energy range, bound eigenstates characterized by the quantization of the difference of the momenta of the degenerate quasiparticles are found for infinite mean free path. Explicit results are presented for the composite film systems In-Al and In-Pb for several values of the elctron mean free path.