Influence of electron-phonon coupling on superconducting contacts and the properties of superconductor-semimetal (or semiconductor) systems

Consideration of the proximity effect, electron-phonon coupling, and size-quantization results in peculiar behavior of the critical temperature $T_c$ of a contact containing superconducting and semimetal (or semiconductor) thin films. The method of thermodynamic Green's functions is applied. The dependence of $T_c$ on the thickness of the barrier is discussed. Size quantization leads to additional oscillations of $T_c$ and to the possibility of observing peculiar charge-density waves. The experimental data are discussed.