Of Mgb <sub> 2 </ Sub> Superconducting Thin Films, Quantum Size Effect

Using the pseudopotential method based on the first-principle calculation, the MgB₂ films from three mololayer to nineteen mololayer are studied respectively in the B terminated and Mg terminated. We study their interlayer relaxtions, the density of states, the quantum well, the incremental energy, the total energy. Because of the quantum size effects, the interlayer relaxtions, the electron energy of occupied quantum well states, the density of states at Fermi level and the incremental energy, all of them exhibit oscillatory behavior with the number of MgB₂ film. Furthermore, the stability of films is analyzed.Using the density-functional perturbation theory by the linear response method, the lattice dynamics and the electron-phonon interaction of MgB₂ film from three mololayer to nine mololayer respective in the B terminated and Mg terminated are calculated. We study the surface modes, the density of states of phonon and Eliashberg spectrum function. The vibrational frequencies at theΓpoint of MgB₂ film of nine mololayer are given. The calculated electron-phonon coupling constant exhibits oscillatory behavior with the number of MgB₂ film. For B terminated films, the phonons in the outmost B layer become soft and this softness increase the electron-phonon interaction, resulting in the enhancement of the superconductivity of MgB₂ film. But for Mg terminated films, the phonons in the sublayer B layer become stiff, resulting in the decrease of the electron-phonon interaction.