Tc map and superconductivity of simple metals at high pressure

We calculate Tc map in region of weak electron-phonon coupling based on simple phonon spectrum. By using linear-response method and density functional theory, we calculate phonon spectra and Eliashberg functions of simple metals under pressure. Based on the evolutions of superconducting parameters of simple metals on the Tc map with increasing pressure, we find that there are two different responses to pressure for simple metals: (1) enhancing electron-phonon interaction $\lambda$ such as for La and Li, (2) increasing phonon frequency such as for Pb, Pt. The $\lambda$ threshold effect is found, which origins from the competition between electron-phonon interaction and electron-electron Coulomb interaction and is the reason why Tc of most superconductors of simple metals are higher than 0.1K.