Superconductivity and lattice instability in compressed lithium from Fermi surface hot spots

The highest superconducting temperature Tc observed in any elemental metal (Li with Tc approximately 18-20 K at pressure 35-48 GPa) is shown to arise from increasingly strong electron-phonon coupling concentrated along intersections of Kohn anomaly surfaces with the evolving Fermi surface. First-principles linear response calculations of the phonon spectrum and spectral function alpha2F(omega) reveal very strong Q- and phonon-polarization dependence of coupling strength, resulting in values of in the observed range. The sharp momentum dependence of the coupling even for the simple Li Fermi surface indicates more generally that a fine Q mesh is required for precise evaluation of lamda.