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

The highest superconducting temperature T-c observed in any elemental metal (Li with T-c similar to 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 alpha F-2(omega) reveal very strong Q- and phonon-polarization dependence of coupling strength, resulting in values of T-c 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 lambda.