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$_c$ ~ 20 K at pressure P ~ 40 GPa) is shown to arise from critical (formally divergent) electron-phonon coupling to the transverse T$_1$ phonon branch along intersections of Kohn anomaly surfaces with the Fermi surface. First principles linear response calculations of the phonon spectrum and spectral function $\alpha^2 F(\omega)$ reveal (harmonic) instability already at 25 GPa. Our results imply that the fcc phase is anharmonically stabilized in the 25-38 GPa range. 
Deepa Kasinathan, J. Kunes, A. Lazicki, H. Rosner, C. S. Yoo, R. T.   Scalettar, and W. E. Pickett