Superconductivity and electron-phonon coupling in lithium at high pressures

Using a first-principles pseudopotential approach we study the origin of superconductivity in lithium under pressure. A recently developed Wannier interpolation based technique that allows for ultradense sampling of electron-phonon parameters throughout the Brillouin zone was employed. The electron-phonon coupling strength as a function of pressure was calculated, precisely resolving many of the fine features of its distribution. The contributions to coupling arising from the Fermi surface topology, phonon dispersions, and electron-phonon matrix elements were separately analyzed. It is found that of the constituent components, the electron-phonon matrix elements are the most sensitive to pressure changes, and a particular phonon is responsible for high values of coupling. Additionally, the distribution of matrix elements over the Fermi surface is seen to be non-uniform and possesses a two-peak structure. Analysis of the Eliashberg spectral function ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ shows a considerable increase in spectral weight in the low-frequency region with the application of pressure. We estimate the superconducting transition temperature and find that the obtained values are in good accord with experiment.