Superconductivity in lithium under high pressure investigated with density functional and Eliashberg theory

Structural phase transitions and superconducting properties in three phases (9R, fcc, and cI16) of solid Li are investigated using a pseudopotential plane-wave method based on density functional perturbation theory. In particular, it is shown that phonon softening is responsible for a pressure-induced fcc -> cI16 transition as well as for a significant enhancement of electron-phonon coupling and superconducting transition temperature T-c preceding this structural transformation. The nature of superconductivity in the fcc and cI16 phases is examined by solving the Eliashberg equations with the spectral function alpha F-2(omega) obtained from first-principles calculations and by evaluating the functional derivative delta T-c/delta alpha F-2(omega). The calculated T-c reaches a maximum at pressure close to the fcc -> cI16 transition and is significantly reduced in the cI16 phase, in agreement with the trend observed experimentally. The variation in T-c as a function of pressure is explained in terms of the functional derivative and shifts of the spectral weight.