  Recently reported structural complexity and superconducting transition in
lithium under pressure has increased the interest in light alkalis, otherwise
considered as simple metals and well known systems under normal conditions. In
this work we present an analysis of the pressure induced Fermi surface
deformation in lithium with increasing pressure. According to our calculations,
under pressure the Fermi surface becomes highly anisotropic and around 30 GPa
develops an extended nesting, which could be the origin of the complex phase
transitions observed at this pressure via a phonon instability. On the other
hand, the phonon softening induced by the observed distortion and nesting in
the Fermi surface could also imply an increasing electron-phonon interaction
with pressure, which might also allow a better understanding of the observed
superconducting transition in lithium at around the same pressure range.
