  Lithium, a prototypical simple metal under ambient conditions, has a
surprisingly rich phase diagram under pressure, taking up several structures
with reduced symmetry, low coordination numbers, and even semiconducting
character with increasing density. Using first-principles calculations, we
demonstrate that some predicted high-pressure phases of elemental Li also host
topological electronic structures. Beginning at 80 GPa and coincident with a
transition to the Pbca phase, we find Li to be a Dirac nodal line semimetal. We
further calculate that Li retains linearly-dispersive energy bands in
subsequent predicted higher pressure phases, and that it exhibits a Lifshitz
transition between two Cmca phases at 220 GPa. The Fd-3m phase at 500 GPa forms
buckled honeycomb layers that give rise to a Dirac crossing 1 eV below the
Fermi energy. The well-isolated topological nodes near the Fermi level in these
phases result from increasing p-orbital character with density at the Fermi
level, itself a consequence of rising 1s core wavefunction overlap, and a
preference for nonsymmorphic symmetries in the crystal structures favored at
these pressures. Our results provide evidence that under pressure, bulk 3D
materials with light elements, or even pure elemental systems, can undergo
topological phase transitions hosting nontrivial topological properties near
the Fermi level with measurable consequences; and that, through pressure, we
can access these novel phases in elemental lithium.
