High-pressure lithium as an elemental topological semimetal

Topological semimetals generally contain heavy elements. Using density-functional theoretic calculations, we predict that three dense lithium polymorphs in the pressure range 200–360 GPa display nontrivial semimetallic electronic structure. Specifically, these high-pressure phases exhibit Fermi pockets which are degenerate over a loop in $\mathit{k}$ space, around which an encircling $\mathit{k}$-space path is threaded by $\pm \pi$ Berry phase. Accordingly, these dense lithium phases are topological nodal loop semimetals involving a single light element.

Figure 1

Enthalpies of the most competitive lithium structure computed relative to the ${P4}_2/mbc$ structure.

Figure 2

Calculated electronic band structures and density of states of Li (a) Cmca-24 structure at 200 GPa, (b) Cmca-56 at 260 GPa, and (c) ${P4}_2/mbc$ at 360 GPa.

Figure 3

3D illustrations of the Li crystal structure unit cells and Fermi surfaces. The blue balls are isosurface plots of one of the Wannier functions which show electron localization in the interstitials. (a) Cmca-24 phase at 200 GPa. (b) Cmca-56 at 260 GPa, and (c) ${P4}_2/mbc$ at 360 GPa.

Figure 4

Calculated valence and conduction energy bands along (a) $k_x=k_y=0$ for the $Cmca$-24 phase at 200 GPa, (c) $k_x=k_y=0.5$ for $Cmca$-56 at 260 GPa, and (e) $k_y=0,k_z=0.5$ for $P{4}_2/mbc$ at 360 GPa. (b), (d), and (f) are energy dispersion surfaces in the $k_y=0$ plane for the $Cmca$-24, $k_y=0.5$ for $Cmca$-56, and $k_z=0.5$ for $P{4}_2/mbc$, respectively.

Figure 5

Brillouin zones, degenerate nodal loops (magenta curves) for the $Cmca$-24 (a), $Cmca$-56 (b), and $P{4}_2/mbc$ (c) phases. High-symmetry points are denoted by green points. (d) An example of the closed path $\ell$ (blue rectangle) that encircles the nodal loop $C$ (magenta loop).

Figure 6

(a) Energy dispersion of $P{4}_2/mbc$ phase at the $k_x=0$ plane. The nodal loop is depicted by a magenta line and a dashed line. (b) Eigenvalues of the symmetry operation $c$-glide plane at the $k_x=0$ plane.