Origin of Transitions between Metallic and Insulating States in Simple Metals

Unifying principles that underlie recently discovered transitions between metallic and insulating states in elemental solids under pressure are developed. Using group theory arguments and first-principles calculations, we show that the electronic properties of the phases involved in these transitions are controlled by symmetry principles. The valence bands in these systems are described by simple and composite band representations constructed from localized Wannier functions centered on points unoccupied by atoms, and which are not necessarily all symmetrical. The character of the Wannier functions is closely related to the degree of $s\text{−}p(\text{−}d)$ hybridization and reflects multicenter chemical bonding in these insulating states. The conditions under which an insulating state is allowed for structures having an integer number of atoms per primitive unit cell as well as reentrant (i.e., metal-insulator-metal) transition sequences are detailed, resulting in predictions of behavior such as phases having band-contact lines. The general principles developed are tested and applied to the alkali and alkaline earth metals, including elements where high-pressure insulating phases have been reported (e.g., Li, Na, and Ca).

Figure 1

Electronic properties of $hP4\text{−}\mathrm{Li}$ for lattice parameters $a=2.784\AA$,$c=3.873\AA$ (90 GPa). The parameters are intentionally kept the same as for $hP4\text{−}\mathrm{Na}$ at 320 GPa (see Ref. 4). (a) Band structure; the size of red circles is proportional to the $s$ character of the Bloch wave functions. (b),(c) Valence charge density and crystal potential in the (110) plane, respectively. The ions are centered in the blue regions.

Figure 2

Bottom and top valence band wave functions at $\mathrm{\Gamma }$ in $hP4\text{−}\mathrm{Na}$ at 320 GPa (corresponding to ${\mathrm{\Gamma }}_1^{+}$ and ${\mathrm{\Gamma }}_4^{-}$ energy levels) in the primitive unit cell. (a),(b) Isocontours of ${\mathrm{\Gamma }}_1^{+}$ at $\pm 2.5$ and $\pm 1.1$, respectively (yellow for $+$ and light blue for $-$). (c),(d) Same as (a),(b) but for ${\mathrm{\Gamma }}_4^{-}$.

Figure 3

Bottom and top valence band wave functions at $\mathrm{\Gamma }$ in $Aba2\text{−}\mathrm{Li}$ at 80 GPa in the primitive unit cell. (a),(b) Isocontours of the bottom wave function at $\pm 1.2$ and $\pm 1.1$, respectively. (c),(d) Same as (a),(b) but for the top wave function at $\pm 1.8$ and $\pm 1.2$.

Figure 4

Electronic properties of fcc-Ca at $a=4.706\AA$ and 19.0 GPa. (a) Band structure. (b) Valence charge density in the (100) planes passing through the Ca atoms ($\text{electrons}/{\text{Bohr}}^3$).