Graphite intercalation compounds under pressure: A first-principles density functional theory study

Motivated by recent experimental work, we use first-principles density functional theory methods to conduct an extensive search for low enthalpy structures of ${\mathrm{C}}_6\mathrm{Ca}$ under pressure. As well as a range of buckled structures, which are energetically competitive over an intermediate range of pressures, we show that the high-pressure system $(\gtrsim 18\mathrm{GPa})$ is unstable toward the formation of a class of layered structures, with the most stable compound involving carbon sheets containing five- and eight-membered rings. As well as discussing the energetics of the different classes of low enthalpy structures, we comment on the electronic structure of the high-pressure compound and its implications for superconductivity.

Figure 1

Low enthalpy structures of ${\mathrm{C}}_6\mathrm{Ca}$ found during the structure space search. The top panel shows the familiar $R\overline{3}m$ structure, which is stable under ambient conditions. The Ca ions (large) are situated between the layers, occupying sites above the centers of the hexagonal rings in an $\alpha \alpha$ stacking arrangement. The following two panels show lower-symmetry variants, with $C2∕m$ and $Cm$ structures, where in each case the graphene sheets are buckled (as depicted in the side views shown as insets) and the Ca ions are rearranged. While all of these buckled structures are energetically competitive, it is not possible to conclude from our calculations whether any become globally stable at intermediate pressures. The bottom two panels show structures in which the hexagonal carbon rings of the graphene sheets are transformed, by a sequence of Stone-Wales bond rotations, into five-, six-, and seven-membered $\left(Pmma\right)$ or five- and eight-membered rings $\left(Cmmm\right)$. At high enough pressure, the latter structure is expected to become globally stable.

Figure 2

(Color online) The enthalpy differences per ${\mathrm{C}}_6\mathrm{Ca}$ f.u. of our new structures, referenced to the $R\overline{3}m$ structure.

Figure 3

The band structure of the $Cmmm$ structure (left) and the corresponding “empty” structure with the metal ions removed (right). The two panels have been aligned vertically using the bottom of the sigma bands (not shown); the respective Fermi levels are indicated by dashed lines. Since the space group of this structure is almost hexagonal, we have used the corresponding notation for the points of high symmetry in the Brillouin zone and indicated the small discrepancy by using primed letters. Note the increase in the Fermi level upon intercalation, accompanied by the lowering and subsequent occupation of the dispersive interlayer band (marked by an arrow).

Figure 4

Density of states, resolved into contributions on the C and Ca atoms, corresponding to the $Cmmm$ (top) and $R\overline{3}m$ (bottom) structures, calculated at $15\mathrm{GPa}$.