Chemical differences between K and Na in alkali cobaltates

${\mathrm{K}}_x\mathrm{Co}{\mathrm{O}}_2$ shares many similarities with ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$, as well as some important differences (no hydration-induced superconductivity has been reported). At $T_{c2}=20\mathrm{K}$, ${\mathrm{K}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$ becomes an insulator with a tiny optical gap, as happens in ${\mathrm{Na}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$ at $52\mathrm{K}$. This similarity, with a known common structure, enables direct comparisons to be made. Using the K-zigzag structure recently reported and the local density approximation, we compare and contrast these cobaltates at $x=0.5$. Although the electronic structures are quite similar as expected, substantial differences are observed near the Fermi level. These differences are found to be attributable mostly to the chemical rather than the structural difference. Although Na is normally considered to be fully ionic, K has a somewhat more highly ionic character than does Na in these cobaltates.

Figure 1

(Color online) Enlarged band structures of nonmagnetic ${\mathrm{K}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$ at the $t_{2g}$ manifold regime. The large $t_{2g}\text{−}{e}_g$ crystal field splitting of $2.5\mathrm{eV}$ makes the $e_g$ manifold (not shown here) unimportant for low energy excitations. The thickened (and colored) lines highlight bands having strong Co $a_g$ character. The $S$ point is a zone boundary along the ⟨110⟩ direction. The horizontal dashed line indicates the Fermi energy $E_F$ (set to zero).

Figure 2

(Color online) Fermi surfaces of nonmagnetic ${\mathrm{K}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$, showing a strong two dimensionality. The band structure leads to six Fermi surfaces (FSs), but the first and sixth FSs are not shown here. The first FS is similar to (a), except for a smaller cap at the $Z$ points. The sixth FS has the same shape as (d), but it has no $\Gamma$ centered egg. The pink (darker) colored surfaces contain holes, whereas the green (lighter) colored surfaces hold electrons.

Figure 3

(Color online) A comparison of electronic structure between nonmagnetic ${\mathrm{K}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$ and ${\mathrm{Na}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$. Top: Enlarged band structures near $E_F$. Differences between the band structures are more noticeable at $E_F$, particularly at the $X$ and $Y$ points and along the $\Gamma \text{−}Z$ line. Bottom: Total densities of states per formula unit at the $t_{2g}$ manifold. ${\mathrm{K}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$ has about 10% larger $N\left(0\right)$ than 5.4 states/eV per formula unit of ${\mathrm{Na}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$ (but invisible in this figure). The vertical dashed line denotes $E_F$.

Figure 4

(Color online) Comparison of band structure between nonmagnetic ${\mathrm{K}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$ and ${\mathrm{Na}}_{0.5}\mathrm{Co}{\mathrm{O}}_2^{*}$ near $E_F$. ${\mathrm{Na}}_{0.5}\mathrm{Co}{\mathrm{O}}_2^{*}$ is assumed to have the same crystal structure as ${\mathrm{K}}_{0.5}\mathrm{Co}{\mathrm{O}}_2$ in order to investigate pure effects of K substitution.