Crossover from itinerant to localized states in the thermoelectric oxide ${\left[{\mathrm{Ca}}_2{\mathrm{CoO}}_3\right]}_{0.62}\left[{\mathrm{CoO}}_2\right]$

The layered cobaltite ${\left[{\mathrm{Ca}}_2{\mathrm{CoO}}_3\right]}_{0.62}\left[{\mathrm{CoO}}_2\right]$, often expressed as the approximate formula ${\mathrm{Ca}}_3{\mathrm{Co}}_4{\mathrm{O}}_9$, is a promising candidate for efficient oxide thermoelectrics, but an origin of its unusual thermoelectric transport is still in debate. Here we investigate in-plane anisotropy of the transport properties in a broad temperature range to examine the detailed conduction mechanism. The in-plane anisotropy between $a$ and $b$ axes is clearly observed both in the resistivity and the thermopower, which is qualitatively understood with a simple band structure of the triangular lattice of Co ions derived from the angle-resolved photoemission spectroscopy experiments. On the other hand, at high temperatures the anisotropy becomes smaller and the resistivity shows a temperature-independent behavior, both of which indicate a hopping conduction of localized carriers. Thus, the present observations reveal a crossover from low-temperature itinerant to high-temperature localized states, signifying both characters for the enhanced thermopower.

Figure 1

Schematic view of the crystal structure of layered ${\left[{\mathrm{Ca}}_2{\mathrm{CoO}}_3\right]}_{0.62}\left[{\mathrm{CoO}}_2\right]$ projected from (a) $a$ axis and (b) $c$ axis drawn by vesta [21]. While the $a$-axis lattice parameter $a$ is common, the $b$-axis lattice parameter of the rocksalt layer $b_2$ is different from that of ${\mathrm{CoO}}_2$ layer $b_1$, resulting in a misfit structure with incommensurate ratio of $b_1/b_2\simeq 0.62$. The Co ions in ${\mathrm{CoO}}_2$ (green) and rocksalt (blue) layers are shown in different colors for clarity.

Figure 2

(a) Photograph of a single crystal of ${\left[{\mathrm{Ca}}_2{\mathrm{CoO}}_3\right]}_{0.62}\left[{\mathrm{CoO}}_2\right]$ and (b) Laue pattern. (c) Photographs of samples for the resistivity measurements. Two samples with the rectangular shape of $\sim 1\times 0.3{\mathrm{mm}}^2$ were obtained by cutting one single crystal. (d) SEM image of ${\left[{\mathrm{Ca}}_2{\mathrm{CoO}}_3\right]}_{0.62}\left[{\mathrm{CoO}}_2\right]$ for the sample thickness measurement.

Figure 3

Temperature variations of (a) resistivity ${\rho }_i$ ($i=a,b$), (b) conductivity ${\sigma }_i={\rho }_i^{-1}$, and (c) thermopower $Q_i$ measured along the $a$- (red) and $b$-axis (blue) directions in ${\left[{\mathrm{Ca}}_2{\mathrm{CoO}}_3\right]}_{0.62}\left[{\mathrm{CoO}}_2\right]$.

Figure 4

Temperature variations of the transport anisotropy in (a) thermopower $Q_b/Q_a$ and (b) electrical conductivity ${\sigma }_b/{\sigma }_a$ below room temperature. The SDW transition temperature $T_{\mathrm{SDW}}\simeq 30\mathrm{K}$ and its onset $T_{\mathrm{SDW}}^{\mathrm{ON}}\simeq 100\mathrm{K}$ are indicated by the dashed lines. The insets depict these anisotropies in the whole temperature range measured in the present study.

Figure 5

(a) Constant-energy surfaces near the Fermi energy calculated by using the tight-binding model [Eq. (4)]. (b) Dispersion relations along $\mathrm{\Gamma }\to \mathrm{K}$ ($a^{*}$ direction, red) and $\mathrm{\Gamma }\to \mathrm{M}$ ($b^{*}$ direction, blue).

Figure 6

(a) Electronic velocity $v_i=1/\hslash (\partial \varepsilon /\partial k_i)$ as a function of energy measured from the Fermi energy for $a$ (red) and $b$ (blue) directions. The velocity $v_a$ ($v_b$) is calculated for $k_b=0$ ($k_a=0$). (b) A velocity ratio $x_i\equiv (v_{i,h}^2-v_{i,e}^2)/(v_{i,h}^2+v_{i,e}^2)$ for $a$ (red) and $b$ (blue) directions as a function of the energy measured from ${\varepsilon }_F$ in magnitude.