Novel electronic states realized by the interplay between Li diffusion and Co$^{\rm 3+}$$/$Co$^{\rm 4+}$ charge ordering in Li$_{\rm x}$CoO$_2$

Measurements of dc magnetization ($M$) and electrical resistivity ($\rho$) have been carried out as a function of temperature ($T$) for layered oxide Li$_{\rm x}$CoO$_2$ (0.51$\leq$$x$$\leq$1.0) using single crystal specimens. After slow cool of the specimens down to 10 K, both of the $M$($T$) and $\rho$($T$) curves are found to exhibit a clear anomaly due to the occurrence of Co$^{\rm 3+}$$/$Co$^{\rm 4+}$ charge ordering (CO) at $T_{\rm S}$$\sim$155 K for 0.6$\leq$$x$$\leq$0.98 (at $T_{\rm S}$$\sim$180$-$190 K for 0.5$\leq$$x$$\leq$0.55). After rapid cool of the specimens, additional anomalies are observed related to the onset of Li diffusion at $T_{\rm F1}$$\sim$370 K and$/$or $T_{\rm F2}$=120$-$130 K. Due to phase mixing with compositions of nearly LiCoO$_2$ and Li$_{\rm 2/3}$CoO$_2$, the specimens with 0.7$\lesssim$$x$$\lesssim$0.9 show anomlies both at $T_{\rm F1}$ and $T_{\rm F2}$. For 0.6$\lesssim$$x$$\lesssim$0.9, the resistivity measured after rapid cool is found to be fairly larger than that measured after slow cool below $T_{\rm S}$. The enhanced resistivity can be explained by the scenario that disordered Co$^{\rm 3+}$$/$Co$^{\rm 4+}$ arrangements, which have been observed and revealed to have an insulating electronic structure contrasting to the regular CO state in the previous scanning tunneling microscopy measurements [Phys. Rev. Lett. {\bf 111}, 126104 (2013)], are realized due to the formation of an amorphous-like structure of Li ions after rapid cool via the interlayer Coulomb coupling. An electronic phase diagram for 0.5$\leq$$x$$\leq$1.0 is proposed.