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Measurements of dc magnetization ($M$) and electrical resistivity ($\rho$)have been carried out as a function of temperature ($T$) for layered oxideLi$_{\rm x}$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 occurrenceof Co$^{\rm 3+}$$/$Co$^{\rm 4+}$ charge ordering (CO) at $T_{\rm S}$$\sim$155 Kfor 0.6$\leq$$x$$\leq$0.98 (at $T_{\rm S}$$\sim$180$-$190 K for0.5$\leq$$x$$\leq$0.55). After rapid cool of the specimens, additionalanomalies are observed related to the onset of Li diffusion at $T_{\rmF1}$$\sim$370 K and$/$or $T_{\rm F2}$=120$-$130 K. Due to phase mixing withcompositions of nearly LiCoO$_2$ and Li$_{\rm 2/3}$CoO$_2$, the specimens with0.7$\lesssim$$x$$\lesssim$0.9 show anomlies both at $T_{\rm F1}$ and $T_{\rmF2}$. For 0.6$\lesssim$$x$$\lesssim$0.9, the resistivity measured after rapidcool is found to be fairly larger than that measured after slow cool below$T_{\rm S}$. The enhanced resistivity can be explained by the scenario thatdisordered Co$^{\rm 3+}$$/$Co$^{\rm 4+}$ arrangements, which have been observedand revealed to have an insulating electronic structure contrasting to theregular CO state in the previous scanning tunneling microscopy measurements[Phys. Rev. Lett. {\bf 111}, 126104 (2013)], are realized due to the formationof an amorphous-like structure of Li ions after rapid cool via the interlayerCoulomb coupling. An electronic phase diagram for 0.5$\leq$$x$$\leq$1.0 isproposed.

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