  Transparent conducting oxides (TCOs) are essential components of
optoelectronic devices and various materials have been explored for highly
efficient TCOs having a combination of high transmittance and low sheet
resistance. Here, we focus on a misfit thermoelectric oxide
[Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$] and fabricate the transparent low-layered
crystals by a mechanical tape-peeling method using the single-crystalline
samples. From the transmittance measurement, we find that the thickness of
low-layered samples is several orders of hundred nanometers, which is
comparable with the estimation from the scanning electron microscopy images.
Compared to the previous results on the polycrystalline and $c$-axis oriented
transparent films, the electrical resistivity is reduced owing to the
single-crystalline nature. The figure of merit for the transparent conducting
materials in the present low-layered samples is then evaluated to be higher
than the values in the previous reports. The present results on the low-layered
single-crystalline [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$] may offer a unique class
of multi-functional transparent thermoelectric oxides.
