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Origin of the high Seebeck coefficient of the misfit [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$] cobaltate from site-specific valency and spin-state determinations

Layered misfit cobaltate [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$], which emerged as an important thermoelectric material~[A. C. Masset et al. Phys. Rev. B, 62, 166 (2000)], has been explored extensively in the last decade for the exact mechanism behind its high Seebeck coefficient. Its complex crystal and electronic structures have inhibited consensus among such investigations. This situation has arisen mainly due to difficulties in accurate identification of the chemical state, spin state, and site symmetries in its two subsystems (rocksalt [Ca$_2$CoO$_3$] and triangular [CoO$_2$]). By employing resonant photoemission spectroscopy and x-ray absorption spectroscopy along with charge transfer multiplet simulations (at the Co ions), we have successfully identified the site symmetries, valencies and spin states of the Co in both layers. Our site-symmetry observations explain the experimental value of the high Seebeck coefficient and also confirm that the carriers hop within the rocksalt layer, which is in contrast to earlier reports where hopping within triangular CoO$_2$ layer has been held responsible for the large Seebeck coefficient.