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The effects of an electron-phonon ($e$-ph) interaction on the thermoelectricproperties of Na$_x$CoO$_2$ are analyzed. By means of dynamical mean fieldtheory calculations we find that the $e$-ph coupling acts in a cooperative waywith the disorder, enhancing the effective binary disorder potential strengthon the Co sites, which stems from the presence or absence of a neighboring Naatom. Hence, the inclusion of the $e$-ph coupling allows us to assume smallervalues of the binary disorder potential strength -- which for Na$_x$CoO$_2$ arein fact also more reasonable. More generally, we can conclude that theinterplay between disorder effects and coupling to the lattice can be exploitedto engineer more efficient thermoelectric materials.

Enhancement of the effective disorder potential and the thermopower in Na$_x$CoO$_2$ through the electron-phonon coupling