# Thermoelectric properties of the misfit cobaltate Ca$_3$Co$_4$O$_9$

## TL;DR

This study uses density functional theory and Boltzmann transport calculations to analyze the electronic structure and thermoelectric properties of Ca$_3$Co$_4$O$_9$, revealing strain-induced anisotropy and the influence of sample inhomogeneities.

## Contribution

It provides the first detailed theoretical analysis of the strain and temperature dependence of thermoelectric properties in Ca$_3$Co$_4$O$_9$ using first-principles calculations.

## Key findings

- Strain significantly enhances thermopower in one direction while reducing it in another.
- Temperature has a weak effect on conductivity above 200 K.
- Transport properties are dominated by sample inhomogeneities, not intrinsic material behavior.

## Abstract

The layered misfit cobaltate Ca$_3$Co$_4$O$_9$, also known as Ca$_2$CoO$_3$[CoO$_2$]$_{1.62}$, is a promising p-type thermoelectric oxide. Employing density functional theory, we study its electronic structure and determine, on the basis of Boltzmann theory within the constant-relaxation-time approximation, the thermoelectric transport coefficients. The dependence on strain and temperature is determined. In particular, we find that the $xx$-component of the thermopower is strongly enhanced, while the $yy$-component is strongly reduced, when applying 2% tensile strain. A similar anisotropy is also found in the power factor. The temperature dependence of the conductivity in the $a$-$b$ plane is found to be rather weak above 200 K, which clearly indicates that the experimentally observed transport properties are dominated by inhomogeneities arising during sample growth, i.e., are not intrinsic.