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A potential thermoelectric material CuAlO$_2$ is theoretically studied. Wefirst construct a model Hamiltonian of CuAlO$_2$ based on the first principlesband calculation, and calculate the Seebeck coefficient. Then, we compare themodel with that of a well-known thermoelectric material Na$_x$CoO$_2$, anddiscuss the similarities and the differences. It is found that the twomaterials are similar from an electronic structure viewpoint in that they havea peculiar pudding-mold type band shape, which is advantageous asthermoelectric materials. There are however some differences, and we analyzethe origin of the difference from a microscopic viewpoint. The band shape ofCuAlO$_2$ is found to be even more ideal than that of Na$_x$CoO$_2$, and wepredict that once a significant amount of holes is doped in CuAlO$_2$,thermoelectric properties (especially the power factor) even better than thatof Na$_x$CoO$_2$ can be expected.

Pudding-mold type band in a potential thermoelectric material CuAlO$_2$ : comparison with Na$_x$CoO$_2$