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The well-known Mott's formula links the thermoelectric power characterised bySeebeck coefficient to conductivity. We calculate analytically thethermoelectric current and Seebeck coefficient in one-dimensional systems andshow that, while the prediction of Mott's formula is valid for Dirac fermions,it is misleading for the carriers having a parabolic dispersion. We apply thedeveloped formalism to metallic single wall carbon nanotubes and obtain anon-trivial non-monotonic dependence of the Seebeck coefficient on the chemicalpotential. We emphasize that, in contrast to the Mott's formula, the classicalKelvin's formula that links thermoelectric power to the temperature derivativeof the chemical potential is perfectly valid in carbon nanotubes in theballistic regime. Interestingly, however, the Kelvin's formula fails in two-and three-dimensional systems in the ballistic regime.

Failure of the Mott's formula for the Thermopower in Carbon Nanotubes