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We have theoretically investigated thermoelectric (TE) effects of narrow-gapsingle-walled carbon nanotubes (SWCNTs) with randomly substituted nitrogen (N)impurities, i.e., N-substituted (20,0) SWCNTs with a band gap of 0.497 eV. Forsuch a narrow-gap system, the thermal excitation from the valence band to theconduction band contributes to its TE properties even at the room temperature.In this study, the N-impurity bands are treated with both conduction andvalence bands taken into account self-consistently. We found the optimal Nconcentration per unit cell, $c_{\rm opt}$, which gives the maximum powerfactor ($PF$) for various temperatures, e.g., $PF=$0.30$\rm{W/K^2m}$ with$c_{\rm opt}=3.1\times 10^{-5}$ at 300K. In addition, the electronic thermalconductivity has been estimated, which turn out to be much smaller than thephonon thermal conductivity, leading to the figure of merit as $ZT\sim 0.1$ forN-substituted (20,0) SWCNTs with $c_{\rm opt}=3.1\times 10^{-5}$ at 300K.

Optimal Thermoelectric Power Factor of Narrow-Gap Semiconducting Carbon Nanotubes with Randomly Substituted Impurities