A nonequilibrium Green's function study of thermoelectric properties in single-walled carbon nanotubes

The phonon and electron transport in single-walled carbon nanotubes (SWCNT) are investigated using the nonequilibrium Green's function approach. In zigzag SWCNT ($n$, 0) with $mod(n,3)\not=0$, the thermal conductance is mainly attributed to the phonon transport, while the electron only has few percentage contribution. The maximum value of the figure of merit ($ZT$) is about 0.2 in this type of SWCNT. The $ZT$ is considerably larger in narrower SWCNT because of enhanced Seebeck coefficient. $ZT$ is smaller in the armchair SWCNT, where Seebeck coefficient is small due to zero band gap. It is found that the cluster isotopic doping can reduce the phonon thermal conductance obviously and enhance the value of $ZT$. The uniaxial elongation and compress strain depresses phonons in whole frequency region, leading to the reduction of the phonon thermal conductance in whole temperature range. Interestingly, the elongation strain can affect the phonon transport more seriously than the compress strain, because the high frequency $G$ mode is completely filtered out under elongation strain $\epsilon >0.05$. The strain also has important effect on the subband edges of the electron band structure by smoothing the steps in the electron transmission function. The $ZT$ is decreased by strain as the reduction in the electronic conductance overcomes the reduction in the thermal conductance.