Thermal conductivity of zigzag single-walled carbon nanotubes: Role of the umklapp process

Considering the three-phonon process, we calculate the thermal conductivity of zigzag tubes. It is found that thermal conductivity of an isolated (6, 0) single-walled carbon nanotube increases with the increase of temperature at low temperature, and would show a peak behavior at about 85 K before falling off at high temperature. Moreover, thermal conductivity is high for single-walled carbon nanotubes with small diameters as compared to the tubes with large diameters. The thermal conductivity at 300 K is approximately inversely proportional to the tube's diameter.