Calculating thermopower due to fluctuation-assisted tunnelling with application to carbon nanotube ropes

We show how Shengʹs theory of fluctuation-assisted tunnelling can be used to calculate thermopower due to the presence of quantum mechanical tunnelling barriers. For a hole-like situation, this calculated thermopower behaviour increases approximately linearly with increasing temperature (commencing from zero in the zero temperature limit) until a knee is reached, after which the thermopower continues to increase linearly but with a reduced slope. In Shengʹs theory, the amplitude for the barrier fluctuations increases with increasing temperature and the knee occurs when the thermal fluctuations become comparable to the magnitude of the tunnelling barriers. Interestingly, this thermopower behaviour compares quite favourably with that measured for systems of metallic single-walled carbon nanotubes (SWCNs) and, in particular, the knee seen in the temperature dependence of the carbon nanotube thermopower data at T∼100 K arises naturally in our calculation. For a system of carbon nanotubes, tunnelling barriers could occur either between individual carbon nanotubes or else due to defects within the carbon nanotubes.