Thermal conductance and the Peltier coefficient of carbon nanotubes

The π-band structure of one-dimensional carbon nanotubes is very special. Their ballistic transport properties are studied theoretically and are found to exhibit rich magnetic-flux-dependent structures. The thermal conductance κ(φ) has many step structures caused by the Zeeman splitting; a similar effect has been found in the electrical conductance G(φ). The Peltier coefficient Π(φ) vanishes in the zero-voltage limit at any magnetic flux due to the symmetric π-band structure about the chemical potential μ=0. However, a finite Peltier effect could be observed by applying a finite voltage or by doping carbon nanotubes. Doping also causes peak structures with quantized maxima in Π(φ), as well as more step structures in κ(φ). Both the quantized peaks and the steps should be observable at T<1 K. These structures and also the validity of Wiedemann-Franz law κ(φ)≊(Formula presented)(Formula presented)(φ)/3(Formula presented) are found to depend upon the temperature, the chemical potential, the π-band property, and the Zeeman effect.