Thermal conductance and the Peltier coefficient of carbon nanotubes

Abstract

The pi-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 kappa(phi) has many step structures caused by the Zeeman splitting; a similar effect has been found in the electrical conductance G(phi). The Peltier coefficient Pi(phi) vanishes in the zero-voltage limit at any magnetic flux due to the symmetric pi-band structure about the chemical potential mu=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 Pi(phi), as well as more step structures in kappa(phi). Both the quantized peaks and the steps should be observable at T<1 K. These structures and also the validity of Wiedemann-Franz law kappa(phi)approximate to pi(2)k(B)(2)TG(phi)/3e(2) are found to depend upon the temperature, the chemical potential, the pi-band property, and the Zeeman effect.