Universal Features of Quantized Thermal Conductance of Carbon Nanotubes

The universal features of quantized thermal conductance of carbon nanotubes (CNTs) are revealed through a theoretical analysis based on the Landauer theory of heat transport. The phonon-derived thermal conductance of semiconducting CNTs exhibits a universal quantization in the low-temperature limit, independent of the radius or atomic geometry. The temperature dependence follows a single curve given in terms of temperature scaled by the phonon energy gap. The thermal conductance of metallic CNTs has an additional contribution from electronic states, which also exhibits quantized behavior up to room temperature.

Figure 1

Low-energy phonon dispersion curves for a $(10,10)$ carbon nanotube. Four acoustic modes are present: a longitudinal acoustic mode, doubly degenerate transverse acoustic modes, and a twisting acoustic mode (in order from the top). The inset shows the energy gap $\hslash {\omega }_{\mathrm{o}\mathrm{p}}$ of the lowest optical modes.

Figure 2

(a) Low-temperature phonon-derived thermal conductance for various types of carbon nanotubes (CNTs) with several chiral vectors $(n,m)$. (b) Thermal conductance as a function of temperature scaled by the energy gap of the lowest optical mode.

Figure 3

Ratio of thermal conductance by electrons, ${\kappa }_{\mathrm{e}\mathrm{l}}$, to that by phonons, ${\kappa }_{\mathrm{p}\mathrm{h}}$, for a $(10,10)$ CNT. The inset gives results at low temperatures on an expanded scale.