Thermal conductance quantum

In physics, the thermal conductance quantum $g_0$ describes the rate at which heat is transported through a single ballistic phonon channel with temperature $T$. It is given by

$g_0=\frac{{\pi }^2{k_{\mathrm{B}}}^{2}T}{3h}\approx (9.464\times 10^{-13}{\mathrm{W}/\mathrm{K}}^2)T$.

The thermal conductance of any electrically insulating structure that exhibits ballistic phonon transport is a positive integer multiple of $g_0.$ The thermal conductance quantum was first measured in 2000. These measurements employed suspended silicon nitride (Si
₃N
₄) nanostructures that exhibited a constant thermal conductance of 16 $g_0$ at temperatures below approximately 0.6 kelvin.

Relation to the quantum of electrical conductance

For ballistic electrical conductors, the electron contribution to the thermal conductance is also quantized as a result of the electrical conductance quantum and the Wiedemann–Franz law, which has been quantitatively measured at both cryogenic (~20 mK) and room temperature (~300K). The thermal conductance quantum, also called quantized thermal conductance, may be understood from the Wiedemann-Franz law, which shows that

$\frac{\kappa }{\sigma }=LT,$

where $L$ is a universal constant called the Lorenz factor,

$L=\frac{{\pi }^2{k}_{\mathrm{B}}^2}{3e^2}.$

In the regime with quantized electric conductance, one may have

$\sigma =\frac{n{e}^2}{h},$

where $n$ is an integer, also known as TKNN number. Then

$\kappa =LT\sigma =\frac{{\pi }^2{k}_{\mathrm{B}}^2}{3e^2}\times \frac{n{e}^2}{h}T=\frac{{\pi }^2{k}_{\mathrm{B}}^2}{3h}nT=g_{0}n,$

where $g_0$ is the thermal conductance quantum defined above.

See also

• Thermal transport in nanostructures