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

$g_{0}={\frac {\pi ^{2}{k_{\rm {B}}}^{2}T}{3h}}\approx (9.464\times 10^{-13}{\rm {W/K}}^{2})\;T$.

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

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

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

$L={\pi ^{2}k_{\rm {B}}^{2} \over 3e^{2}}.$

In the regime with quantized electric conductance, one may have

$\sigma ={ne^{2} \over h},$

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

$\kappa =LT\sigma ={\pi ^{2}k_{\rm {B}}^{2} \over 3e^{2}}\times {ne^{2} \over h}T={\pi ^{2}k_{\rm {B}}^{2} \over 3h}nT=g_{0}n,$

where $g_{0}$ is the thermal conductance quantum defined above.

See also

• Thermal transport in nanostructures