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


 * $$g_{0} = \frac{\pi^2 {k_{\rm B}}^2 T}{3h} \approx (9.464\times10^{-13} {\rm W/K}^{2})\;T$$.

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 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 = {n e^2 \over h}, $$

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



\kappa = L T \sigma = {\pi^2 k_{\rm B}^2 \over 3e^2}\times {n e^2 \over h} T = {\pi^2 k_{\rm B}^2 \over 3h} n T = g_0 n, $$

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