# Thermal conductance quantum

In physics, the thermal conductance quantum ${\displaystyle g_{0}}$ describes the rate at which heat is transported through a single ballistic phonon channel. It is given by:

${\displaystyle g_{0}={\frac {\pi ^{2}{k_{B}}^{2}T}{3h}}\approx (9.456\times 10^{-13}W/K^{2})T}$.

The thermal conductance of any electrically insulating structure that exhibits ballistic phonon transport is a positive integer multiple of ${\displaystyle g_{0}}$. The thermal conductance quantum was first measured in 2000.[1] These measurements employed suspended silicon nitride nanostructures that exhibited a constant thermal conductance of 16${\displaystyle g_{0}}$ at temperatures below approximately 0.6 kelvin.

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.

## References

1. ^ Schwab, K.; E. A. Henriksen; J. M. Worlock; M. L. Roukes (2000). "Measurement of the quantum of thermal conductance". Nature. 404 (6781): 974–7. doi:10.1038/35010065. PMID 10801121.