# 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 of temperature ${\displaystyle T}$. 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, which has been quantitatively measured at both cryogenic (~20 mK) [2] and room temperature (~300K)[3] [4].

## 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. Bibcode:2000Natur.404..974S. doi:10.1038/35010065. PMID 10801121.
2. ^ Jezouin, S.; et al. (2013). "Quantum Limit of Heat Flow Across a Single Electronic Channel". Science. 342: 601. arXiv:. Bibcode:2013Sci...342..601J. doi:10.1126/science.1241912. PMID 24091707.
3. ^ Cui, L.; et al. (2017). "Quantized thermal transport in single-atom junctions". Science. 355: 1192. Bibcode:2017Sci...355.1192C. doi:10.1126/science.aam6622. PMID 28209640.
4. ^ Mosso, N.; et al. (2017). "Heat transport through atomic contacts". Nature Nanotechnology. 12 (5): 430-433. arXiv:. doi:10.1038/nnano.2016.302.