In physics, the thermal conductance quantum describes the rate at which heat is transported through a single ballistic phonon channel with temperature .

It is given by

.

The thermal conductance of any electrically insulating structure that exhibits ballistic phonon transport is a positive integer multiple of The thermal conductance quantum was first measured in 2000.[1] These measurements employed suspended silicon nitride (Si
3
N
4
) nanostructures that exhibited a constant thermal conductance of 16 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) [2] and room temperature (~300K).[3][4]

The thermal conductance quantum, also called quantized thermal conductance, may be understood from the Wiedemann-Franz law, which shows that

where is a universal constant called the Lorenz factor,

In the regime with quantized electric conductance, one may have

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

where is the thermal conductance quantum defined above.

See also

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. S2CID 4415638.
  2. Jezouin, S.; et al. (2013). "Quantum Limit of Heat Flow Across a Single Electronic Channel". Science. 342 (6158): 601–604. arXiv:1502.07856. Bibcode:2013Sci...342..601J. doi:10.1126/science.1241912. PMID 24091707. S2CID 8364740.
  3. Cui, L.; et al. (2017). "Quantized thermal transport in single-atom junctions" (PDF). Science. 355 (6330): 1192–1195. Bibcode:2017Sci...355.1192C. doi:10.1126/science.aam6622. PMID 28209640. S2CID 24179265.
  4. Mosso, N.; et al. (2017). "Heat transport through atomic contacts". Nature Nanotechnology. 12 (5): 430–433. arXiv:1612.04699. Bibcode:2017NatNa..12..430M. doi:10.1038/nnano.2016.302. PMID 28166205. S2CID 5418638.
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