Physics:Thermal conductance quantum
In physics, the thermal conductance quantum [math]\displaystyle{ g_0 }[/math] describes the rate at which heat is transported through a single ballistic phonon channel with temperature [math]\displaystyle{ T }[/math]. It is given by
- [math]\displaystyle{ g_{0} = \frac{\pi^2 {k_{\rm B}}^2 T}{3h} \approx (9.464\times10^{-13} {\rm W/K}^{2})\;T }[/math].
The thermal conductance of any electrically insulating structure that exhibits ballistic phonon transport is a positive integer multiple of [math]\displaystyle{ g_0. }[/math] The thermal conductance quantum was first measured in 2000.[1] These measurements employed suspended silicon nitride (Si3N4) nanostructures that exhibited a constant thermal conductance of 16 [math]\displaystyle{ g_0 }[/math] 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
- [math]\displaystyle{ {\kappa \over \sigma} = LT, }[/math]
where [math]\displaystyle{ L }[/math] is a universal constant called the Lorenz factor,
- [math]\displaystyle{ L = {\pi^2 k_{\rm B}^2 \over 3e^2}. }[/math]
In the regime with quantized electric conductance, one may have
- [math]\displaystyle{ \sigma = {n e^2 \over h}, }[/math]
where [math]\displaystyle{ n }[/math] is an integer, also known as TKNN number. Then
- [math]\displaystyle{ \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, }[/math]
where [math]\displaystyle{ g_0 }[/math] is the thermal conductance quantum defined above.
See also
- Thermal properties of nanostructures
References
- ↑ 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. Bibcode: 2000Natur.404..974S.
- ↑ Jezouin, S. (2013). "Quantum Limit of Heat Flow Across a Single Electronic Channel". Science 342 (6158): 601–604. doi:10.1126/science.1241912. PMID 24091707. Bibcode: 2013Sci...342..601J.
- ↑ Cui, L. (2017). "Quantized thermal transport in single-atom junctions". Science 355 (6330): 1192–1195. doi:10.1126/science.aam6622. PMID 28209640. Bibcode: 2017Sci...355.1192C. https://kops.uni-konstanz.de/bitstream/123456789/38281/1/Cui_0-399840.pdf.
- ↑ Mosso, N. (2017). "Heat transport through atomic contacts". Nature Nanotechnology 12 (5): 430–433. doi:10.1038/nnano.2016.302. PMID 28166205. Bibcode: 2017NatNa..12..430M.
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