Thermal conductance quantum explained

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} = (\pi ^{2} {k _{\rm})/(^{2}) T}{ 3 h} ≈ ( 9 . 464 x 10 ^{-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.^[1] 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) ^[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

{\kappa \over \sigma} = LT,

where

L is a universal constant called the Lorenz factor,L = {\pi ^{2} k ^{2} _{\rm B} \over 3 e ^{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 ^{2} _{\rm B} \over 3 e ^{2} x} {n e ^{2} \over h} T = {\pi ^{2} k ^{2} _{\rm B} \over 3 h} n T = g _{0} n,

where

g _{0} is the thermal conductance quantum defined above.

See also

• Thermal transport in nanostructures

Notes and References

1. Measurement of the quantum of thermal conductance. Nature. 2000. K.. Schwab. E. A. Henriksen . J. M. Worlock . M. L. Roukes . 404. 974–7. 10.1038/35010065. 10801121. 6781. 2000Natur.404..974S. 4415638.
2. Quantum Limit of Heat Flow Across a Single Electronic Channel. Science. 2013. S. . etal . Jezouin . 342. 6158. 601–604. 10.1126/science.1241912. 24091707. 1502.07856. 2013Sci...342..601J. 8364740.
3. Quantized thermal transport in single-atom junctions. Science. 2017. L. . etal . Cui. 355. 6330. 1192–1195. 10.1126/science.aam6622. 28209640. 2017Sci...355.1192C. 24179265. free.
4. Mosso . N. . etal . Heat transport through atomic contacts . Nature Nanotechnology . 2017 . 12 . 5 . 430–433 . 10.1038/nnano.2016.302 . 28166205 . 1612.04699 . 2017NatNa..12..430M . 5418638 .