Thermal Conductance Quantum

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

:$g_ = \frac \approx (9.464\times10^ ^)\;T$.

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. 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) and room temperature (~300K).

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

:$= LT,$

where $L$ is a universal constant called the Lorenz factor,

:$L = .$

In the regime with quantized electric conductance, one may have

:$\sigma = ,$

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

:$\kappa = L T \sigma = \times T = n T = g_0 n,$

where $g_0$ is the thermal conductance quantum defined above.

See also

* Thermal transport in nanostructures

References

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Mesoscopic physics
Nanotechnology
Quantum mechanics
Condensed matter physics
Physical quantities
Heat conduction