Thermal Conductance Quantum
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In physics, the thermal conductance quantum g_0 describes the rate at which
heat In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...
is transported through a single ballistic
phonon A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined a ...
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 The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...
.


Relation to the quantum of electrical conductance

For ballistic electrical conductors, the
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
contribution to the thermal conductance is also quantized as a result of the electrical
conductance quantum The conductance quantum, denoted by the symbol , is the quantized unit of electrical conductance. It is defined by the elementary charge ''e'' and Planck constant ''h'' as: : G_0 = \frac = 4 \alpha \epsilon_0 c = It appears when measuring the co ...
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

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