In physics, the thermal conductance quantum g 0 {\displaystyle g_{0}} describes the rate at which heat is transported through a single ballistic phonon channel with temperature T {\displaystyle T} . It is given by
g 0 = π 2 k B 2 T 3 h ≈ ( 9.464 × 10 − 13 W / K 2 ) T {\displaystyle g_{0}={\frac {\pi ^{2}{k_{\rm {B}}}^{2}T}{3h}}\approx (9.464\times 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 . {\displaystyle g_{0}.} The thermal conductance quantum was first measured in 2000. These measurements employed suspended silicon nitride (Si3N4) nanostructures that exhibited a constant thermal conductance of 16 g 0 {\displaystyle 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
κ σ = L T , {\displaystyle {\kappa \over \sigma }=LT,}
where L {\displaystyle L} is a universal constant called the Lorenz factor,
L = π 2 k B 2 3 e 2 . {\displaystyle L={\pi ^{2}k_{\rm {B}}^{2} \over 3e^{2}}.}
In the regime with quantized electric conductance, one may have
σ = n e 2 h , {\displaystyle \sigma ={ne^{2} \over h},}
where n {\displaystyle n} is an integer, also known as TKNN number. Then
κ = L T σ = π 2 k B 2 3 e 2 × n e 2 h T = π 2 k B 2 3 h n T = g 0 n , {\displaystyle \kappa =LT\sigma ={\pi ^{2}k_{\rm {B}}^{2} \over 3e^{2}}\times {ne^{2} \over h}T={\pi ^{2}k_{\rm {B}}^{2} \over 3h}nT=g_{0}n,}
where g 0 {\displaystyle g_{0}} is the thermal conductance quantum defined above.
See also Thermal transport in nanostructures
References