Mesoscopic Description of Radiative Heat Transfer at the Nanoscale

We present a formulation of the nanoscale radiative heat transfer using concepts of mesoscopic physics. We introduce the analog of the Sharvin conductance using the quantum of thermal conductance. The formalism provides a convenient framework to analyze the physics of radiative heat transfer at the nanoscale. Finally, we propose a radiative heat transfer experiment in the regime of quantized conductance.

Figure 1

Sketch of the conductance geometry: (a) Two thermal reservoirs are separated by a vacuum gap with width $d$; (b) two electron reservoirs with a voltage difference $V$ are connected through a nanowire.

Figure 2

Illustration of the contribution of (b) propagating modes ($\kappa <k_0$), (c) modes propagating in the dielectric but evanescent in the gap ($k_0<\kappa <n{k}_0$), and (d) evanescent modes confined in the gap ($\kappa >n{k}_0$).

Figure 3

Plot of ${\overline{T}}_p^{12}$ and $\exp (-2\kappa d)$ for 100 nm by choosing temperature $T=300\mathrm{K}$ and two SiC [39] slabs. The modes with $\kappa <n{k}_0$ have ${\overline{T}}_p^{12}\approx 1$. The surface phonon polaritons with $\kappa >n{k}_0$ have a relatively small MTF but give the dominant contribution to the heat flux due to the large number of contributing modes. The MTF shows for very large $\kappa$ an exponential cutoff $\propto \exp (-2\kappa d)$.

Figure 4

Plot of (a) ${\overline{T}}_p^{12}$ ($d=100\mathrm{nm}$ and $T=300\mathrm{K}$) and (b) resulting heat flux $\Phi$ for SiC and silica [40] normalized to the blackbody value ${\Phi }_{\mathrm{BB}}=459.3\mathrm{W}{\mathrm{m}}^2$.

Figure 5

Sketch of a setup suitable for measuring the quantized radiative conductance between two wires with a cross section $L\times L$.