Heat Superdiffusion in Plasmonic Nanostructure Networks

The heat transport mediated by near-field interactions in networks of plasmonic nanostructures is shown to be analogous to a generalized random walk process. The existence of superdiffusive regimes is demonstrated both in linear ordered chains and in three-dimensional random networks by analyzing the asymptotic behavior of the corresponding probability distribution function. We show that the spread of heat in these networks is described by a type of Lévy flight. The presence of such anomalous heat-transport regimes in plasmonic networks opens the way to the design of a new generation of composite materials able to transport heat faster than the normal diffusion process in solids.

Figure 1

Thermal conductance $G$ in log-log scale for a chain of SiC spherical particles with different interparticle distances $h$ and different particle numbers $N$ as a function of the separation distance $\Delta x=\mid \mathbf{r}-{\mathbf{r}}^{\prime }\mid$ at temperature $T=300\mathrm{K}$. All particles are identical (radius of $R=100\mathrm{nm}$), and their electric polarizability is given by the simple Clausius-Mossotti form $\alpha =4\pi R^3[(ϵ-1)/(ϵ+2)]$ [17]. The dielectric permittivity of the particles is described by a Drude-Lorentz model [32]. The maximum distance for a given system is at half the chain length.

Figure 2

Averaged thermal conductance $⟨G⟩$ in log-log scale for clusters of SiC spherical particles as a function of the separation distance $x$ for a different filling factor $f$ and at temperature $T=300\mathrm{K}$. The statistical averaging is performed with $m=250$ realizations generated with a uniform random distribution probability. The inset shows an example of a network with a volumic fraction $f=1.5\%$ generated with $N=100$.