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Heat Superdiffusion in Plasmonic Nanostructure Networks

Abstract : 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. It is commonly admitted that heat conduction in a bulk solid is governed by a normal diffusion process. Heat carriers (phonons or electrons) move through the atomic lattice of material following a random walk [1] with a step length probability density which is a Gaussian. The heat spatial spreading from regions of high temperature to regions of low temperature is therefore intrinsically limited both by the speed of heat carriers and by the distance covered by them between two successive collision events. To go beyond this transport mechanism and accelerate the heat propagation within the medium, we propose here to add a supplementary channel for heat exchanges with long-range interactions such as those that exist in generalized random walks (GRW), processes where the step length probability is broadband. Lévy flights [2,3] are probably the most famous class of GRW in which extremely long jumps can occur as well as very short ones. The existence of photonic Lévy flights has been recently demonstrated [4] in self-similar materials, the so-called Lévy glasses. In those media, appropriately engineered so that photons perform random jumps with a probability distribution of step lengths which decays algebraically, the transport of propagative photons becomes superdiffusive. However, the magnitude of heat flux which can be transported with radiative photons is limited by the famous Stefan-Boltzmann law [5] and is several orders of magnitude smaller than the flux carried by conduction in solids. The situation radically changes when these photons become nonradiative. As predicted by Polder and Van Hove [6] 40 years ago and experimentally verified during the last few years [7–10], when two media out of thermal equilibrium are separated by a small distance (compared with their thermal wavelength), they exchange energy mainly by photon tunneling. In such a situation, the heat flux transported from one medium to the other one can surpass by several orders of magnitude the flux exchanged between two blackbodies [11,12] in the far field. In two recent works [13,14], we have established that a similar exalted heat transport can also exist at larger distances, thanks to many-body interactions. In this Letter, we investigate in detail how heat is transported throughout different plasmonic nanostructure networks which are either ordered or disordered. By analyzing the transport process through these structures as a GRW of a passive tracer in a medium, we demonstrate the existence of anomalous (superdiffusive) regimes driven by the collective near-field interactions. To start this analysis, let us consider a three-dimensional network of spherical particles of radius R i at temperature T i , distributed inside an environment at temperature T env. When the mean separation distance between two arbitrary particles is larger than their respective diameters and their size is small enough compared with the thermal wavelengths T i ¼ c@=ðk B T i Þ, then this network can be modeled by a set of pointlike dipoles in mutual interaction and coupled to the surrounding bath. The time evolution of particle temperatures is governed by the following energy balance:
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Philippe Ben-Abdallah, Riccardo Messina, Svend-Age Biehs, Maria Tschikin, Karl Joulain, et al.. Heat Superdiffusion in Plasmonic Nanostructure Networks. Physical Review Letters, American Physical Society, 2013, 111 (17), pp.174301. ⟨10.1103/PhysRevLett.111.174301⟩. ⟨hal-01334889⟩

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