Ballistic near-field heat transport in dense many-body systems

Radiative heat transport mediated by near-field interactions is known to be superdiffusive in dilute, many-body systems. Here we use a generalized Landauer theory of radiative heat transfer in many-body planar systems to demonstrate a nonmonotonic transition from superdiffusive to ballistic transport in dense systems. We show that such a transition is associated to a change of the polarization of dominant modes. Our findings are complemented by a quantitative study of the relaxation dynamics of the system in the different regimes of heat transport. This result could have important consequences on thermal management at nanoscale of many-body systems.

Figure 1

(a) Schematic of an $N$-body system comprising $N-2$ planar slabs (purple) interacting with one another and with two external slabs at fixed temperatures $T_1$ (red) and $T_N$ (blue). All internal separation distances $d$ are identical while the coupling to the external thermostats depends on the separation distance $D$. In the steady state, each internal slab reaches a local equilibrium temperature $T_j^{\mathrm{eq}}$. (b) Steady-state temperature profile as a function of the normalized position $z_j/z_N$ for a system of $N=60$ SiC slabs of thickness 200 nm, for different $d$ and fixed $D=500\mathrm{nm}$. The inset shows the ratio of the effective internal conductivities ${\kappa }_j/{\kappa }_1$ (see text).

Figure 2

Heat-transfer coefficients $h_{\ell ,j}$ (see text) with respect to the normalized separation $z_{\ell ,j}/z_N$, for fixed values of $j$ and $D=500\mathrm{nm}$, and three values of (a) $d=500\mathrm{nm}$, (b) $d=40\mathrm{nm}$, and (c) $d=5\mathrm{nm}$. Dashed lines indicate the asymptotic behavior of $h_{\ell ,j}\sim 1/z_{\ell ,j}^{\gamma }$ at large separations. The value of $\gamma$ indicates the nature of the heat-transport regime, from superdiffusive ($1<\gamma <3$) to ballistic ($\gamma \to 1$). The insets decompose $h_{\ell ,j}$ for $j=30$ into TE and TM polarization contributions. (d) Exponent $\gamma$ as a function of $d$.

Figure 3

Heat-transfer coefficients $h_{\ell ,j}$ as a function of the normalized separation $z_{\ell ,j}/z_N$, for $D=d=5\mathrm{nm}$, along with the corresponding steady-state temperature profile (inset).

Figure 4

Temporal evolution of the temperature profile for a system ($N=60$) interacting with a thermal bath at $T_B=T_0=T_{N+1}=300\mathrm{K}$. At $t=0$, all bodies have temperature $T_B$ except the two central slabs, which have $T_{N/2}=T_{N/2+1}=400\mathrm{K}$. (a) Ballistic regime ($D=d=5\mathrm{nm}$). (b) Superdiffusive regime ($D=d=500\mathrm{nm}$). (c) Temperature of slab $N/2$ as a function of time in the two previous cases.

Figure 5

Heat-transfer coefficients $h_{\ell ,j}$ for gold slabs with respect to the normalized separation $z_{\ell ,j}/z_N$ for fixed values of $j$. Here $D=500\mathrm{nm}$ and (a) $d=500\mathrm{nm}$, (b) $d=100\mathrm{nm}$, (c) $d=40\mathrm{nm}$, and (d) $d=5\mathrm{nm}$. At large $z_{\ell ,j}$, an exponential decay is clearly observed. The insets decompose $h_{\ell ,j}$ for $j=15$ into TE and TM polarization contributions.

Figure 6

(a) Large-distance behavior of the heat-transfer coefficients $h_{\ell ,j}$ for Au slabs with respect to the separation $z_{\ell ,j}=|z_{\ell }-z_j|$ for $j=15$ and several values of the spacing $d$. (b) Skin depth ${\delta }_0$ as a function of $d$ (see Table 1). The limit $d\to 0$ can be extrapolated from a linear fitting, leading to ${\delta }_0\approx 112\mathrm{nm}$.