Surface-modes mediated long-range radiative heat transfer through a plasmonic Su-Schrieffer-Heeger chain

TL;DR

This work analyzes radiative heat transfer along a bipartite Su-Schrieffer-Heeger (SSH) chain of InSb nanoparticles placed near an InSb substrate. Using a dipole/fluctuational-electrodynamics framework, it derives IP and OP band structures via a Bloch-form eigenproblem and characterizes topological edge modes through Zak phases, revealing a phase transition between trivial and non-trivial regimes. The coupling to substrate surface waves deforms the chain bands and enables robust edge modes that mediate long-range heat transfer; the enhancement is quantified by comparing substrate-enabled transfer to the vacuum case and is governed by the surface-wave propagation length $\Lambda_{SPP}$, which can be tuned by substrate doping. Part of the significance lies in showing that topological edge modes can enhance thermally mediated communication along nanoscale chains, with practical implications for engineered thermal transport in plasmonic networks.

Abstract

We study the radiative heat transfer through a Su-Schrieffer-Heeger chain of plasmonic InSb nanoparticles in close vicinity of an InSb substrate. We show how the frequency bands of the in-plane and out-of-plane modes in the chain are deformed by the coupling to the surface waves in the InSb substrate by considering different carrier concentrations. By calculating the Zak phase we show that also in the presence of the substrate there is a topological phase transition and that topologically protected edge modes emerge for finite chains. Finally, we demonstrate the long-range heat transport along the chain due to the coupling to the surface waves of the sample. We find an enhanced heat transfer in the topological non-trivial phase compared to the trivial phase due to the contribution of the edge modes.

Figures (7)

• Figure 1: Sketch of the considered system. A bipartite SSH chain of nanoparticles of radius $R$ with lattice constant $d$ in each sublattice $A$ and $B$ and separation distance $t$ within each unit cell is placed at a distance $z$ in close vicinity of a semi-infinite planar substrate.
• Figure 2: Real part of the eigenfrequencies of IP and OP modes form frequency bands in the first Brillouin zone. The left panels show the IP band structure and the right ones the OP band structure. The bands are evaluated for different charge carrier densities $n_{\rm sub}$ in the substrate: $n=1.30\times10^{19}$ cm$^{-3}$ for (a-b), $n=1.32\times10^{19}$ cm$^{-3}$ for (c-d), $n=1.34\times10^{19}$ cm$^{-3}$ for (e-f), and $n=1.36\times10^{19}$ cm$^{-3}$ for (g-h). The dashed lines are the light line in vacuum $k_x = \omega/c$ (red) and the surface mode dispersion relation from Eq. (\ref{['Eq:DispSPP']}) (green). Here, we use $\beta = 0.7$.
• Figure 3: Accumulated Zak phase $\gamma_\nu(k_x)$ from Eq. \ref{['Eq:Zak2']} for $n=1.36 \times 10^{19}$ cm$^{-3}$. The left panels show the accumulated Zak phase for IP bands and the right ones for OP bands. The color code is identical to Fig. \ref{['Fig:BandGap']}. The upper panel shows the results for the topological trivial phase with $\beta = 0.7$ and the panel at the bottom shows the result for the topological non-trivial phase $\beta = 1.3$.
• Figure 4: Real part of the eigenfrequencies for a finite chain of 60 particles and $n_{\rm sub} = 1.36 \times 10^{19}$ cm$^{-3}$ for different $\beta$. To highlight the edge modes, we superpose the results for $\beta < 1$ (orange) and $\beta > 1$ (blue) by projecting the values for $\beta<1$ into the range $1 < \beta < 2$ by showing $2 - \beta$ instead.
• Figure 5: Total power $P^{\rm sub}_N$ received by particle $N$ in nanoparticle chains with $N = 2, \ldots, 60$ nanoparticles, i.e. with varying chain lengths $L$, normalized to the power $P^{\rm vac}_N$ of the same chain without substrate choosing different carrier concentrations $n_{\rm sub}$ in the substrate.