# Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire

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## Abstract

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## 1. Introduction

## 2. Theoretical Models

#### 2.1. Numerical Approach

#### 2.2. Analytical Approach

## 3. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Scheme of a polar nanowire supporting the propagation of both SPhPs and phonons due to the temperature difference ${T}_{h}>{T}_{c}$ imposed by two thermal baths.

**Figure 2.**Real and imaginary parts of the relative permittivity $\epsilon ={\epsilon}_{R}+i{\epsilon}_{I}$ of SiN, as a function of frequency [23]. The yellow zone stands for the band in which ${\epsilon}_{R}<0$.

**Figure 3.**Frequency spectrum of the wavevector and propagation length of SPhPs propagating along a SiN nanowire suspended in air (${\epsilon}_{0}=1$). The blue dashed line stands for the wavevector of light in vacuum.

**Figure 4.**(

**a**) Temperature and (

**b**) heat flux profiles in a SiN nanowire with representative lengths l. The solid and dashed-dot lines in (

**b**) represent the respective SPhP and phonon heat fluxes, whereas the dashed one stands for the total heat flux ${q}_{t}$. Calculations were carried out for a SiN nanowire with a radius $a=50$ nm and a typical phonon thermal conductivity of ${k}_{ph}$ = 1 W/m·K.

**Figure 5.**Frequency spectrum of the transmission probability of SPhPs propagating along a SiN nanowire of different lengths.

**Figure 6.**(

**a**) SPhP thermal conductance spectrum along with its integrated counterpart as a function of the (

**b**) length and (

**c**) temperature of a SiN nanowire suspended in air with a radius $a=50$ nm. The solid lines represent the predictions of Equation (17) and the dots the stand for the numerical results obtained with the DOM+FDM described in Section 2.1. Calculations in (

**a**) were carried out for $T=300$ K.

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**MDPI and ACS Style**

Guo, Y.; Nomura, M.; Volz, S.; Ordonez-Miranda, J.
Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire. *Energies* **2021**, *14*, 5110.
https://doi.org/10.3390/en14165110

**AMA Style**

Guo Y, Nomura M, Volz S, Ordonez-Miranda J.
Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire. *Energies*. 2021; 14(16):5110.
https://doi.org/10.3390/en14165110

**Chicago/Turabian Style**

Guo, Yangyu, Masahiro Nomura, Sebastian Volz, and Jose Ordonez-Miranda.
2021. "Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire" *Energies* 14, no. 16: 5110.
https://doi.org/10.3390/en14165110