# Low-Temperature Coherent Thermal Conduction in Thin Phononic Crystal Membranes

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## Abstract

**:**

## 1. Introduction

## 2. Radiated Phonon Power

## 3. Phonon Density of States

## 4. Average Phonon Group Velocity

## 5. Discussion and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

PnC | Phononic crystal |

## References

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**Figure 2.**Radiated phonon thermal power for a selection of different phononic crystals (PnC) membranes with a square lattice hole pattern of period $a=$ 62.5 nm – 8 μm, and a full membrane with the same thickness $d=300$ nm.

**Figure 3.**Radiated power enhancement factor for square PnC membranes with various lattice constants a. The largest ratio of enhancement vs. reduction ${p}_{\text{max}}/{p}_{\text{min}}\approx 92$ occurs at $T=300$ mK.

**Figure 5.**Phonon density of states of a full membrane and four PnC membranes with the same thickness and different lattice constants. The PnC curves are smoothed for visual clarity.

**Figure 6.**Average group velocity of a full membrane and four PnC membranes with the same thickness and different lattice constants. The PnC curves are smoothed for visual clarity.

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**MDPI and ACS Style**

Puurtinen, T.A.; Maasilta, I.J.
Low-Temperature Coherent Thermal Conduction in Thin Phononic Crystal Membranes. *Crystals* **2016**, *6*, 72.
https://doi.org/10.3390/cryst6060072

**AMA Style**

Puurtinen TA, Maasilta IJ.
Low-Temperature Coherent Thermal Conduction in Thin Phononic Crystal Membranes. *Crystals*. 2016; 6(6):72.
https://doi.org/10.3390/cryst6060072

**Chicago/Turabian Style**

Puurtinen, Tuomas A., and Ilari J. Maasilta.
2016. "Low-Temperature Coherent Thermal Conduction in Thin Phononic Crystal Membranes" *Crystals* 6, no. 6: 72.
https://doi.org/10.3390/cryst6060072