# Heat-Mode Excitation in a Proximity Superconductor

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## Abstract

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## 1. Introduction

## 2. Results: Devices and Transport Response

## 3. Results: Shot Noise Response

## 4. Results: Non-Equilibrium DC Transport

## 5. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Outline and charge transport data. (

**a**) Scanning electron microscope image of the typical device (false color). InAs NW is equipped with two N terminals (Ti/Au) on the sides and one S-terminal (Al) in the middle. (

**b**) Separation of charge and heat currents at the InAs/Al interface and two noise measurement configurations. The three-terminal device layout allows studying thermal conductance ${G}_{\mathrm{th}}$ of the proximitized NW region by measuring shot noise in the transmission configuration. Note that in the present experiment, only terminal N2 is connected to the low temperature amplifier, so that switching between the reflection noise ${S}_{\mathrm{R}}$ and transmission noise ${S}_{\mathrm{T}}$ is achieved by interchanging the biased and floating N-terminals, see the Supplemental Materials for the wiring scheme. (

**c**) Local differential conductance of NS junction in device NSN-II measured at $T=50\phantom{\rule{3.33333pt}{0ex}}\mathrm{mK}$ in different magnetic fields. (

**d**) Non-local differential resistance ${r}_{21}\equiv d{V}_{2}/d{I}_{1}$ for two devices plotted at different B and ${V}_{\mathrm{g}}$.

**Figure 2.**Reflected and transmitted shot noise. (

**a**) Reflection noise configuration in device NSN-I. Noise spectral density of the biased NS junction as a function of current at two values of ${V}_{\mathrm{g}}$. Dotted line is the fit with $F=0.30$ and charge ${e}^{*}=1.6e$; dashed line slope corresponds to $F=0.30$ and charge equal to e. Green symbols are shifted vertically by $9\times {10}^{-28}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{A}}^{2}/\mathrm{Hz}$ to coincide with red ones at zero bias. (

**b**) Transmission noise configuration in device NSN-I. Noise spectral density of the floating NS junction as a function of current at different B, T and ${V}_{\mathrm{g}}$ (see legend). (

**c**) Reflected shot noise in the reference two-terminal NS device as a function of current at two values of ${V}_{\mathrm{g}}$. Dotted line is the fit with $F=\phantom{\rule{3.33333pt}{0ex}}0.33,\phantom{\rule{3.33333pt}{0ex}}{e}^{*}=\phantom{\rule{3.33333pt}{0ex}}2e$; dashed line slope corresponds to $F=0.33$ and charge equal to e.

**Figure 3.**Thermal conductance in the device NSN-I. (

**a**) Noise temperature ${T}_{\mathrm{N}}$ measured in the transmission configuration as a function of bias (solid lines, same data as in the lower part of Figure 2b) along with the model fits (dashed lines). (

**b**,

**c**) (symbols) Sub-gap thermal conductance ${G}_{\mathrm{th}}$ and interface resistance parameter r plotted as a function of ${V}_{\mathrm{g}}$. (lines) Linear response conductances of the left/right (${G}_{1}/2$) NS junctions.

**Figure 4.**Resistive thermometry and non-local I-Vs in device NSN-II. (

**a**) Linear response resistance of the floating NS junction as a function of bias in the neighboring junction. (

**b**) The same data converted to the effective temperature ${T}^{*}$. (

**c**) The non-local I-V characteristics measured at three representative ${V}_{\mathrm{g}}$ values. (

**d**) Symmetric component of the non-local I-Vs. The dashed lines are the calculated thermoelectric voltage values for different energy-independent Seebeck coefficients of $S/T=3.0\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}\mathrm{V}/{\mathrm{K}}^{2},\phantom{\rule{3.33333pt}{0ex}}0.9\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}\mathrm{V}/{\mathrm{K}}^{2}$ and $-3.6\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}\mathrm{V}/{\mathrm{K}}^{2}$ (from top to bottom). Upper sketch: setup for resistive thermometry. Lower sketch: setup for non-local I-Vs.

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**MDPI and ACS Style**

Denisov, A.; Bubis, A.; Piatrusha, S.; Titova, N.; Nasibulin, A.; Becker, J.; Treu, J.; Ruhstorfer, D.; Koblmüller, G.; Tikhonov, E.; Khrapai, V. Heat-Mode Excitation in a Proximity Superconductor. *Nanomaterials* **2022**, *12*, 1461.
https://doi.org/10.3390/nano12091461

**AMA Style**

Denisov A, Bubis A, Piatrusha S, Titova N, Nasibulin A, Becker J, Treu J, Ruhstorfer D, Koblmüller G, Tikhonov E, Khrapai V. Heat-Mode Excitation in a Proximity Superconductor. *Nanomaterials*. 2022; 12(9):1461.
https://doi.org/10.3390/nano12091461

**Chicago/Turabian Style**

Denisov, Artem, Anton Bubis, Stanislau Piatrusha, Nadezhda Titova, Albert Nasibulin, Jonathan Becker, Julian Treu, Daniel Ruhstorfer, Gregor Koblmüller, Evgeny Tikhonov, and Vadim Khrapai. 2022. "Heat-Mode Excitation in a Proximity Superconductor" *Nanomaterials* 12, no. 9: 1461.
https://doi.org/10.3390/nano12091461