1. Sukumar Rajauria Néel Institute, CNRS and Université Joseph Fourier, Grenoble, France With H. Courtois, P. Gandit, T. Fournier, F. Hekking, B. Pannetier Inherent Thermometer in a Superconductor – Normal metal – Superconductor cooling junction

2. Outline Introduction Sample and Experiments Extraction of electronic temperature Thermal model Conclusion

3. E 2Δ2Δ I S T = 0 K Empty States Occupied States Forbidden states N Quasiparticle Tunneling in N-I-S junction Principle of N-I-S cooler The superconductor energy gap Induces an energy-selective tunneling.

4. Quasiparticle Tunneling in N-I-S junction E 2Δ2Δ I S T > 0 K N ~4kT Empty States Occupied States Forbidden states Principle of N-I-S cooler The superconductor energy gap Induces an energy-selective tunneling.

5. E 2Δ2Δ I S Empty States Occupied States T > 0 K eV ItIt Forbidden states N Quasiparticle Tunneling in N-I-S junction Principle of N-I-S cooler The superconductor energy gap Induces an energy-selective tunneling.

6. E 2Δ2Δ I S Empty States Occupied States T > 0 K eV Forbidden states N Q Quasiparticle Tunneling in N-I-S junction Principle of N-I-S cooler: Extraction of heat current by tunneling of hot quasiparticle out of the Normal metal in N-I-S junction.

7. F. Giazotto, T. T. Heikkila, A. Luukanen, A. M. Savin and J. P. Pekola, Rev. Mod. Phys. 78, 217 (2006). S-I-N-I-S = 2 × N-I-S junctions in series P cool increases by a factor of 2 Better thermal isolation of N-island V bias S N S Thermometer Need for a thermometer ! E E 2Δ2Δ I S Empty States Occupied States T > 0 K N eV 2Δ2Δ S ItIt ItIt Q Q The S-I-N-I-S geometry I

8. E. Favre-Nicollin et. al. Thermometer Junctions Cooler junctions 2 µm Cu Al Thermometry with N-I-S junctions Additional N-I-S junctions can be used as a thermometer:

9. This work How much can we lower the electronic temperature ? Can we avoid the use of N-I-S thermometer junctions ? What about the phonons ? Is a quantitative analysis possible ?

10. Probe Junction: N electrode is strongly thermalized, litlle cooling effect expected. I 1 µm Cu Al Cooler junctions: N electrode is weakly coupled to external world, strong cooling effect expected. A cooler with improved aspect ratio

11. Probe follows isothermal prediction at T base. High resolution measurement (log scale) « Cooler behaves differently » Probe T base = 304 mK Cooler Al I 1 µm Cu Cooling in N-I-S junction Probe Cooler

12. Superposition of expt data with isotherm gives the electronic temperature at a particular bias. Temperature Determination Determination of the bias-dependent electron temperature

13. N electrons, T e S, T base N phonons, T ph Substrate phonons, T base Power flow from N electrons to the S electrodes remaining at base temperature Electron - phonon coupling Kapitza thermal coupling The thermal model Steady state:

14. N electrons, T e S, T base N phonons, T ph Substrate phonons, T base Power flow from N electrons to the S electrodes remaining at base temperature Electron - phonon coupling Kapitza thermal coupling The thermal model Steady state: Hyp.: N phonons are strongly thermalized

15. For T ph = T base Impossible to fit data with a given  Need to let phonon temperature T ph vary Hypothesis of phonon thermalized to the bath T Base (mK)  (10 9 ) (Wm -3 K -5 ) 2

16. N electrons, T e S, T base N phonons, T ph Substrate phonons, T base Power flow from N electrons to the S electrodes remaining at base temperature Electron - phonon coupling Kapitza thermal coupling The thermal model Steady state: N phonons can be cooled

17. Two free fit parameters:  = 2 nW.µm -3.K -5 K = 55 W.m -2.K -4 Determination of both electron (T e ) and phonon (T ph ) temperature. Phonons cool down by ~ 50 mK at 500 mK Phonon Cooling

18. Conclusion Direct determination of the electronic temperature in the N-metal Quantitative analysis of cooling Including phonon cooling enables a good fit to the data Thanks to: EU STREP SFINX NanoSciERA “NanoFridge“

20. Phonon temperature For d = 50 nm, T > 0.35 K

21. Extrapolation of the model Parameter K governs coupling between the metal phonons and the substrate K = 0: diff. cond. peak at zero bias