Inherent Thermometer in a Superconductor Normal metal Superconductor

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

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

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

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

Quasiparticle Tunneling in N-I-S junction Principle of N-I-S cooler The superconductor energy gap Induces an energy-selective tunneling. It E Empty States e. V 2Δ Forbidden states Occupied States N I S T>0 K

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. Q E Empty States e. V 2Δ Forbidden states Occupied States N I S T>0 K

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

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

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 ?

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

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

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

The thermal model Power flow from N electrons to the S electrodes remaining at base temperature S, Tbase N electrons, Te Electron - phonon coupling N phonons, Tph Kapitza thermal coupling Substrate phonons, Tbase Steady state: S, Tbase

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

Hypothesis of phonon thermalized to the bath For Tph = Tbase TBase (m. K) Impossible to fit data with a given Need to let phonon temperature Tph vary 2 (109) (Wm-3 K-5)

The thermal model Power flow from N electrons to the S electrodes remaining at base temperature S, Tbase N electrons, Te S, Tbase Electron - phonon coupling N phonons, Tph Kapitza thermal coupling Substrate phonons, Tbase Steady state: N phonons can be cooled

Phonon Cooling Two free fit parameters: = 2 n. W. µm-3. K-5 K = 55 W. m-2. K-4 Determination of both electron (Te) and phonon (Tph) temperature. Phonons cool down by ~ 50 m. K at 500 m. K

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 Nano. Sci. ERA “Nano. Fridge“

Phonon temperature For d = 50 nm, T > 0. 35 K

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