Electronic refrigeration using superconducting tunnel junctions - PowerPoint PPT Presentation

Electronic refrigeration using superconducting tunnel junctions Sukumar Rajauria I H. Courtois, F. W. J. Hekking and B. Pannetier

Motivation Quantum nano-electronics: • New devices with new functionality (SET, qubits, …) • High performance at (very) low temperature. On-chip cooling of a nano-device: • Improved efficiency, more compact, • N-I-S micro-coolers promising. Basic knowledge on: • N-I-S junction with a heat perspective, • Heat transport at micro- or nano-scale.

Motivation Prototype cooler – N. I.S.T. First S-I-N-I-S cooler – Helsinki

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

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

Quasiparticle tunneling in N-I-S junction Empty States Quasiparticle tunnel current: ∞ I T 1 [ ] dE ∫ = − − I n ( E ) f ( E eV ) f ( E ) T S N S eR − ∞ N eV 2 1 I T eR n / ∆ T = 0.49T c 0 N I N S S T = 0.07T c -1 T > 0 K -2 -2 -1 0 1 2 eV/ ∆

Quasiparticle tunneling in N-I-S junction Empty States Quasiparticle tunnel current: ∞ P Cool 1 [ ] dE ∫ = − − I n ( E ) f ( E eV ) f ( E ) T S N S eR − ∞ N eV Net Cooling Power: ∞ 1 1 [ [ ] dE ] dE ∫ ∫ = = − − − − − − P P ( ( E E eV eV ) ) n n ( ( E E ) ) f f ( ( E E eV eV ) ) f f ( ( E E ) ) Cool S N S 2 e R − ∞ N Joule heat Cooling N I N S S P Cool ≈ ( Ē /e). I T – V.I T T > 0 K

Quasiparticle tunneling in N-I-S junction Net Cooling Power: Empty States ∞ 1 [ ] dE ∫ = − − − P ( E eV ) n ( E ) f ( E eV ) f ( E ) P Cool Cool S N S 2 e R − ∞ N P Cool ≈ ( Ē /e). I T – V.I T > 0 eV 0.06 0.04 T = 0.49Tc 2 R 2 N / ∆ P Cool e N I N S S 0.02 T > 0 K 0.00 T = 0.07Tc P Cool is symmetric to bias. -1.0 -0.5 0.0 0.5 1.0 eV/ ∆

S-I-N-I-S junction E E S-I-N-I-S = 2 N-I-S P Cool P Cool junction in series Empty States I T I T 2 ∆ eV 2 ∆ eV Cooling power increases by a factor of 2 Occupied States I S S N I Better thermal isolation T > 0 K of N-island F. Giazotto, T. T. Heikkila, A. Luukanen, A. M. Savin and J. P. Pekola, Rev. Mod. Phys. 78 78, 217 (2006).

Cooler with External thermometer Thermometer Junction 2 µm 0 10 Al Cooler OFF Cooler ON hermometer 288 mK 134 mK Cu -1 10 Al dI/dV The Cooler junctions -2 10 − ∆ eV ≈ I I exp( ) k B T 0 -2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 N V Thermometer / ∆ E. Favre-Nicollin et. al.

Outline • Electronic temperature without thermometer • Thermal model • Andreev current contributions • Conclusions

Quasiparticle diffusion based heating in S-I-N-I-S cooler heating in S-I-N-I-S cooler

Cooler with NO external thermometer Probe Junction : N electrode is strongly thermalized, litlle cooling effect expected. 1 µm Al Al Cu Cu I Cooler junctions : N electrode is weakly coupled to external world, strong cooling effect expected .

Cooling in S-I-N-I-S junction 1 µm Cooler Al Cooler Cu 1 10 Cu dI/dV I (norm.) Probe T bath = 304 mK 0.1 1 High resolution measurement (log scale) 0.01 0.1 − ∆ Probe eV ≈ I I exp( ) 0 0.001 0.01 k T B e Probe follows isothermal -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 prediction at T bath . V/(2) ∆

Temperature determination 0 • two refrigerating junction are symmetric; 10 Cooler • N-metal is at quasi-equilibrium; -1 10 • Ideal superconductor; Isotherm n / ∆ I T eR T e = 304 mK -2 10 T e = 98 mK 600 -3 -3 10 10 450 T e (mK) -4 10 300 0.0 0.1 0.2 0.3 0.4 0.5 V (mV) 150 0 0.0 0.2 0.4 V (mV)

Thermal model

The thermal model Power flow from N electrons to the S electrodes remaining at base temperature 1 +∞ [ ] ( ) ∫ ( ) ( ) ( ) ( ) = − − + P V E eV n E f E f E eV dE Cool S S N eR − ∞ N S, T bath N electrons, T S, T bath e ( ) = Σ Electron - phonon coupling 5 5 P U T T - e ph ph e - N phonons, T ph ( ) = − Kapitza thermal coupling 4 4 P KA T T K bath ph Substrate phonons, T bath

The thermal model - Hypothesis Power flow from N electrons to the S electrodes remaining at base temperature 1 +∞ [ ] ( ) ∫ ( ) ( ) ( ) ( ) = − − + P V E eV n E f E f E eV dE Cool S S N eR − ∞ N S, T bath N electrons, T S, T bath e ( ) = Σ Electron - phonon coupling 5 5 P U T T - e ph bath e - Hyp.: N phonons are N phonons, T ph = T bath strongly thermalized Kapitza thermal coupling Substrate phonons, T bath

Hypothesis of phonon thermalized to the bath 1.0 For T ph = T bath 9 Wm -3 K -5 ) T bath (mK) Σ (*10 ( ) = Σ − ------------------------------------ 0.8 5 5 2 P U T T 292 1.21 Cool e bath 489 1.02 586 0.80 0.6 5 (T e /T bath ) ------------------------------------   5 T 1 2 P     0.4 = = − − 1 1 e Cool     Σ Σ   5 5 T T U U T T bath bath 0.2 Impossible to fit data with a given Σ 0.0 0 20 40 60 80 100 5 (pW/K 5 ) 2P Cool /T bath Fitted Σ much smaller than expected (2 nW.µm -3 .K -5 )

The thermal model P P Cool Cool S, T bath N electrons, T S, T bath e ( ) = Σ − 5 5 Electron - phonon coupling P U T T − e ph ph e N phonons, T N phonons, T ph N phonons can be cooled N phonons can be cooled ( ) = − P KA T 4 T 4 Kapitza thermal coupling K bath ph Substrate phonons, T bath

Phonon cooling 600 Two free fit parameters: Σ = 2 nW.µm -3 .K -5 500 K = 55 W.m -2 .K -4 400 T (mK) Kapitza coupling T bath smaller by a factor 300 of 3 than bulk. of 3 than bulk. T ph T 200 T e Phonon cooling model dominant at high experiment 100 temperature. 0 0.0 0.1 0.2 0.3 0.4 V (mV) Sukumar Rajauria, P. S. Luo, T. Fournier, F. W. J. Hekking, H. Courtois and B. Pannetier, PRL (2007) (2007)

What now? • How much can we lower the electronic temperature ? • Can we reach below 10mK starting with a dilution temperature ? • What about the other contribution like Andreev Current etc. ? • What about the other contribution like Andreev Current etc. ? • Is a quantitative analysis possible ?

Andreev current-induced dissipation dissipation

Experiment at a very low temperature Zero-bias anomaly. 0 10 Not a linear leakage. -1 10 450 mK dI/dV norm. Cannot be fitted with a -2 10 10 340 340 smeared D.O.S or a non- smeared D.O.S or a non- equilibrium distribution in N. 240 -3 10 Likely two electron tunneling 90 process. -4 10 -0.8 -0.4 0.0 0.4 0.8 V(mV)

Andreev reflection E < ∆ : No quasiparticle tunneling E Transmission probability proportional: t 2 For tunnel barrier: t is very small eV eV j A Andreev reflection probability vanishes for a tunnel barrier N N I S S T > 0 K A. F. Andreev, Zh. Eksp. Teor. Fiz. ’64 , D. Saint-James, J. Phys. (Paris) ‘64

Confinement-enhanced of the Andreev current Nb-I-InGaAs junction Kastalsky et al PRL 91 van Wees-Klapwijk et al PRL 92 Confinement of electron by disorder + Quantum coherence Enables coherent addition of 2e tunneling amplitudes = Enhances sub gap conductivity = 2 G G . R A N diff

Andreev current in disordered N-I-S junction Hekking and Nazarov model : Tunnel barrier in between N and S. Sub-gap conductivity is more sensitive to disorder. ∞ { } dE ∫ = − − + I ( V ) I ( E ) f ( E / 2 eV ) f ( E / 2 eV ) A N N − ∞ where I(E) is the spectral current 2 hG { } ∫ = + 2 n I ( E ) P ( r ) P ( r ) d r − π ν E E 3 16 Se 0 barrier where P E (r) is the cooperon. Length scale: Phase coherence length, bias or temperature cut off. Hekking et al PRL 93 and PRB 94, Pothier et al PRL 94

Isotherm of Andreev and Quasiparticle current 1 10 Total current = Quasiparticle T bath = 90 mK Andreev current + Current Quasiparticle current 0 10 I Probe = I A + I T -1 10 I (nA) Fit parameters : Fit parameters : Andreev Current Andreev Current -2 -2 10 L ϕ = 1.5 µm Scaling factor 1.4 -3 10 Probe Good fit for the probe. -4 10 0.0 0.2 0.4 0.6 0.8 1.0 eV/ ∆

Quasiparticle cooling fit 1 10 Total current = Cooler T bath = 90 mK Andreev current + Quasiparticle current Extra dissipation missing 0 10 I Cooler = I A + I T in the thermal model? I (nA) Fit parameters : -1 10 L ϕ = 1.5 µm L ϕ = 1.5 µm Scaling factor 0.5 K = 120 W.m -2 .K -4 -2 Andreev current added 10 in cooling model Quasiparticle cooling does not fit experiment. -3 10 0.0 0.2 0.4 0.6 0.8 1.0 eV/ ∆ eV/(2 ∆ )