1. Normal metal - superconductor tunnel junctions as kT and e pumps
Jukka Pekola
Low Temperature Laboratory, Helsinki University of Technology
Coulomb blockade and electronic refrigeration
Radiofrequency single-electron refrigerator
Heat transistor
Hybrid single-electron turnstile for electrons
Collaborators:
M. Meschke, O.-P. Saira, A. Savin, M. Möttönen, J. Vartiainen, A. Timofeev, M. Helle, N. Kopnin (LTL), A. Kemppinen (Mikes)
F. Giazotto (SNS Pisa), D. Averin (SUNY Stony Brook), F. Hekking (CNRS Grenoble)

2. Principle of electronic refrigeration
Conductor 2 T2
Q + W W Q
Conductor 1 T1 Q0
Environment Tbath

3. SINIS in the absence of Coulomb effects
M. Leivo, J.P. and D. Averin, 1996

4. Single electron transistor (SET)
Charging energy of a SET:
Unit of charging energy:

5. NIS single-electron box = single-electron refrigerator (SER)
J. P. , F. Giazotto, O.-P. Saira, PRL 98, (2007)

6. Typical cooling cycle

7. Quantitative performance of SER
Frequency dependence of cooling power
Charge and heat flux under typical operation conditions
Influence of photon assisted tunnelling: N. Kopnin et al., Phys. Rev. B 77, (2008)

8. Heat transistor – Combining Coulomb blockade and electronic refrigeration
VDS S N S
MAXIMUM COOLING
POWER
CgVg = (n+1/2)e
VDS S N S
MINIMUM COOLING
POWER
CgVg = ne

9. Influence of charging energy
The first demonstration of gate controlled refrigeration
O.-P.Saira et al., PRL 99, (2007)
NS contacts

10. Measured performance of a heat transistor

11. Brownian refrigerator
COOLING POWER OF N (fW)
J.P. and F. Hekking, PRL 98, (2007); see poster by Andrey Timofeev today

12. Electron pumps Towards frequency-to- current conversion
Semiconductor, travelling wave:
J.Shilton et al., J. Phys. Condens. Matter 8, L531 (1996)
M. Blumenthal, S. Giblin et al., Nature Physics 3, 343 (2007)
Fast, but needs still improvement
R-pumps:
S. Lotkhov et al.
Fully superconducting pumps:
Fast, hard (but not impossible!) to make accurate
Normal single-electron pump: I =ef
M. W. Keller et al., APL 69, 1804 (1996).
High accuracy but still slow: I < 10 pA

13. Metrological ”Quantum Triangle”?

14. Hybrid single-electron turnstile (SINIS or NISIN)
J.P. Pekola, J.J. Vartiainen, M. Möttönen, O.-P. Saira, M. Meschke, and D.V. Averin, Nature Physics 4, 120 (2008)

15. Stability diagrams Hybrid SET (SINIS or NISIN) Normal SET
Important qualitative difference: stability regions overlap in a hybrid SET unlike in a normal SET

16. Operation cycle Basic operation cycle
Exactly one electron is transferred through the turnstile in each cycle:
I = ef.

17. Expected behaviour based on ”classical” tunnelling
BLACK – HYBRID SET
RED – NORMAL SET
Parameters chosen to correspond to the experiment to be presented.
DC gate positions are 0, 0.1e, 0.2e, 0.3e and 0.4e (hybrid)

18. Dependences from the measurement
f = 12.5 MHz
f = 20 MHz

19. Bias and frequency dependence of the turnstile current
Parameters of the turnstile:
RT = 350 kW
EC = 2 K

20. Low leakage NIS junctions
IMPROVED JUNCTIONS:
A. Kemppinen et al., arXiv:
g = 10-5
g = 10-6
THE FIRST EXPERIMENTS, g > 10-4

21. Error rates (1)
Probability (per cycle) of tunnelling in wrong direction is approximately
Probability (per cycle) of tunnelling an extra electron in forward direction is approximately
Optimum operation point is therefore at eV = D, where the error rate is
At typical temperatures (< 100 mK), with aluminium, this error is << 10-8

22. Error rates (2) Missed tunnelling events due to high frequency:
D = EC assumed above.
Frequency cut-off can be compensated by parallelisation: compared to N-pump, N parallel turnstiles yield N2 higher current (with the same level of complexity)

23. Errors in rectangular drive
backward tunnelling
Parameters:
Red D/kT = 20
Green D/kT = 30
Black D/kT = 40
RT = 50 kW
f = 300 MHz
missed tunnelling

24. Error rates (3) Possible overheating of the island:
The island can cool also!

25. Error rates: quantum tunnelling
Higher order tunnelling processes:
In NISIN elastic virtual processes are harmful
In SINIS these do not contribute
Influence of various inelastic processes?

26. Error rates (4) Threshold: eV = 2D
INELASTIC COTUNNELLING OF QUASIPARTICLES IN A SYMMETRIC SINIS STRUCTURE IS EFFICIENTLY SUPPRESSED eV D
S N S
Threshold: eV = 2D

27. Two-electron process and Cooper pair – electron cotunnelling
D. Averin and J. Pekola, arXiv:
METROLOGICAL REQUIREMENTS SATISFIED IN THEORY

28. Summary
Refrigeration by hybrid tunnel junctions is already a well-established technique as such - Interplay of energy filtering and Coulomb blockade leads to new phenomena and devices
Presented a cyclic electron refrigerator, a heat transistor and a Brownian refrigerator
Hybrid SINIS turnstile looks promising
Simple design and operation
Errors can be suppressed efficiently
Seems straightforward to run many turnstiles in parallel
Possibility for error counting and correction

29. Gate modulation of the SET-transistor
Normal SET
Hybrid SET
(this is one of the measured turnstiles)

30. Raw experimental data Parameters of the turnstile: RT = 350 kW
EC = 2 K

31. Errors due to leakage and temperature

32. Energy relaxation of electrons in metal
In thermal equilibrium:
Electron-electron collisions
e’-w
e+w w
- drive f to feq(e,T) (T= Tph generally) e e’
e+w
Electron-phonon collisions w
effective at high temperatures
drive f to feq(e,Tph) e
At low T electron-phonon relaxation becomes extremely weak

33. Entropy production in the Brownian refrigeratorS
Special case:
ALWAYS ≥ 0

34. Possible implications of the presented effect
Until now good thermal isolation at low T has been taken for granted (vanishing electron-phonon rate, superconductivity,...)
Consequences of e-photon coupling:
Increased heat load and noise of micro-bolometers and calorimeters
A way to tune thermal coupling (heat switches, optimization of bolometers)
Another channel to remove heat from dissipative elements, like shunt resistors of SQUIDs at low T
Acts as a mediator of increased decoherence?

35. Amplitude of temperature variation in response to magnetic fluxen
Symbols: experiment
Lines: theoretical model with the same parameters as in the previous plot

36. NIS-junction
Superconducting gap yields non-linear temperature-dependent IV characteristics

37. Cooling power Cooling power of a double-NIS device:
Optimum cooling power is obtained at V  2D/e:
Optimum cooling power per junction at low temperatures

38. Experimental status Refrigeration of lattice (membrane)
M. Nahum et al (NIS)
M. Leivo, J. Pekola and D. Averin, 1996 (SINIS)
A. Manninen et al (SIS’IS), see also Chi and Clarke 1979 and Blamire et al. 1991
L. Kuzmin et al., cooler + bolometers
A. Luukanen et al (membrane refrigeration by SINIS)
A. Savin et al (S – Schottky – Semic – Schottky – S)
A. Clark et al (x-ray detector refrigerated by SINIS)
Refrigeration of lattice (membrane)
Refrigeration of a bulk object
A. Clark et al., Appl. Phys. Lett. 86, (2005).
A. Luukanen et al., J. Low Temp. Phys. 120, 281 (2000).
For a review, see F. Giazotto et al., Rev. Mod. Phys. 78, 217 (2006).

39. Single-mode heat conduction by photons
Electron
system
Electrical
environment
Lattice
M. Meschke, W. Guichard and J. Pekola, Nature 444, 187 (2006).

40. Quantized conductance
Electrical conductance in a ballistic contact:
Quantum of thermal conductance:
GQ and sQ related by Wiedemann-Franz law
Expression of GQ is expected to hold for carriers obeying arbitrary statistics, in particular for electrons, phonons, photons (Pendry 1983, Greiner et al. 1997, Rego and Kirczenow 1999, Blencowe and Vitelli 1999).

41. Example of quantized thermal conductance: phonons in a nanobridge
K. Schwab et al., Nature 404, 974 (2000).

42. Heat transported between two resistors
Radiative contribution to net heat flow between electrons of 1 and 2:
Impedance matching:
Linear response for small temperature difference
DT = Te1 – Te2:
D. Schmidt, A. Cleland and R. Schoelkopf, Phys. Rev. Lett. 93, (2004).

43. Our experimental set-up
M. Meschke et al., Nature 444, 187 (2006).
Tunable impedance matching using DC-SQUIDs F
Island size: 6 mm x 0.75 mm x 15 nm
Material: PdAu

44. Measured variation of island temperature
Vary bath temperature
Line: P1 = 1 fW, P2 =0 en
Thermal model:

45. Heat flows from hot to cold by photon radiation
The situation is nearly the same if we replace one resistor by an ordinary tunnel junction
This happens between two resistors

46. Harmonic vs stochastic drive in refrigeration
Sinusoidal bias –
Refrigerates N if frequency and amplitude are not too high
Stochastic drive –
Refrigerates N if spectrum is ”suitable”
Brownian refrigerator?