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**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)

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**Principle of electronic refrigeration**

Conductor 2 T2 Q + W W Q Conductor 1 T1 Q0 Environment Tbath

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**SINIS in the absence of Coulomb effects**

M. Leivo, J.P. and D. Averin, 1996

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**Single electron transistor (SET)**

Charging energy of a SET: Unit of charging energy:

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**NIS single-electron box = single-electron refrigerator (SER)**

J. P. , F. Giazotto, O.-P. Saira, PRL 98, (2007)

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Typical cooling cycle

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**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)

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**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

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**Influence of charging energy**

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

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**Measured performance of a heat transistor**

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**Brownian refrigerator**

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

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**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

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**Metrological ”Quantum Triangle”**

?

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**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)

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**Stability diagrams Hybrid SET (SINIS or NISIN) Normal SET**

Important qualitative difference: stability regions overlap in a hybrid SET unlike in a normal SET

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**Operation cycle Basic operation cycle**

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

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**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)

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**Dependences from the measurement**

f = 12.5 MHz f = 20 MHz

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**Bias and frequency dependence of the turnstile current**

Parameters of the turnstile: RT = 350 kW EC = 2 K

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**Low leakage NIS junctions**

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

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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

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**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)

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**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

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**Error rates (3) Possible overheating of the island:**

The island can cool also!

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**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?

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**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

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**Two-electron process and Cooper pair – electron cotunnelling**

D. Averin and J. Pekola, arXiv: METROLOGICAL REQUIREMENTS SATISFIED IN THEORY

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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

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**Gate modulation of the SET-transistor**

Normal SET Hybrid SET (this is one of the measured turnstiles)

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**Raw experimental data Parameters of the turnstile: RT = 350 kW**

EC = 2 K

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**Errors due to leakage and temperature**

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**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

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**Entropy production in the Brownian refrigerator**

S Special case: ALWAYS ≥ 0

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**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?

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**Amplitude of temperature variation in response to magnetic flux**

en Symbols: experiment Lines: theoretical model with the same parameters as in the previous plot

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

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**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

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**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).

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**Single-mode heat conduction by photons**

Electron system Electrical environment Lattice M. Meschke, W. Guichard and J. Pekola, Nature 444, 187 (2006).

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**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).

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**Example of quantized thermal conductance: phonons in a nanobridge**

K. Schwab et al., Nature 404, 974 (2000).

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**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).

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**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

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**Measured variation of island temperature**

Vary bath temperature Line: P1 = 1 fW, P2 =0 en Thermal model:

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**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

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**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?

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Single Electron Transistor (SET)

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