Jukka PekolaLow Temperature Laboratory, Helsinki University of Technology

Normal metal - superconductor tunnel junctions as kT and e pumps

Coulomb blockade and electronic refrigeration Radiofrequency single-electron refrigeratorHeat 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)

Principle of electronic refrigeration

EnvironmentTbath

Conductor 2 T2

Conductor 1 T1

Q + W

WQ

Q0

SINIS in the absence of Coulomb effects

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

Single electron transistor (SET)Charging energy of a SET:

Unit of charging energy:

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

J. P. , F. Giazotto, O.-P. Saira, PRL 98, 037201 (2007)

Typical cooling cycle

Quantitative performance of SERFrequency 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, 104517 (2008)

Heat transistor – Combining Coulomb blockade and electronic refrigeration

S SN

CgVg = (n+1/2)e

VDS

MAXIMUM COOLINGPOWER

S SN

CgVg = ne

VDS

MINIMUM COOLINGPOWER

Influence of charging energy

NS contacts

The first demonstration of gate controlled refrigeration

O.-P.Saira et al., PRL 99, 027203 (2007)

Measured performance of a heat transistor

Brownian refrigerator

CO

OL

ING

PO

WE

R O

F N

(f

W)N S

R, TR

RT, TN,S

N S

R, TR

RT, TN,S

J.P. and F. Hekking, PRL 98, 210604 (2007); see poster by Andrey Timofeev today

Electron pumps

Normal single-electron pump: I =ef

M. W. Keller et al., APL 69, 1804 (1996).

High accuracy but still slow: I < 10 pA

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

Metrological ”Quantum Triangle”

?

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)

Stability diagrams

Normal SETHybrid SET (SINIS or NISIN)

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

n = 0 n = -1

Normal SET Hybrid SET

n = 0 n = -1

Gate voltage

Dra

in-s

ou

rce

volt

age

Gate voltage

Dra

in-s

ou

rce

volt

age

Operation cycle

Basic operation cycle

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

Expected behaviour based on ”classical” tunnelling

0 1 2 3 4 50123456789

10

CU

RR

EN

T (

ef)

GATE AMPLITUDE (e)

BLACK – HYBRID SETRED – 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)

Dependences from the measurementf = 12.5 MHz

f = 20 MHz

Bias and frequency dependence of the turnstile current

Parameters of the turnstile:RT = 350 kEC = 2 K

Low leakage NIS junctions

-400 -300 -200 -100 0 100 200 300 400-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

I (p

A)

V (µV)

= 10-5

= 10-6

-600 -400 -200 0 200 400 600-20

-15

-10

-5

0

5

10

15

20

I (p

A)

V (µV)

505mK 435mK 335mK 128mK

THE FIRST EXPERIMENTS, > 10-4

IMPROVED JUNCTIONS:A. Kemppinen et al., arXiv:0803.1563

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 = , where the error rate is

At typical temperatures (< 100 mK), with aluminium, this error is << 10-8

Error rates (2)

Missed tunnelling events due to high frequency:

= 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)

Errors in rectangular drive

0.3 0.4 0.5 0.610-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

ER

RO

R

GATE AMPLITUDE (e)

Parameters:Red /kT = 20Green /kT = 30Black /kT = 40RT = 50 kf = 300 MHz

missed tunnelling

backward tunnelling

Error rates (3)

0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

CO

OL

ING

PO

WE

R (2

/e2R

T)

GATE AMPLITUDE (e)

EC = = 20kT, f = 20 MHz

= 0.00001 R

T = 1 M

RT = 100 k

Possible overheating of the island:

The island can cool also!

0.0 0.5 1.0 1.5-0.1

0.0

0.1

0.2

0.3

CO

OLI

NG

RA

TE

(2 /e

2 RT)

GATE AMPLITUDE (e)

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?

Error rates (4)INELASTIC COTUNNELLING OF QUASIPARTICLES IN A SYMMETRIC SINIS STRUCTURE IS EFFICIENTLY SUPPRESSED

Threshold: eV = 2

eV

S N S

Two-electron process and Cooper pair – electron cotunnelling

METROLOGICAL REQUIREMENTS SATISFIED IN THEORY

D. Averin and J. Pekola, arXiv:0802.1364

0.5 0.6 0.7 0.8 0.9 1.0

100

101

102

NO

RM

ALI

ZE

D R

AT

ES

ng

(a)

10-8 10-7 10-6

10-11

10-10

10-9

I MA

X (

A)

p

(b)

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

Gate modulation of the SET-transistor

Normal SET

Hybrid SET(this is one of the measured turnstiles)

Raw experimental data

Parameters of the turnstile:RT = 350 kEC = 2 K

Errors due to leakage and temperature

’

’

Electron-electron collisions

- drive f to feq(,T) (T= Tph generally)

Energy relaxation of electrons in metal

In thermal equilibrium:

At low T electron-phonon relaxation becomes extremely weak

Electron-phonon collisions

- effective at high temperatures- drive f to feq(,Tph)

Entropy production in the Brownian refrigerator R

N S

Special case:

ALWAYS ≥ 0

N S

R, TR

RT, TN,S

N S

R, TR

RT, TN,S

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?

Amplitude of temperature variation in response to magnetic flux

Symbols: experimentLines: theoretical model with the same parameters as in the previous plot

100 120 140 160 180 200 2200

1

2

3

4

5

6

T (

mK

)

Te1

(mK)

105 mK118 mK

167 mK

T0 = 60 mK

75 mK

157 mK

e

NIS-junctionSuperconducting gap yields non-linear temperature-dependent IV characteristics

Cooling power

Optimum cooling power is obtained at V 2/e:

Cooling power of a double-NIS device:

eV/2

Optimum cooling power per junction at low temperatures

Experimental status

A. Clark et al., Appl. Phys. Lett. 86, 173508 (2005).A. Luukanen et al., J. Low Temp. Phys. 120, 281 (2000).

Refrigeration of lattice (membrane) Refrigeration of a bulk object

M. Nahum et al. 1994 (NIS)M. Leivo, J. Pekola and D. Averin, 1996 (SINIS)A. Manninen et al. 1999 (SIS’IS), see also Chi and Clarke 1979 and Blamire et al. 1991L. Kuzmin et al., cooler + bolometersA. Luukanen et al. 2000 (membrane refrigeration by SINIS)A. Savin et al. 2001 (S – Schottky – Semic – Schottky – S)A. Clark et al. 2005 (x-ray detector refrigerated by SINIS)

For a review, see F. Giazotto et al., Rev. Mod. Phys. 78, 217 (2006).

Single-mode heat conduction by photons

Lattice

Electrical environment

Electron system

M. Meschke, W. Guichard and J. Pekola, Nature 444, 187 (2006).

Quantized conductance

Electrical conductance in a ballistic contact:

Quantum of thermal conductance:

GQ and Q 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).

Example of quantized thermal conductance: phonons in a nanobridge

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

Heat transported between two resistors

Impedance matching:

Radiative contribution to net heat flow between electrons of 1 and 2:

Linear response for small temperature difference T = Te1 – Te2:

D. Schmidt, A. Cleland and R. Schoelkopf, Phys. Rev. Lett. 93, 045901 (2004).

Our experimental set-up

10 µm

Island size: 6 m x 0.75 m x 15 nmMaterial: PdAu

R2 R1

x

xx

x

LJ

CJ

Tunable impedance matching using DC-SQUIDs

M. Meschke et al., Nature 444, 187 (2006).

Measured variation of island temperature

90

95

100

105

110

115

120

125

155

160

165

170

105mK

118mK

T0 = 167mK

60mK

75mK

157mK

T

(m

K)

(a.u.)

e1

Vary bath temperature

Line: P1 = 1 fW, P2 =0

40 60 80 100 120 140 1600

1

2

3

4

5

6

T (

mK

)

T0 (mK)

e

Thermal model:

Heat flows from hot to cold by photon radiation

This happens between two resistors

The situation is nearly the same if we replace one resistor by an ordinary tunnel junction

N N

R, TR

RT, TN

N N

R, TR

RT, TN

Harmonic vs stochastic drive in refrigeration

N S

R, TR

RT, TN,S

N S

R, TR

RT, TN,S

N S

R, TR

RT, TN,S

N S

R, TR

RT, TN,S

N S

R, TR

RT, TN,S

N S

R, TR

RT, TN,SSinusoidal bias –Refrigerates N if frequency and amplitude are not too high

Stochastic drive –Refrigerates N if spectrum is ”suitable”

Brownian refrigerator?