Sukumar RajauriaNéel Institute,

CNRS and Université Joseph Fourier, Grenoble, France

With H. Courtois, P. Gandit, T. Fournier, F. Hekking, B. Pannetier

Inherent Thermometer in a Superconductor – Normal metal – Superconductor cooling

junction

Outline

• Introduction

• Sample and Experiments

• Extraction of electronic temperature

• Thermal model

• Conclusion

E

2Δ

I ST = 0 K

Empty States

Occupied States

Forbidden states

N

Quasiparticle Tunneling in N-I-S junction

Principle of N-I-S coolerThe superconductor energy gapInduces an energy-selectivetunneling.

Quasiparticle Tunneling in N-I-S junction

E

2Δ

I ST > 0 K

N

~4kT

Empty States

Occupied States

Forbidden states

Principle of N-I-S coolerThe superconductor energy gapInduces an energy-selectivetunneling.

0 1 2 30

1

2

3

T = 0.49Tc

IeR

n/

V/

T = 0.07Tc

d)eV(f)eV(f)(NeR

I NNSN

1

E

2Δ

I S

Empty States

Occupied States

T > 0 K

eV

It

Forbidden states

N

Quasiparticle Tunneling in N-I-S junction

Principle of N-I-S coolerThe superconductor energy gapInduces an energy-selectivetunneling.

d)(f)eV(f)eV)((NRe

Q NSSN

2

1

E

2Δ

I S

Empty States

Occupied States

T > 0 K

eV Forbidden states

N

Q

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.

-1,5 -1,0 -0,5 0,0 0,5 1,0 1,50,00

0,01

0,02

0,03

0,04

0,05

0,06

T = 0.49Tc

Pe2 R

N/

(0)2

V/(0)

T = 0.07Tc

F. Giazotto, T. T. Heikkila, A. Luukanen, A. M. Savin and J. P. Pekola, Rev. Mod. Phys. 78, 217 (2006).

S-I-N-I-S = 2 × N-I-S junctions in series

Pcool increases by a factor of 2

Better thermal isolation of N-island

Vbias

S N S

Thermometer

Need for a thermometer !

EE

2Δ

I S

Empty States

Occupied States

T > 0 KN

eVeV

2Δ

S

ItIt

QQ

The S-I-N-I-S geometry

I

)Tk

eVexp(II

N,eB

0

E. Favre-Nicollin et. al.

Thermometer Junctions

Cooler junctions

2 µm

Cu

Al

Al

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0

10-2

10-1

100

Cooler ON 134 mK

dI/dV

The

rmom

eter

VThermometer

/

Cooler OFF 288 mK

Thermometry with N-I-S junctions

Additional N-I-S junctions can be used as a thermometer:

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 ?

Probe Junction: N electrode is strongly thermalized, litlle cooling effect expected.

I

1 µm

Cu

Cu

Al

Cooler junctions: N electrode is weakly coupled to external world,

strong cooling effect expected.

A cooler with improved aspect ratio

0.001

0.01

0.1

1

0.01

0.1

1

10

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

dI/dV(norm.)

V/(2)

Cooler

Probe

Probe follows isothermal prediction at Tbase.

High resolution measurement(log scale)

« Cooler behaves differently »

)Tk

eVexp(II

N,eB

0

Probe

Tbase = 304 mK

Cooler

Al

I

1 µm

CuCu

Cooling in N-I-S junction

ProbeCooler

0.0 0.1 0.2 0.3 0.4 0.510-4

10-3

10-2

10-1

100

IeR

n/

V (mV)

T = 98 mK

IsothermT = 304 mK

Cooler Superposition of expt data with isotherm gives the electronic temperature at a particular bias.

Temperature Determination

Determination of the bias-dependent electron temperature

-0.4 -0.2 0.0 0.2 0.40

100

200

300

T (

mK

)

V (mV)

Tbase

dEEfeVEfEneVE

eR1

VP SNSn

cool

55ephphe TTUP

44phbaseK TTKAP

N electrons, TeS, Tbase S, Tbase

N phonons, Tph

Substrate phonons, Tbase

Power flow from N electrons to the S electrodes remaining at base temperature

Electron - phonon coupling

Kapitza thermal coupling

The thermal model

Kphecool PPP2 Steady state:

dEEfeVEfEneVE

eR1

VP SNSn

cool

55ephphe TTUP

N electrons, TeS, Tbase S, Tbase

N phonons, Tph

Substrate phonons, Tbase

Power flow from N electrons to the S electrodes remaining at base temperature

Electron - phonon coupling

Kapitza thermal coupling

The thermal model

Kphecool PPP2 Steady state:

PK KA Tbase4 Tph

4

Hyp.: N phonons are strongly thermalized

For Tph = Tbase

Impossible to fit data with a given

Need to let phonon temperature Tph vary

5base

5ecool TTUP2

5base

cool5

base

e

T

P2U1

1T

T

Hypothesis of phonon thermalized to the bath

0 10 20 30 40 50 600,0

0,2

0,4

0,6

0,8

1,0

T (K) (*109 Wm-3K-5

)------------------------------------292 1,21489 1,02586 0,80------------------------------------

(Te/

Tba

se)5

Pcool

/Tbase

5 (pW/K5)

TBase (mK) (109) (Wm-3K-5)

2

dEEfeVEfEneVE

eR1

VP SNSn

cool

55ephphe TTUP

44phbaseK TTKAP

N electrons, TeS, Tbase S, Tbase

N phonons, Tph

Substrate phonons, Tbase

Power flow from N electrons to the S electrodes remaining at base temperature

Electron - phonon coupling

Kapitza thermal coupling

The thermal model

Kphecool PPP2 Steady state:

N phonons can be cooled

Two free fit parameters:

= 2 nW.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 mK at 500 mK

0,0 0,1 0,2 0,3 0,40

100

200

300

400

500

600

Electrons

T (

mK

)

V (mV)

Phonons

Phonon Cooling

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

NanoSciERA “NanoFridge“

0.0 0.1 0.2 0.3 0.4 0.510-4

10-3

10-2

10-1

100

IeR

n/

V (mV)

T = 98 mK

IsothermT = 304 mK

Cooler

0,0 0,1 0,2 0,3 0,40

100

200

300

400

500

600

ElectronsT

(m

K)

V (mV)

Phonons

Phonon temperature

dk

hvT

B

s

2

For d = 50 nm, T > 0.35 K

Extrapolation of the model

0.001

0.01

0.1

1

10

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

dI/dV(norm.)

V (mV)

K = 0525125

isotherm320 mK

Parameter K governs coupling between the metal phonons and the substrate

K = 0: diff. cond. peak at zero bias

-1

-0.5

0

0.5

1

V

0.2

0.4

0.6

0.8

T

-0.05

-0.025

0

0.025

0.05

P

-1

-0.5

0

0.5

1

V