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
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
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