Sukumar Rajauria Néel Institute, CNRS and Université Joseph Fourier, Grenoble, France With H....
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Transcript of Sukumar Rajauria Néel Institute, CNRS and Université Joseph Fourier, Grenoble, France With H....
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