heat conduction by photons through superconducting leads
DESCRIPTION
Heat conduction by photons through superconducting leads. W.Guichard Université Joseph Fourier and Institut Neel, Grenoble, France. M. Meschke, and J.P. Pekola Low Temperature Laboratory, Helsinki University of Technology, Espoo, Finland. Thermal conductance. T 2. T 1. Heat flow. - PowerPoint PPT PresentationTRANSCRIPT
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Heat conduction by photons through superconducting leads
G R E N O B L E 1
UNIVERSITEJOSEPH F OURIERSCIENCES. TECHNOLOGIE. MEDECINE
W.Guichard Université Joseph Fourier and Institut Neel, Grenoble, France
M. Meschke, and J.P. Pekola Low Temperature Laboratory, Helsinki University of Technology, Espoo, Finland
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Thermal conductance
TK
nncqQ
ph
kcoldkhotsoundk k
kkph
)(
TKQ
TK
ffL
Q
el
kcoldkhotkk
kel
1
T1
Heat flow (T1 > T2)
T2
Heat flow Thermal conductance
What conducts heat in a solid ?
Phonons (lattice vibrations)
Quantum of thermal conductanceT T +T
Q
Th
kK B
Q 3
22
and what about photons ?
Electrons (important for metals)
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Measurement of quantized thermal conductance
2DEG in a GaAs-AlGaAs heterostructure
Molenkamp et al. Phys. Rev. Lett 68 (1992)
Quantized electronic thermal conductance
Quantized phonon thermal conductance
K. Schwab et al. , Nature 404 (2000)
Silicon nitride membrane
Th
kK B
Q 3
22
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Energy relaxation in a submicron metal island
1
1),(
/)(
eBTkµEe
eTEf
0 100 200 300 400 500
100
80
60
40
20
0
RS
INIS
[M]
TBATH
[mK]
0
100
200
300
400
500
Te[m
K]
M.Meschke et al.
In thermal equilibrium:
Electron-electron collissions
Electron-phonon collisions T0
TenvTe
Ge
Gep
fWPmKT
mmm
mKWT
PT
TTP
exe
phex
e
pheex
1100
025.06.04
102
3595 5
55
Pex
Pep
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Energy relaxation in a submicron metal island
1
1),(
/)(
eBTkµEe
eTEf
0 100 200 300 400 500
100
80
60
40
20
0
RS
INIS
[M]
TBATH
[mK]
0
100
200
300
400
500
Te[m
K]
M.Meschke et al.
In thermal equilibrium:
Electron-electron collisions
Electron-phonon collisions T0
TenvTe
Ge
Gep
fWPmKT
mmm
mKWT
PT
TTP
exe
phex
e
pheex
1100
025.06.04
102
3595 5
55
+Electron-photon „radiative“ relaxation ?
Pex
Pep
Pe
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Heat transported between two resistors
2
1
1e
1**4)(
/
th
hRvS iiV
21
22
22
21
02121
32
)]()([
TTh
krP
dhnhnhrP
B
net
1,
)(
42
21
21
rRR
RRr
Voltage noise emitted by resistor Ri:Ge= ?
1D Black body radiation
R2,T2R1,T1
Th
kKrK
dT
dPK B
QQ 3 ,
22 Quantum of thermal
Conductance:
Net heat flow from hot to cold resistor:
Schmidt et al.,Phys. Rev. Lett., 93 (2004)
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Competition between ep- and e- coupling
3/122
15
Vh
krT B
cr
0.05 0.1 0.15 0.2 0.250.310-15
10-14
10-13
10-12
Gep
, = 2.0 109, = 6.0 10-20
Ge, r = 1
Ge, r = 0.2
G (
WK
-1)
T (K)
TCO
Cross-over temperature:
Th
krVTK
TTKr
PTTVP
Bep
enveQeeep
3K 5
)(2
22
e4
221
50
51
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Typical experimental set-up
Island size:6.6 m x 0.8 m x 20 nm
SINIS junction size:3 m x 0.1 m
SQUID junction size:3 m x 0.1 m
Iheat
V
Ib
Electrical circuit
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Actual experimental configuration: tunable impedance between the resistors
)(
* 21
totZ
RRr
QSQUIDceffe GRRCIrG ,...),,,( 21h
Tkvvx B
thth with /
dxe
exxr
G
G
x
x
thQ
e2
2
0 1
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Electrical Model I
0.0 0.5 1.0 1.5 2.00.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
G/G
Q
Ic=1nA Ic=10nA Ic=200nA
cmc
thth 1
cJ I
L2
0
Transmission line:C0 C0 C0
L0 L0 L0
C0 C0 C0
L0 L0 L0
R1 R2
R1 R2
Tunable inductance:
Here:
cJ I
L2
0
L~30 μm
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Electrical Model II
0.0 0.5 1.0 1.5 2.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
G/G
Q
Ic=500nA Ic=100nA Ic=20nA Ic=0.1nA
LSQ
CSQ R2R1LSQ
CSQ
CSQUID=30fF
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Thermal model
Typical parameter values:P1 = 1 fWP2 = 0
50
522
222
211
2
2
50
511
222
211
2
1
12
12
TTTrTrh
kP
TTTrTrh
kP
eeeB
eeeB
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SINIS thermometer
0 100 200 300 400 500 600 700 8000.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
V (
mV
)
T (mK)
Measured at I = 9 pA
Probes electron temperature of N island (and not of S!) in the case of T/Tc<0.4
Low leakage of junctions
-0.6 -0.4 -0.2 0.0 0.2 0.4-6
-4
-2
0
2
4
6
215mK 250mK 285mK 320mK 360mK 395mK 430mK
I (n
A)
V (mV)
38mK 48mK 78mK 110mK 145mK 180mK
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Measured variation of island temperature:
T0
Te2Te1
Ge
Gep1 Gep2
P2P1
-0.162
-0.161
-0.160
-0.159
-0.158
-0.157
-0.156
-0.155
V S
INIS
[mV
]
Flux [a.u.]
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Measured variation of island temperature:variation of bath temperature
Flux Φ0
T0
Te2Te1
Ge
Gep1 Gep2
P2P1
-2 -1 0 1 2
90
100
110
120
130
140
150
160
170 TBATH
= 157mK 147mK 114mK 102mK 75mK 60mK
T[m
K]
Ic=20nACSQUID=15fFR1=R2=200P1=1fWP2=0
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Increase island temperature Te1
-2 -1 0 1 2
160
170
180
190
200
210
220
17800 fW2700 fW180 fW70 fW30 fW0 fW
T[m
K]
-2 -1 0 1 290
100
110
120
130
140
150
160
170
180
190
200
210 17800 fW7100fW2700 fW1100 fW450 fW180 fW70 fW30 fW5 fW2 fW0 fW
T[m
K]
Flux Φ0 Flux Φ0
T0<40mK T0=150mKT0
Te2Te1
Ge
Gep1 Gep2
P2P1
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Measured variation of island temperature:amplitude of modulation
<40mK 75mK 102mK 114mK 147mK 157mK
T0
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Conclusion
-First observation of the crossover from phonon relaxation to radiative photon relaxation at temperatures of about 100 mK
-Thermal and electrical model explain quite well the measured data
-Implications on:performance of bolometers (sensitivity): coupling to the heat bath
removing excessive heat from devices at milli-kelvin range