Ruolo delle correlazioni superconduttive in conduttori
mesoscopici: utilizzo per l’implementazione di rilevatori
quantistici
Francesco Giazotto
NEST Istituto Nanoscienze-CNR & Scuola Normale Superiore
Pisa, Italia
Universita’ di Perugia
15 Aprile 2010
Collaboration
J. T. Peltonen
M. Meschke
J. P. Pekola
Low Temperature Laboratory, Helsinki University of Technology, 02015TKK, Finland
Outline
• Part I: Andreev reflection and proximity effect in superconducting hybrid systems – impact on
the density of states
• Basic concepts of electron transport in hybrid systems: AR and PE
•Proximity-induced modification of the DOS
• Probing the proximized DOS: experiments with tunnel junctions and STM spectroscopy
• Consequences
• Part II: Superconducting quantum interference proximity transistor (SQUIPT)
• Theoretical behavior of the SQUIPT
• Structure fabrication details
• Experimental results and comparison with theory
• Advantages
• Future perspectives
Andreev reflection in SN contacts
Andreev reflection
BdG equations
BTK, PRB 25, 4515 (1982)
Proximity effect and supercurrent
Metallic contact between a normal metal and a superconductor
S
N
S
Andreev reflection
Normal metal
(Semiconductor)
Electron-hole correlations: proximity effect
S
N
S
Superconductor
Cooper pair
Incident electron
Reflected hole
Supercurrent
Andreev bound states (ABS)
Proximity effect in SNS systems: basic formalism
Diffusive mesoscopic N wire:
quasi-1D geometry
L >L >> le
D = diffusion coefficient
 = superconducting order parameter
 = macroscopic phase of the order parameter
ETh = D/L2 Thouless energy
Usadel equations
LDOS properties:
LDOS
N(-E) = N(E)
Eg for |E|  Eg
Eg( = 0)  3.2ETh for >>ETh
Eg( = ) = 0
Modification of the LDOS in SNS systems due to proximity effect
Length and position dependence
J. C. Cuevas et al., PRB 73, 184505 (2006)
Phase dependence
J. C. Hammer et al., PRB 76, 064514 (2007)
Spatial spectroscopy of PE probed with tunnel junctions
Al/Cu SN structure
with tunnel probes
Phase-dependence of PE probed with STM spectroscopy
Al/Ag SNS
proximity SQUIDs
Phase-dependence of PE probed with STM spectroscopy
Phase-evolution of
PE
Full phase-control
of the minigap
amplitude
Experiment to theory
comparison
H. le Sueur et al., PRL 100, 197002 (2008)
I) -tuning of specific heat: quantum control of a thermodynamic variable
Electron entropy
H. Rabani, F. Taddei, F. G. and R. Fazio, JAP 105, 093904 (2009);
H. Rabani, F. Taddei, R. Fazio, and F. G., PRB 78, 012503 (2008)
Electron specific heat
II) -tuning of e-ph interaction: quantum control of relaxation
T. T. Heikkila and F. G., PRB 79, 094514 (2009)
Sensitivity through proximity
SQUIPT: a novel quantum interferometer
Active manipulation of the DOS of a proximity N metal
Phase control (through magnetic flux)
SQUIPT
Detection (through tunnel junctions)
High sensitivity for flux detection
SQUIPT: fabrication details and configurations
Fabrication details
Shadow-mask evaporation
27 nm Al @ 25
Oxidation 4.4 mbar 5’ (tunnel junctions)
27 nm Cu @ -25
60 nm Al @ 60 (clean SN interfaces)
Geometry and materials details
L  1.5 m
Probe width  200 nm
N wire width  240 nm
SN overlapping  250 nm
Rt  50-70 k
LG  40 pH
IJ  3 A
 = 200 eV
SQUIPT (theo): prediction of its behavior in the current-bias mode
A-type configuration
quasiparticle current
Usadel equations
SQUIPT (theo): current-voltage characteristic vs 
N-region DOS
2
ETh = 4 eV
Low-temperature I-V characteristic
/0
DOS ()
3
0
1/8
1/4
3/8
1/2
/0
0.0
1/8
1/4
3/8
1/2
1
I(nA)
2
0
-23
-4.0x10
1
 to V transformer
0
V
160
4.0x10
-23
 (J)
I = const.
0
0.0
200
V(V)
240
modulation amplitude
Calculation parameters
from the samples:
T = 0.1 Tc
Tc = 1.3 K
ETh = 4 eV
D = 110 cm2/s (Cu)
= 200 eV
Rt = 50 k
SQUIPT (theo): voltage modulation and transfer function
Voltage modulation V()
2.8
50
I(nA)
V/ [V/0]
V(V)
240
Transfer function V/
2.4
2.0
220
1.6
0.8
1
/
0
-25
1.2
200
0
25
2
Features:
• nonmonotonic behavior in I
• change of concavity
3
-50
0.0
0.5
1.0
/0
1.5
Features:
• nonmonotonic behavior in I
• change of sign
2.0
A-type SQUIPT (exp): current-voltage characteristic vs 
4
Rt = 50 k
T = 68 mK
Rt = 50 k
T = 53 mK
3
/0
3.0
2
2.5
Theory
3
/0
0
I (nA)
-1
-2
-3
2.0
-5
-300
2
1.5
-4
1
I = const.
-150
0
150
300
0
1/8
1/4
3/8
1/2
I(nA)
I (nA)
1
0.0
0.15
0.29
0.5
I = const.
1.0
V (V)
0
V
0.5
V
160
200
0
240
280
V (V)
Coherent modulation of the N DOS
160
200
V(V)
240
A-type SQUIPT (exp): Josephson coupling in the proximity metal
Rt = 50 k
T = 53 mK
40
20
20
10
I (pA)
I (pA)
Rt = 50 k
T = 68 mK
0
-20
-10
-40
-200
0
-20
-100
0
V (V)
IJ  17 pA
100
200
100 V
V
0  0.17 Oe
A  120 m2
A-type SQUIPT (exp): voltage modulation vs 
theory
2.8
240
I (nA)
I(nA)
2.4
3.0
V(V)
10 V
Rt = 50 k
T = 54 mK
2.6
2.2
1.8
2.0
220
1.6
1.2
V
Change of concavity
0.8
1.4
200
0
1.0
1
/
2
exp  50-60% theory
0.6
0.2
-4
-2
0
/0
2
V  7V @ 1 nA
4
• device parameters
• non ideal phase-biasing
3
A-type SQUIPT (exp): transfer function
theory
50
V/ [V/0]
V/ (V/0)
Rt = 50 k
T = 54 mK
I (nA)
0.2
1.0
1.6
2.2
3.0
20
0
0
-25
-50
0.0
1
2
/0
3
V/  30 V/0 @ 1 nA
4
Max |V /| (V/0)
-20
0
25
0.5
30
20
10
0
0
1
2
I (nA)
3
1.0
/0
1.5
2.0
B-type SQUIPT (exp): voltage modulation vs  and transfer function
Rt = 70 k
T = 53 mK
I (nA)
Max |V /| (V/0)
20 V
Rt = 70 k
T = 53 mK
3.0
2.6
2.2
V
1.8
1.4
60
40
20
1.0
1
2
I (nA)
0.6
V/  60 V/0 @ 0.6 nA
0.2
-4
0
0
-2
0
/0
2
V  12V @ 1 nA
4
doubled response
in B-type SQUIPT
3
A-type SQUIPT (exp): temperature dependence
Rt = 50 k
I = 1 nA
T (mK)
730
618
512
452
411
376
353
313
288
Max |V /| (V/0)
V
20 V
Rt = 50 k
I = 1 nA
244
200
123
50
40
30
20
10
54
-4
-2
0
/0
2
4
0
0
400
T (mK)
change of concavity between 376 mK and 411 mK
800
SQUIPT: dissipation and flux sensitivity
Power dissipation
lowered
Pdiss = VI  100 fW
DC SQUIDS
increasing the probing junction resistance
4-5 orders of magnitude smaller in the SQUIPT
Ultralow dissipation cryogenic applications
Flux sensitivity
NEF = <V2N>1/2/|V/|1/2
NPre  1.2 nV/Hz1/2
NEF  2  10-5 0/Hz1/2
NEF  4  10-7 0/Hz1/2 with Nb (1.5 meV) and L = 150 nm
SQUIPT: advantages
•simple DC readout scheme, similar to DC SQUID
• current- or voltage-biased measurements
• flexibility in farication parameters and materials
(semiconductors NWs, carbon nanotubes, graphene)
• Nb or V to enhance response and operating temperature
• ultralow dissipation (1-100 fW)
• implementation in series or parallel array for enhanced output
• implementation with S coolers to “actively” tune the working temperature
SQUIPT: future perspectives
(i)
Short junction limit (<<ETh)
Al and L = 150 nm
(ii)
V SNS junction SQUIPT
C. Pascual Garcia and F. G., APL 94, 132508 (2009)
(iii)
Noise? Both theory and experiment