perugia giazotto
TRANSCRIPT
Universita’ di Perugia
15 Aprile 2010
Ruolo delle correlazioni superconduttive in conduttori mesoscopici: utilizzo per l’implementazione di rilevatori
quantistici
Francesco GiazottoNEST Istituto Nanoscienze-CNR & Scuola Normale Superiore
Pisa, Italia
Collaboration
J. T. PeltonenM. MeschkeJ. P. PekolaLow 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
BdG equationsAndreev reflection
BTK, PRB 25, 4515 (1982)
Proximity effect and supercurrent
S SN
Metallic contact between a normal metal and a superconductor
SS SSNN
Electron-hole correlations: proximity effect
Supercurrent Andreev bound states (ABS)
Reflected hole
Incident electron
SuperconductorSuperconductorNormal metal Normal metal (Semiconductor)(Semiconductor)
Cooper pair
Andreev reflection
Proximity effect in SNS systems: basic formalism
Diffusive mesoscopic N wire:quasi-1D geometryLφ >L >> leD = diffusion coefficient∆ = superconducting order parameterφ = macroscopic phase of the order parameterETh = D/L2 Thouless energy
LDOS properties:
N(-E) = N(E)Eg for |E| ≤ Eg
Eg(φ = 0) ≈ 3.2ETh for ∆>>ETh
Eg(φ = π) = 0
Usadel equations
LDOS
Modification of the LDOS in SNS systems due to proximity effect
J. C. Hammer et al., PRB 76, 064514 (2007)
Phase dependence
J. C. Cuevas et al., PRB 73, 184505 (2006)
Length and position dependence
Al/Cu SN structure with tunnel probes
Spatial spectroscopy of PE probed with tunnel junctions
Phase-dependence of PE probed with STM spectroscopy
Al/Ag SNS proximity SQUIDs
Experiment to theory comparison
Phase-dependence of PE probed with STM spectroscopy
H. le Sueur et al., PRL 100, 197002 (2008)
Phase-evolution of PE
Full phase-control of the minigap
amplitude
I) φ-tuning of specific heat: quantum control of a thermodynamic variable
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 entropy Electron specific heat
II) φ-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)
Detection (through tunnel junctions)
High sensitivity for flux detection
SQUIPT
SQUIPT: fabrication details and configurations
Shadow-mask evaporation27 nm Al @ 25°Oxidation 4.4 mbar 5’ (tunnel junctions)27 nm Cu @ -25°60 nm Al @ 60° (clean SN interfaces)
Fabrication details
Geometry and materials details
L ≈ 1.5 µmProbe width ≈ 200 nmN wire width ≈ 240 nmSN overlapping ≈ 250 nmRt ≈ 50-70 kΩLG ≈ 40 pHIJ ≈ 3 µA∆ = 200 µeV
SQUIPT (theo): prediction of its behavior in the current-bias mode
A-type configuration
Usadel equations
quasiparticle current
SQUIPT (theo): current-voltage characteristic vs Φ
Calculation parameters from the samples:T = 0.1 Tc
Tc = 1.3 KETh = 4 µeVD = 110 cm2/s (Cu)∆= 200 µeVRt = 50 kΩ
0 160 200 240
0
1
2
3
I(n
A)
V(µV)
0 1/8 1/4 3/8 1/2
Φ/Φ0
I = const.
δV
Low-temperature I-V characteristic
modulation amplitude
Φ to V transformer
N-region DOS
-4.0x10-23 0.0 4.0x10-230
1
2
0.0 1/8 1/4 3/8 1/2
DO
S (
ε)ε (J)
Φ/Φ0
ETh
= 4 µeV
SQUIPT (theo): voltage modulation and transfer function
0 1 2 3200
220
2402.8
2.0
0.8
1.2
1.6
2.4
V(µ
V)
Φ /Φ0
I(nA)
Voltage modulation V(Φ)
Features:• nonmonotonic behavior in I• change of concavity
0.0 0.5 1.0 1.5 2.0-50
-25
0
25
50
∂V/∂
Φ [µ
V/Φ
0]Φ /Φ
0
Transfer function ∂V/∂Φ
Features:• nonmonotonic behavior in I• change of sign
A-type SQUIPT (exp): current-voltage characteristic vs Φ
-300 -150 0 150 300-5
-4
-3
-2
-1
0
1
2
3
4
I (n
A)
V (µV)
Rt = 50 kΩT = 68 mK
Coherent modulation of the N DOS
160 200 240 280
0.5
1.0
1.5
2.0
2.5
3.0
I (n
A)
V (µV)
0.0 0.15 0.29 0.5
Φ/Φ0
I = const.
δV
Rt = 50 kΩT = 53 mK
0 160 200 240
0
1
2
3
I(nA
)
V(µV)
0 1/8 1/4 3/8 1/2
Φ/Φ0
I = const.
δV
Theory
A-type SQUIPT (exp): Josephson coupling in the proximity metal
-200 -100 0 100 200
-40
-20
0
20
40
I (p
A)
V (µV)
Rt = 50 kΩT = 68 mK
IJ ≈ 17 pA
-20
-10
0
10
20
I (
pA)
V100 µ V
Rt = 50 kΩT = 53 mK
Φ0 ↔ 0.17 OeA ∼ 120 µm2
A-type SQUIPT (exp): voltage modulation vs Φ
-4 -2 0 2 4
3.0
2.6
2.2
1.8
1.4
1.0
0.6
0.2
V
Φ/Φ0
I (nA)
10
µV
Rt = 50 kΩT = 54 mK
δV ≈ 7µV @ 1 nA
Change of concavity
0 1 2 3200
220
2402.8
2.0
0.8
1.2
1.6
2.4
V(µ
V)
Φ /Φ0
I(nA)
theory
exp ≈ 50-60% theory
• device parameters• non ideal phase-biasing
A-type SQUIPT (exp): transfer function
0 1 2 3 4
-20
0
20
∂V/∂
Φ (
µV/Φ
0)
Φ/Φ0
0.2 1.0 1.6 2.2 3.0
I (nA)
Rt = 50 kΩT = 54 mK
∂V/∂Φ ≈ 30 µV/Φ0 @ 1 nA
0.0 0.5 1.0 1.5 2.0-50
-25
0
25
50
∂V/∂
Φ [µ
V/Φ
0]
Φ /Φ0
theory
0 1 2 30
10
20
30
Ma
x |∂
V /∂
Φ| (
µV/Φ
0)
I (nA)
B-type SQUIPT (exp): voltage modulation vs Φ and transfer function
-4 -2 0 2 4
3.0
2.6
2.2
1.8
1.4
1.0
0.6
I (nA)
0.2
V
Φ/Φ0
20 µ
V
Rt = 70 kΩT = 53 mK
δV ≈ 12µV @ 1 nA
∂V/∂Φ ≈ 60 µV/Φ0 @ 0.6 nA
Rt = 70 kΩT = 53 mK
0 1 2 30
20
40
60
Max
|∂V
/∂Φ
| (µV
/Φ0)
I (nA)
doubled response in B-type SQUIPT
A-type SQUIPT (exp): temperature dependence
0 400 8000
10
20
30
40
50
Max
|∂V
/∂Φ
| (µV
/Φ0)
T (mK)
Rt = 50 kΩI = 1 nA
Rt = 50 kΩI = 1 nA
-4 -2 0 2 4
411
730
512618
452
54
123
200
244
288
313353376
V
Φ/Φ0
T (mK)
20 µ
V
change of concavity between 376 mK and 411 mK
SQUIPT: dissipation and flux sensitivity
Pdiss = VI ∼ 100 fW increasing the probing junction resistancelowered
DC SQUIDS 4-5 orders of magnitude smaller in the SQUIPT
Ultralow dissipation cryogenic applications
Power dissipation
Flux sensitivity
NEF = <V2N>1/2/|∂V/∂Φ|δυ1/2
NPre ∼ 1.2 nV/Hz1/2 NEF ≈ 2 × 10-5 Φ0/Hz1/2
NEF ≈ 4 × 10-7 Φ0/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
Short junction limit (∆<<ETh) Al and L = 150 nm
(i)
(ii)
V SNS junction SQUIPT
C. Pascual Garcia and F. G., APL 94, 132508 (2009)
(iii) Noise? Both theory and experiment