1. 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

2. Collaboration J. T. Peltonen M. Meschke J. P. Pekola
Low Temperature Laboratory, Helsinki University of Technology, 02015TKK, Finland

3. 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

4. Andreev reflection in SN contacts
BdG equations
BTK, PRB 25, 4515 (1982)

5. Normal metal (Semiconductor)
Proximity effect and supercurrent S N
Metallic contact between a normal metal and a superconductor
Reflected hole
Incident electron
Superconductor
Normal metal (Semiconductor)
Cooper pair
Andreev reflection S N
Electron-hole correlations: proximity effect
Supercurrent
Andreev bound states (ABS)

6. 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
LDOS properties:
N(-E) = N(E)
Eg for |E|  Eg
Eg( = 0)  3.2ETh for >>ETh
Eg( = ) = 0

7. Modification of the LDOS in SNS systems due to proximity effect
J. C. Cuevas et al., PRB 73, (2006)
Length and position dependence
J. C. Hammer et al., PRB 76, (2007)
Phase dependence

8. Spatial spectroscopy of PE probed with tunnel junctions
Al/Cu SN structure
with tunnel probes

9. Phase-dependence of PE probed with STM spectroscopy
Al/Ag SNS
proximity SQUIDs

10. Phase-dependence of PE probed with STM spectroscopy
Experiment to theory comparison
H. le Sueur et al., PRL 100, (2008)
Phase-evolution of PE
Full phase-control of the minigap amplitude

11. I) -tuning of specific heat: quantum control of a thermodynamic variable
H. Rabani, F. Taddei, F. G. and R. Fazio, JAP 105, (2009);
H. Rabani, F. Taddei, R. Fazio, and F. G., PRB 78, (2008)
Electron entropy
Electron specific heat

12. II) -tuning of e-ph interaction: quantum control of relaxation
T. T. Heikkila and F. G., PRB 79, (2009)

13. Sensitivity through proximity

14. 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

15. SQUIPT: fabrication details and configurations
Shadow-mask evaporation
27 nm 25
Oxidation 4.4 mbar 5’ (tunnel junctions)
27 nm -25
60 nm 60 (clean SN interfaces)
Fabrication details
Geometry and materials details
L  1.5 m
Probe width  200 nm
N wire width  240 nm
SN overlapping  250 nm
Rt  k
LG  40 pH
IJ  3 A
 = 200 eV

16. SQUIPT (theo): prediction of its behavior in the current-bias mode
A-type configuration
quasiparticle current
Usadel equations

17. SQUIPT (theo): current-voltage characteristic vs 
N-region DOS
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
Low-temperature I-V characteristic
modulation amplitude
 to V transformer

18. SQUIPT (theo): voltage modulation and transfer function
Voltage modulation V()
Features:
nonmonotonic behavior in I
change of concavity
Transfer function V/
Features:
nonmonotonic behavior in I
change of sign

19. A-type SQUIPT (exp): current-voltage characteristic vs 
Rt = 50 k
T = 68 mK
Rt = 50 k
T = 53 mK
Theory
Coherent modulation of the N DOS

20. A-type SQUIPT (exp): Josephson coupling in the proximity metal
Rt = 50 k
T = 68 mK
IJ  17 pA
Rt = 50 k
T = 53 mK
0  0.17 Oe
A  120 m2

21. A-type SQUIPT (exp): voltage modulation vs 
Rt = 50 k
T = 54 mK
V  1 nA
Change of concavity
theory
exp  50-60% theory
device parameters
non ideal phase-biasing

22. A-type SQUIPT (exp): transfer function
Rt = 50 k
T = 54 mK
V/  30 V/0 @ 1 nA
theory

23. B-type SQUIPT (exp): voltage modulation vs  and transfer function
Rt = 70 k
T = 53 mK
V  1 nA
V/  60 V/0 @ 0.6 nA
Rt = 70 k
T = 53 mK
doubled response
in B-type SQUIPT

24. A-type SQUIPT (exp): temperature dependence
Rt = 50 k
I = 1 nA
change of concavity between 376 mK and 411 mK
Rt = 50 k
I = 1 nA

25. SQUIPT: dissipation and flux sensitivity
Power dissipation
Pdiss = VI  100 fW
increasing the probing junction resistance
lowered
DC SQUIDS
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

26. 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

27. 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, (2009)
(iii)
Noise? Both theory and experiment