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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

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**Collaboration J. T. Peltonen M. Meschke J. P. Pekola**

Low Temperature Laboratory, Helsinki University of Technology, 02015TKK, Finland

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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

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**Andreev reflection in SN contacts**

BdG equations BTK, PRB 25, 4515 (1982)

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**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)

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**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

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**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

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**Spatial spectroscopy of PE probed with tunnel junctions**

Al/Cu SN structure with tunnel probes

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**Phase-dependence of PE probed with STM spectroscopy**

Al/Ag SNS proximity SQUIDs

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**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

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**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

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**II) -tuning of e-ph interaction: quantum control of relaxation**

T. T. Heikkila and F. G., PRB 79, (2009)

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**Sensitivity through proximity**

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**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

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**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

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**SQUIPT (theo): prediction of its behavior in the current-bias mode**

A-type configuration quasiparticle current Usadel equations

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**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

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**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

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**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

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**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

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**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

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**A-type SQUIPT (exp): transfer function**

Rt = 50 k T = 54 mK V/ 30 V/0 @ 1 nA theory

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**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

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**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

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**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

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**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

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**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

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