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