Superconducting electronics - PowerPoint Presentation

Slide1

Superconducting electronics

from

Josephson

effects

to

quantum

computing

by

Pascal

Febvre

and

Paul Seidel

Slide2

Superconducting electronics – Part 1

Josephson

effects

Slide3

Superconductors

Cooper pairs (CP)

CP density n

s

Common wave function

ψ

Quantum mechanical phase

London penetration depth

λ

Coherence length

ξ

Abrikosov

vortex

Slide4

Tunneling effects

1961 Ivar Giaever

Quasiparticle

tunneling

and

energy

gap

è

S

1

S

2

Insulator

è

I

V

Slide5

Tunneling

experiments

[

Daghero

,

Gonelli

]

[Y.

Noat

]

[ F.

Massee

]

5

Slide6

Tunneling spectroscopy

I

T

~ N

1

(E) N

2

(

E+eU

) [f

1

(E)-f

2

(

E+eU

)]

für

T = 0, S-I-N, N

N

(E) ≡ N(0) = const.

I

T

~ N

S

(

E+eU

)

→ ~ N

S

(

E+eU

) “Tunneling spectrum”

Slide7

[ Y.

Noat

]

Slide8

YBCO

as

d-

wave

superconductor

8

Slide9

Density

of

states

of

a d-

wave

superconductor

Gemittelt über die Richtungen für 2-D Supraleiter

[

A.Carrington

]

9

Slide10

T = 0

T > 0

N (E)

N-I-N

N-I-S

S-I_S

Quasiparticle

tunneling

Slide11

Josephson effects

1962: Brian Josephson

Tunneling of

Cooper

pairs

!dc

current

without

resistanceac currents (Josephson oscillations

)

Slide12

Different Josephson effects

DC

effectAC

effect

Inverse AC

effect

„Inverse“ AC

effect

(zero

current steps)Intrinsic

Josephson effect(s)

Slide13

From SIS to different “weak links“

Slide14

Different transport in “weak links“

Tunneling of CP in SIS

Multiple Andreev reflection (scattering) in SNSDirect ballistic transport in

ScS

Mixed transport in

heterostructures

Macroscopic Quantum effects

Non-linear IV characteristics as basis of superconducting electronics

Slide15

Josephson coupling after Feynman

15

Slide16

Josephson coupling after Feynman

16

Slide17

Josephson coupling after Feynman

17

Slide18

Josephson coupling after Feynman

18

Slide19

DC Josephson current

19

dc current

periodically depends on phase difference of wave functions!

I

s

=

I

c

sin

φ, φ = φ

2

– φ

1

sometimes

non-sinusoidal current phase relations

Slide20

Critical Josephson current Ic

For

SIS

and

tunneling

like

junctions

Slide21

K

ellipt

.

Int. 1.Ord

.

Only

for

ΔL ΔR

K (x) for x

→ 0 and

and if ΔL = ΔR = Δ

VC = I

CRN = (

π/4) VG = 0,78 VG mit V

G = 2Δ /e

21

Slide22

Temperature

dependece

for

T

≠0

Ambegaokar

a

nd Baratoff

got

for

ΔL = ΔR

= Δ one gets Reminder:

for T → 0 tanh( ) gives

just 1

22

Slide23

Measurement

of

I

c

(T)

Experimentally

verified

1964 by

Fiske on Sn-SnOx

-Sn and Pb-PbO

x-Sn tunneling

junctions

Near TC for SIS:

IC ~ Δ2 ~

23

Slide24

[ C. P. Poole et al. ]

24

Slide25

DC

effect

at

weak

links

Temperature dependence

I

c

(T)

is related to the contact type, e.g. near T

c :

Tc ~ (1 – T/T

c)m m = 1 (SIS), 2/3 (SINS), 2 (SNS)→ reason: different coupling and transport mechanisms

25

Slide26

Bridge-

like

junction

26

Slide27

For bridge-like junctions length compared to the coherence length

[ B. H.

Moeckly

]

27

Slide28

Current-phase relations

[ E. Heinz ]

28

Slide29

Dependence

on

barrier

transmission

coefficient

[ E. Heinz ]

29

Slide30

I

C

in an

external

magnetic

field

Modulation of dc current in an external magnetic field (flux

Φ

=BA)with the elementary Flux quantum Φ

0 „

Fraunhofer pattern“

Ic

= Icmax ‌ abs(sin x / x )‌, x = π Φ/Φ0

30

Slide31

Current density modulation by external magnetic field for short junctions

31

[W.

Buckel

]

Slide32

[ J. Richter, P. Seidel,

Exp

. Tech. Phys. 26 (1978) 217 ]

Homogeneity of

j

c

32

Slide33

Fluctuations

[ J. Richter, P. Seidel,

Exp

. Tech. Phys. 26 (1978) 217 ]

33

Slide34

I

c

(H)

YBCO

With and without

illumination by light

(Photodoping)

[J. Elly et al.

PRB 56 (1997),

R 8507.]

34

Slide35

External

magnetic

field

at

long

junctions

35

For „long“ or better „wide“ junctions the spatial dependence of the phase has to be taken into

account

Results in a

Sine-Gordon equation

With

λ

J

= (Φ

0

/ 2πμ

0

J

c

d )

½

as the

Josephson

penetration depth

Slide36

Wide

junction

L/

λ

J

= 8,4 [N. W.

Sawaritzki

]

36

Slide37

AC Josephson effect

alternating

current

with

a

frequency

f

connected

to the

voltage V across

the

junction by

V = Φ0 ∙ f37

Slide38

rf currents !

[ K. K.

Likharev

]

38

Slide39

AC Josephson effect

- Oscillating current if voltage applied

Irradiation of electromagnetic waves

→ Josephson Oscillator

39

Slide40

Experiments

1963: S. Shapiro indirect proof of the ac Josephson effect (

Shapiro steps

)

→ inverse AC Josephson effect

40

Slide41

Inverse Josephson effect

Response to external radiation with a frequency

fex

Voltage steps (Shapiro steps)

Slide42

RCSJ model

42

DC current source

Slide43

IVC in the RSJ model

43

Slide44

RCSJ Model

Phase difference across the junction

β

c

φ” + φ’ + sin φ = i

0

+i

1

sin

Ωτ

+ iF (τ)

βc = (2e/ħ

) ICRN C (McCumber

- Parameter) τ = ω0 t , ω0 = (2e/ħ) ICRN ,

Ω = ωex / ω0

44

Slide45

Bessel

function

behaviour

Shapiro step

heigth

in the case of current biasing:

Δ I

n

= 2 IC

abs( J

n (A)) , with J

n as Bessel function n-

th order and

45F. W. Bessel (1784-1846)

Slide46

Power

dependence

[ P. Russer ]

46

Slide47

Experiments on the ac effect

1965

:

D

. N. Langenberg, D. J.

Scalapino

,

B.N

. Taylor

and in parallel L.K

. Yanson, V. M. Svistunov, J. M. Dmitrenko

direct proof

of

the Josephson radiation47

D. N. Langenberg

et al. said that the detectable power was compareable

to the light which a human eye gets from a 100 W lamp which is about 500 km away!

Slide48

„

Inverse“ AC Josephson

effect

Zero current steps (voltage across junction without current biasing)

→ Voltage standard

Jose

phson constant

K

J

= 483 597,898(19) 10

9

Hz/V

48

Slide49

Modelling

Werthamer theory

RSJ Model and variations

Andreev reflexions, Weak-link models

49

Slide50

Werthamer Model

for

SIS

50

[ M. Riedel ]

Slide51

Riedel Peak

[C. P. Poole et al. ]

51

Slide52

Intrinsic Josephson effects in anisotropic superconductors

52

Slide53

[ R. Kleiner, P. Müller ]

53

Slide54

IVC

with

many

branches

BSCCO

[ R. Kleiner ]

54

Slide55

Mesa

junction

55

Slide56

Mesa

junction

56

Slide57

Josephson

junctions

with

HTS

57

Slide58

Applications

of

Josephson

junctions

in

sc

electronics

→ Voltage standard

→

Magnetic field sensors → SQUID, SQUIF

→ Radiation detectors

→ Josephson-Oscillator („Josephson-Laser“)

→ Digital electronics (logic, memory, …)

58

Slide59

Elementary flux quantum

Φ

0

=

Φ

0

= 2,07

· 10

-15

Vs

= 2,07 · 10

-15

T · m

2

= 2,07 · 10

-3

V · 10

-12

s = 2,07 mV ·

ps