P. M. Grant Superconductivity 101 Superconductivity Workshop Charlotte, 24 May 1999 Superconductivity 101 A Primer for Engineers Paul M. Grant [email protected]

P. M. Grant

Superconductivity 101

Superconductivity Workshop

Charlotte, 24 May 1999


A Primer for Engineers

Paul M. Grant

[email protected]/staff_papers/sst

P. M. Grant



Charlotte, 24 May 1999 Fathers of Electricity

DiscoverersDiscoverers

P. M. Grant



Charlotte, 24 May 1999Fathers of Electricity

PractitionersPractitioners

P. M. Grant



Charlotte, 24 May 1999 Fathers of Cryogenics

Dewar Kammerlingh-Onnes

CH4 112 KO 90N2 77Ne 27H2 20He 4.2

P. M. Grant




(((

Models of Electrical Conductivity

The First Idea:R

T

Just Goesto Zero!

(((

(((

(((

• •e-e-

P. M. Grant




The Most Popular:R

T

Freezes Out!e-

Models of Electrical Conductivity

P. M. Grant



Charlotte, 24 May 1999 Models of Electrical Conductivity

Reality:R

T

Limited byImpurities!

•e-

P. M. Grant




Thus the mercury at 4.2 K has entered a new state, which, owing to its particular electrical properties, can be called the state of superconductivity

H. Kamerlingh-Onnes (1911)

1911A Big Surprise!

P. M. Grant



Charlotte, 24 May 1999 Magnetic Properties

0

-1/4

T

H offH on0

-1/4

T

H onH on

Expected (Lenz’ Law) Weird ! (Meissner Effect)

P. M. Grant



Charlotte, 24 May 1999They all tried…

and failed!

P. M. Grant




They came close...FritzLondon

LevLandau

IrwinFroehlich

“The B-field does penetrate.”

E ~ 2 dJ/dt, B ~ 2 J

“Since SC is a second-order phase transition, there must be an order parameter involved.”

“TC depends on the mass of the atoms (isotope effect), so the SC must be tied to lattice vibrations (phonons).”

P. M. Grant



Charlotte, 24 May 1999 They Got It Right!B ----- C ----- S

Bardeen: “It’s a macroscopic quantum state”Cooper: “It’s got twice the charge you’d expect”Schrieffer: “’s a statistical wavefunction”

There has to be a regimewhere the lattice vibrationsact to bind electrons togetherrather than scatter them withloss as given by Ohm’s Law.

P. M. Grant



Charlotte, 24 May 1999 Physics of Superconductivity

+ +

+ +•e-

•e-

Electrons Pair Off!

)/1exp( 14.1 DCT

BCS Equation

(Niobium) K 5.9

,28.0

,K 275

C

D

T

P. M. Grant



Charlotte, 24 May 1999 “Cooper’s Problem”

F er m ion -B oson F eyn m an D iagr am

q

k1

k'1

k2

k'2

C ooper P r ob lem

·

·

2D

s ingle partic les

pairs

e ik r1

e -ik r2

H(k) + H(-k ) + V(k)

V(k) = -V0 0 k f dk e ik (r1 - r2)

y(r1-r2) = f(r1-r2)(s 1,s 2)

2D ~ e -2/N(E f)V 0

P. M. Grant



Charlotte, 24 May 1999 Important Numbersin Superconductivity

Transition Temperature, TC Way below 300 K

Critical Current Density, JC 10-2 - 106 A/cm2

Critical Magnetic Field, HC 10-4 - 10 T

London Penetration Depth, 10 - >1000 Å

Pippard Coherence Length, 10 - >1000 Å

G-L Parameter, = / 0.01 - 100

NB! All these numbers depend on eachother. E.g., HC ~

P. M. Grant



Charlotte, 24 May 1999 TC vs. Year:1911 - 1980

Year

0

5

10

15

20

25

1900 1910 1920 1930 1940 1950 1960 1970 1980

Te

mp

era

ture

(K

)

Hg

Pb

NbN V3Si

Nb3Sn

Nb3Ge

Cubic Metals

P. M. Grant




MRI & “Big Physics”

Magnetic Resonance ImagingPhilips

TevatronFermi National Laboratory

P. M. Grant



Charlotte, 24 May 1999 1986Another Big Surprise!

Bednorz and MuellerIBM Zuerich, 1986

Onset TC = 40 K !

P. M. Grant



Charlotte, 24 May 1999 1987“The Prize!”

P. M. Grant



Charlotte, 24 May 1999 March 3, 1987“123” Discovered

P. M. Grant



Charlotte, 24 May 1999Woodstock of Physics

NYC, 1987Physicists’ Night Out!

P. M. Grant




Y-123

Bi-2223

HTS Layered Perovskites

P. M. Grant



Charlotte, 24 May 1999 TC vs. Year:1911 - 1999

1900 1920 1940 1960 1980 2000 0

50

100

150

200T

emp

erat

ure

, T

C (K

)

Year

Low-TC

Hig

h-T

C

164 K

P. M. Grant



Charlotte, 24 May 1999 HTSC Phase Diagram

P. M. Grant




HTS Theories

Phil Anderson

“It can’t be just an accident that hightemperature superconductivity occurs in ahost material whose insulating state is anantiferromagnet, and, which when dopedwith holes to a level where magnetic behavior disappears, we get superconductivity.”

Current Situation:• The pair coupling is believed to be magnetically mediated.• The normal conducting state is believed not to be a Landau liquid.• The superconducting state is domain- like, occurring as electronic “stripes.”

However, there is yet no generally accepted model today!

P. M. Grant



Charlotte, 24 May 1999 Boson Flavors

Phonons

P olar ons

A n yon s

S lav e -B o so n s

P las mons

E xci ton s

F er m ion -B oson F eyn m a n D ia g r a m

q

k1

k'1

k2

k'2

H ubbar d H amiltonian

H = åi [t(c ic*i+1 + h .c .) + U n in i]

t = Hopping Integral

U = C oulomb R epuls ion

P. M. Grant




Ultimate Boson

Put-ons!

P. M. Grant




GLAG

( ) ( )

( ) ( )

(| | )

( / )

/

* *

i f f f

i f f f f f

a b f

A

L

f

A

A A

A

2 2

2 12

2

12

0

1 0

0

2

1 2

1 2

I

II

G d rm

i e A i e A a b[ ] [*

( * ) *( * ) * * *]f f f ff ff ff 3 12

1

2

Lev Gor’kov

P. M. Grant




IrreversibilityLine

Mixed

NormalHC2

Mag

net

ic F

ield

TCTemperature HC2

1/4

Type II Superconductivity

Mixed

HC2

Meissner

HC1

HC2Normal

P. M. Grant




H

J

FLorentz Defects (pin sites)

Abrikosov Vortex Lattice

DipoleForce

FLorentz

J

H

Type II Superconductor in the Mixed State

P. M. Grant



Charlotte, 24 May 1999 Hg-1212:Fission-Induced Defects

• L. Krusin-Elbaum, et al., Nature

• World record Hirr at 77 K in Hg-1212

• Hg-1212 Prototype Tapes made at TCSUH

• Potential for high-field magnet inserts

P. M. Grant




Extrinsic Pinning

10 m 10 m

DECORATED VORTEX ARRAYS

with random heavy ion tracksclean

M. Leghissa, et al. Phys. Rev. B48, 1341 (1993)

P. M. Grant




FLorentzMoving Vortex Lattice

(elastic flow)

(plastic flow)

(moving liquid)

H

T

HC2

HC1

TC

Normal State

Meissner State

Vortex Liquid

Mag

neti

c F

ield

Static Phase Diagram

Vortex Glass

Bose Glass

Polymer Glass

Vortex Lattice

Vortex MatterStatic Phase Diagram

Temperature

Mag

neti

c F

ield

Dynamic

Phase D

iagra

m

TC

HC2

HC1

FLorentzElastic Flow

Plastic Flow

Liquid Flow

Normal

LiquidGlass

SolidBose Glass

Polymer Glass

Melting Line

Meissner State

SC

Flu

ctuatio

n

Regim

e

P. M. Grant




0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.008.00 9.00

10.00

85

70

50200

1

2

3

4

5

6

Jc(B

,T)/J

c(0,

77)

B(T)

T(K)

ASC Bi-2223 OPIT TapeNormalized Jc, B||ab

85777064503520

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.009.00 10.00

2050

70

85

0

1

2

3

4

5

6

Jc(B

,T)/J

c(0,

77)

B(T)

T(K)

ASC Bi-2223 OPIT TapeNormalized Jc, B||c

20355064707785

JC(B,T) for BSCCO

P. M. Grant



Charlotte, 24 May 1999BSCCO OPIT/Ag E-J Characteristic

Typical E vs J Power Law

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

0 25000 50000 75000

J (A/cm^2)

E (

V/c

m)

E = aJn

n = 15

T = 77 K

E = 1 V/cm

P. M. Grant



Charlotte, 24 May 1999 Solenoid Loop Current: t > t0

L

R(I)

I(t)

bI LdIdt

0

I(t)b(n 1)L

(t t ) I

n

0 01 n

1

1 n

P. M. Grant



Charlotte, 24 May 1999 “Persistent” Current Decay

Persistent Current Decay

0

50

100

150

200

250

300

350

400

450

1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07t (sec)

I (A

)

B = 0.50 T

B = 0.25 T12 Days

P. M. Grant




Type II Hysteresis

H

M

P. M. Grant




Hysteretic ac Loss

P. M. Grant




The Future 2028

P. M. Grant




The Future

700 K !

May, 2028

P. M. Grant



Charlotte, 24 May 1999Electricity:

A Life NecessityCalifornia, Summer 1996

Quebec, Winter 1997

P. M. Grant



Charlotte, 24 May 1999“You can’t always get

what you want…”

P. M. Grant



Charlotte, 24 May 1999“…you get what you

need!”

Documents

P. M. Grant Superconductivity 101 Superconductivity Workshop Charlotte, 24 May 1999 Superconductivity 101 A Primer for Engineers Paul M. Grant [email protected]