1

2

3

Jean François Champollion was a young student, when

he met in Grenoble the famous mathematician Joseph

Fourier, secretary of the Egyptian Institute of Cairo.

Fourier noticed Champollion and

invited that student to visit his

Egyptian collection.

Looking at the hieroglyphics, the young Champollion

asked if deciphering those signs would have ever

been possible or not.

Once obtained a negative answer from Fourier,

Champollion decided that in future he would have

solved the mistery!

http://it.wikipedia.org/wiki/Immagine:Jean-Francois_Champollion_2.jpghttp://it.wikipedia.org/wiki/Immagine:Rosetta_Stone.jpg

4

The desire to discover and understand secrets is deeply rooted inside the man-kind.

Even the less curious mind is stimulated by the perspective

to reach knowledge levels that remain unachievable

to others.

Someone has the luck to find a job that consists of the

search for solving mysteries, as the Physicist that looks for a still undiscovered elementary particle or the investigator

that discovers the author of a crime!

5

However the only possibility given to the majority of people for

satisfying this fundamental need is the application of its “own genius” to the solution of enigmas invented for our

enjoyment.

For the majority of people there are detective stories and crosswords:

The deciphering of secret codes, the discovery of a new

particle, or of a new material, can only be an hobby for a limited

number of lucky people!

6

7

APPLIED SUPERCONDUCTIVITY(Phenomenology of a Superconductor)

Enzo Palmieri

ISTITUTO NAZIONALE DI FISICA NUCLEARELaboratori Nazionali di Legnaro

andPADUA UNIVERSITY

Material Science and Engineering

__________________________CERN, Academic Training, Jan 17 2007

Lecture 1 of 3

8

APPLIED SUPERCONDUCTIVITY(CERN, Academic Training)

Wednesday, Jan 17, 2007

Lecture 1 / 3 Phenomenology of a Superconductor

Thursday, Jan 18, 2007

Lecture 2 / 3 Some Industrial Applications

Friday, Jan 19, 2007

Lecture 3 / 3 Superconducting materials

9Ele

ctrical

Resi

stivity

vsTem

peratu

re

of som

e com

mon m

aterial

s

10

ELECTRICAL CONDUCTION in metals

DRUDE MODEL of a free Electron Gas (1900)

“Electrons Wonder freely through a background of positive ions strongly pinned in Ordered Positions”

eZa

-eZ

-e(Za-Z)Es.:

Na 1s2 2s2 2p6 3s1eZa

-e(Za-Z)

eZa

-e(Za-Z)

eZa

-e(Za-Z)

eZa

-e(Za-Z)

Nucleus

Core Electrons

Valence Electrons

Nucleus

Core

Conduction Electrons

Ion

11

The Hovland Rule for remembering the ground state electron configurations

1s2s

2p 3s

3d 4p3p 4s

4d 5p4f 5d

5f 6d6p 7s

7p 8s

6s5s

The electron configuration for a given element is then obtained by starting at the lower left and reading from left to right on successive rows

12

DRUDE MODEL of a free Electron Gas

Approximations:

i. e-e interactions and e-ion interactions are neglectedii. Fixed ions, instantaneous collisions

iii. After any collisions, electron loose memory

ENo field

Limits:Hall effect; Magneto-resistance; ; m.f.p.; σ(Τ); σ(ω); Boron vs Alluminum)(TfT

k=

⋅σ

13

Low Temperature Resistivity

K

MD

Lord Kelvin: Electrons become free due to the thermal vibrations

Matthiessen: Phonons + Residual (1984)

Sir J. Dewar: Electron motion gets obstructed by thermal vibrations

Dewar liquified H2, but he was not able to liquify He, then he switched to study soap films

14

EEr

Eedtpd rr

−=

mne τ

ρσ2

1 == == f1τ Time between two collisions

EEm

ndtpd

mneJ e rr

rr⋅=⋅⋅=⋅−= σττ

2

Ohm Law

τττ resph111

+=ff resphf +=The collision frequency is addiive:

ρρρ resph +=

15

ρρρ resph +=Matthiessen Law

(Valid only for low concentration of impurities)

ρres

Impurities

Lattice imperfections

Grain boudaries

Dρres

ρ(T)

ρph

D > limp τττ impph111

+= ττττ GBimpph1111

++=D < limp

16

ρρ

ρρ

residual

phonons

residual

KKRRR)300(

1)300( +==

][4

112.4

−− ⋅⋅= KmWRRRKλ

17

18

19

20

Heike Kamerlingh Onnes (left) and Van der Waals in Leiden at the helium 'liquefactor' (1908)

21

22

23

0RR

Temperature [K]

Au in pure form

Hg distilled(28th° Apr 1911)

24

)exp()0( tLRII −=

Persistent currents in superconducting rings ~ 2,5 years of experiment

(Collings, 1956) ρ < 10-21 Ω cm(Quinn, Ittner, 1962) ρ < 10-23 Ω cm

25

26

H

Ta

Ni

Li

Ca

Mg

Be

Sc

Sr Nb

H

Ba

Rb

K

Na

Cs

Fr

Cr Mn FeV

Y Zr

Lu Hf

Co

PdMo Tc Ru Rh

PtW Re Os Ir

Ag Cd In

Au Hg Tl

GaCu Zn AsGe

SbSn

BiPb

Te I Xe

Po At Rn

KrSe Br

Al

B NC

PSi S Cl Ar

NeO F

He

Ac

La SmCe Pr Nd Pm

PuTh Pa U Np

Eu Gd Tb HoDy Er Tm YbRa

Legend:

Superconducting Elementsbefore MgB2 Discovery

Al BSuperconducting Non metallic elements

Si FeSuperconducting under high pressure or in thin filmsElements with Magnetic order

Li PdMetallic but not yet found to be SuperconductingSuperconducting in thin films when irradiated by α-particles

27

28

Pb

2 4 6 T [K]

1000

800

600

400

200

HC

[Gau

ss] V

TaHg

SnInTl

29

30

The Meissner-Ochsenfeld effect

When a material undergoes the superconducting transition, the

magnetic induction B is shrunk out of the sample

B = 0

Walter Meissner

Walter Meissner

31

A Superconductor is not only a perfect conductor,

but also a perfect DiamagnetT>TC TTC T

32

270 1022

cmGausse

hc⋅×== −Φ

33

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅=

2

1)(C

CC TTHTH

I Kind Superconductors (Sn,In, Hg,Pb,…….Soft SC)

B = H + 4πM = 0

34

II Type Superconductors(hard materials, alloys, Refractory Materials

A current I < IC will interact with Vortexes 0Φ×=rrr

JFL

35I Kind II Kind

36

Two Fluid modelElectrical Conduction mechanism due to 2 different components

J = Jn + JSNormal

nnn

Superfluidnn

nn nS −=1

TC T

1nS/n

nn/n

37

J = Jn + JS

Jn = σ E JS = ns e vs

m vs = -e ELondon equation

02µλL

SAJr

r−= Is the Analogous of the“Ohm Law” for Superconductors

22

L

BBλ

rr

=∇ ⎟⎟⎠

⎞⎜⎜⎝

⎛ −

⋅=2

)0()( Lx

eBxB λ

38

SuperconductorsI type

II type

Pippard

London

The l dependence vs mfpinduced Pippard to modify London’s model

He borrowed from Chambers the non local approach that relates Current and Electric field

39

Strong Correlations among Superelectronswithin a coherence length ξ0

∫ ⋅−=0

111 )()()( ξ rdrArrfrJsrrrrrrr

instead of 0

2µλLS

AJr

r−=

ξo

λ

London

ξo

λ

Pippard

40

ξ = ξ0 if l ∞l

111

0

+=ξξ

otherwise

ξo

λ

London

London ξ < λ

ξo

λ

Pippard

Pippard ξ > λ

If l then

ξ

λ

21

021

0 1 ⎟⎠⎞

⎜⎝⎛ +⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

l

ξλξξλλ LL

41

dG = - SdT + VdP - MdH

Gs(T,H) – GN(T,H) = [H2 – HC2(T)]18π

The SC-state is an equilibrium state for H < HCHC

TC

H0

T

First order transition

Second order transition

The SC Transition is a transition to an ordered state

Ss(T,H) – SN(T,H) = HC(T) dHC(T)4π dT

42

Properties that do not change when crossing TC:X-Ray diffraction pattern

Optical and Photoelectrical properties (reflectivity)

Elastic Properties (thermal expansion)

No transition in lattice structure

Properties that change when crossing TC:Exponential behavior of specific heat and thermal conductivity

Sharp edge in adsorption in microwave spectrum

.., Ultrasonic attenuation, Tunneling, Nuclear spin-lattice relaxation time, …

The electronic structure change

43

Metals C = γ T + B T3Electrons + Phonons

)(3

22

FB ENkπγ =

Superconductors TkBeC∆

−

=

Specific heat

In the energy spectrum of electrons there is a GAPbetween the fundamental state and the first excited state

44

Resuming:

For a Superconductor

HC, IC

ehc20

=φ

An Ordered State

There is a GAP

TC , if P

45

J. Bardeen L. CooperR.Schrieffer

46

EF

Cooper Principle:

Between 2 electrons excited above Fermi Energy, it exists a pair bound state separated by ∆ from EF, however weak an attractive interaction is supposed

-p , p Bose Condensation

47

An electron moving in the lattice polarizes and distorces the adiacent portion

Fluctuations of the lattice charge distribution

Interaction e-e mediated by the lattice

48

49

Bose Condensation

1=+nn

nn sn

Tkn Benn ∆−

≈

Tks B20=∆

50

Tks B20=∆

αMTC

1=

The Isotopical Effect

λθ1

14.1−

⋅= eT DCλ = (N(EF) V =

= electron-phonon interaction

µ = electron-electron interaction( )µλθ −−

⋅=1

14.1 eT DC