superconductivity and superfluidity phys3430 professor bob cywinski “superconductivity is perhaps...

SuperconductivitySuperconductivityandandSuperfluiditySuperfluidity

PHYS3430PHYS3430

Professor Professor Bob CywinskiBob Cywinski “Superconductivity is perhaps the

most remarkable physical property in the Universe” David Pines

Superconductivity and Superfluidity

Text BooksText Books

Introduction to SuperconductivityA C Rose-Innes and E H RhoderickPergamon Press

Superfluidity and SuperconductivityDr Tilley and J TilleyInstitute of Physics Publishing

Introduction to Superconductivity and High-Tc MaterialsM Cyrot and D PavunaWorld Scientific

plus appropriate chapters in Solid State Physics books

Good introduction to phenomenology, without too much maths - now quite out of date

Both topics covered well, but it flips between the two topics too much and tries to draw too many analogies

A good introduction, and cheap, but now hard to get

Lecture 1


SyllabusSyllabus

Lectures will focus primarily on superconductivity but the salient features of the phenomenon of superfluidity in liquid helium will be discussed towards the end of the course

We shall cover the history of superconductivity and the early phenomenological theories leading to a description of the superconducting state

The microscopic quantum mechanical basis of superconductivity will be described, introducing the concepts of electron pairing, leading to the BCS theory

Superconductivity as a manifestation of macroscopic quantum mechanics will be presented, together with the implication for superconducting devices, such as SQUIDS

An overview of the principal groups of superconducting materials, and their scientific and industrial interest will be given

Lecture 1


Discovery of SuperconductivityDiscovery of Superconductivity

Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K

Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium

In 1912 he found that the resistive state is restored in a magnetic field or at high transport currents 19131913

Lecture 1


The superconducting elementsThe superconducting elements

Li Be0.026

B C N O F Ne

Na Mg Al1.1410

Si P S Cl Ar

K Ca Sc Ti0.3910

V5.38142

Cr Mn Fe Co Ni Cu Zn0.875

5.3

Ga1.091

5.1

Ge As Se Br Kr

Rb Sr Y Zr0.546

4.7

Nb9.5198

Mo0.929.5

Tc7.77141

Ru0.51

7

Rh0.03

5

Pd Ag Cd0.56

3

In3.429.3

Sn3.7230

Sb Te I Xe

Cs Ba La6.0110

Hf0.12

Ta4.483

83

W0.012

0.1

Re1.420

Os0.65516.5

Ir0.141.9

Pt Au Hg4.153

41

Tl2.3917

Pb7.1980

Bi Po At Rn

Transition temperatures (K)Critical magnetic fields at absolute zero (mT)

Transition temperatures (K) and critical fields are generally low

Metals with the highest conductivities are not superconductors

The magnetic 3d elements are not superconducting

Nb(Niobium)

Tc=9KHc=0.2T

Fe(iron)Tc=1K

(at 20GPa)

Fe(iron)Tc=1K

(at 20GPa)

...or so we thought until 2001

Lecture 1


1910 1930 1950 1970 1990

20

40

60

80

100

120

140

160

Su

per

con

du

ctin

g t

ran

siti

on

tem

per

atu

re (

K)

Superconductivity in alloys and oxidesSuperconductivity in alloys and oxides

Hg Pb NbNbCNbC NbNNbN

V3SiV3Si

Nb3SnNb3Sn Nb3GeNb3Ge

(LaBa)CuO(LaBa)CuO

YBa2Cu3O7YBa2Cu3O7

BiCaSrCuOBiCaSrCuO

TlBaCaCuOTlBaCaCuO

HgBa2Ca2Cu3O9HgBa2Ca2Cu3O9

HgBa2Ca2Cu3O9

(under pressure)

HgBa2Ca2Cu3O9

(under pressure)

Liquid Nitrogen temperature (77K)

Lecture 1


Zero resistance?Zero resistance?

In a metal a current is carried by free conduction electrons - ie by plane waves

temperature

resi

stiv

ity

Plane waves can travel through a perfectly periodic structure without scattering…..

….but at finite temperatures phonons destroy the periodicity and cause resistance

“ideal metal”T5

T

Take, eg, pure copper with a resistivity at room temperature of 2cm, and a residual resistivity at 4.2K of 210-5 cm

………….a typical Cu sample would thus have a resistance of only 210-11 at 4.2K

Even at T=0, defects such as grain boundaries, vacancies, even surfaces give rise to residual resistivity

Re

sid

ua

l re

sist

ivity

“impure metal”

Lecture 1


Zero resistance?Zero resistance?

In a metal a current is carried by free conduction electrons - ie by plane waves

Plane waves can travel through a perfectly periodic structure without scattering…..

….but at finite temperatures phonons destroy the periodicity and cause resistance

Even at T=0, defects such as grain boundaries, vacancies, even surfaces give rise to residual resistivity

Take, eg, pure copper with a resistivity at room temperature of 2cm, and a residual resistivity at 4.2K of 210-5 cm

………….a Cu typical sample would thus have a resistance of only 210-11 at 4.2K

Lecture 1


Zero resistance? Zero resistance?

The resistance of pure copper is so small is there really much difference between it and that of a superconductor?

Take an electromagnet consisting of a 20cm diameter coil with 10000 turns of 0.3mmx0.3mm pure copper wire

R300K = 1 k R4.2K= 0.01

Pass a typical current of 20 Amps through the coil

P300K = 0.4MW P4.2K= 4 Watts

At 4.2K this is more than enough to boil off the liquid helium coolant!

Lecture 1


Measuring zero resistanceMeasuring zero resistance

Can we determine an upper limit for the resistivity of a superconductor?

This enables the decay constant of the effective R-L circuit to be measured:

t)L/R(e)0(i)t(i)t(B

Using this technique, no discernable change in current was observed over two years:

sc 10-24.cm !!

This is done by injecting current into a loop of superconductor

iThe current generates a magnetic field, and the magnitude of this field is measured as a function of time

B

Lecture 1



In practice the superconducting ring is cooled in a uniform magnetic field of flux density BA to below TC

If the area of the ring is A, the flux threading the loop is

AAB

BA

Cool the ring in an applied magnetic field -

Now change BA: by Lenz’s law a current will flow to oppose the change, hence

then decrease the field to zero

Lecture 2



In practice the superconducting ring is cooled in a uniform magnetic field of flux density BA to below TC

If the area of the ring is A, the flux threading the loop is

AAB

Now change BA: by Lenz’s law a current will flow to oppose the change, hence

dtdi

LRidt

dBA A

In a “normal” loop, the Ri term quickly kills the current, but if R=0

dtdi

Ldt

dBA A

Therefore Li+ABA = constant (=total flux in loop)

i

Currents will flow to maintain the field in the loop….

So if R=0 the current will persist forever !!

forever

emfemf


……..and the corollary..and the corollary

Li+ABA = constant (=total flux in loop)

dtdi

LRidt

dBA A If

and Ri = 0 such that

The flux in the superconducting loop must remain constant however the field changes

Therefore if a loop is cooled into the superconducting state in zero field and then the magnetic field is applied supercurrents must circulate to maintain the total flux threading the loop at zero.

A superconducting cylinder can therefore provide perfect magnetic shielding

A Meissner Shield

Lecture 2

superconductivity and superfluidity phys3430 professor bob cywinski “superconductivity is perhaps...

Documents

history of superconductivity

remarkable physical

superfluidityzero resistance

superconducting devices

pure copper

free conduction electrons

room temperature

residual resistivitytake