9. Superconductivity

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Superconductivity

o Zero resistivity

o Meissner effect

o Magnetic effects

o Type I & II



Introduction

Zero electrical resistance

◦ Superconductors carry current without energy loss

Perfect diamagnetism

◦ Superconductors float (levitate) above magnetic fields



History of superconductors

1911: Onnes finds that at 4.2K the

resistance of mercury suddenlydrops to zero. He called this effect

superconductivity and the

temperature at which this occurs,

critical temperature Tc

1933: Walter Meissner and Robert

Ochsenfeld discover that a

superconducting material repels a

magnetic field (Meissner effect)



1957: First widely-accepted theory by John Bardeen, Leon

Cooper, and John Schrieffer (BCS theory)

1962: Brian D. Josephson predicts that electrical current

would flow between two superconducting materials - even

when they are separated by a non-superconductor or

insulator. “Josephson effect”.

1986: Alex Müller and Georg Bednorz created the first

superconducting cuprate: La2-xBaxCuO4 (Tc =30 K). Got

Nobel in 1987. “High Tc superconductivity”

1987: Discovery of YBa2Cu3O6+ (YBCO) a material thatsuperconducts at temperatures above the temperature of

liquid nitrogen - a commonly available coolant

The current world record Tc of 138 K is held by

Hg0.8Tl0.2Ba2Ca2Cu3O8.33

History contd.



Perfect diamagnet & superconductor

Perfect diamagnet

If a conductor already had a

steady magnetic field through itand was then cooled through the

transition to a zero resistance

state, becoming a perfect

diamagnet, the magnetic field

would be expected to stay thesame.

Superconductor

Remarkably, the magnetic

behavior of a superconductor isdistinct from perfect

diamagnetism. It will actively

exclude any magnetic field

present when it makes the phase

change to the superconductingstate.

Two mutually independent properties defining SC are r = 0 and B



Effect of magnetization

Superconductivity can be destroyed also by an

external magnetic field H c which is also called thecritical one

Phase

diagra

m

2

2( 0) 1

C C

C

T H H T

T



There are two types of superconductors, Type I and Type

II, according to their behaviour in a magnetic field

Type I superconductors are pure metals and alloys

Type I

superconducting state

normal state

This transition is

abrupt

Types





superconducting normal state is gradual

Type II



Types I & II comparison

The Type II superconductors

have much higher critical

magnetic fields than Type I, but

for most of that field range they

are mixtures of normal and

superconducting.



Thermodynamic properties

E n t r o p

y

T

Al



BCS Theory (1957) deals with the behaviour of electrons in

superconducting materials at very low temperatures

Low temperatures minimize the vibrational energy of individual

atoms in the crystal lattice

An electron moving freely through

the material encounters lessimpedance due to vibrational

distortions of the lattice at low

temperatures

The Coulomb attraction betweenthe passing electron and the

positive ion distorts the crystal

structure

BCS Theory



- -2 1

The region of increased positive charge density propagates

through the crystal as a quantized sound wave called a phonon

The passing electron has emitted a phonon

A second electron experiences a Coulomb attraction from the

increased region of positive charge density created by the first

electron



Electrons are said to pair into Cooper pairs through interaction with

the crystal lattice (indicated by isotope effect where TC is different for

different isotopes)

Cooper pairs are formed by two electrons, which overcome their

Coulomb repulsion and experience an attraction through phonon

exchanges

The electrons in a Cooper Pair possess antiparallel spin, resulting in

a total spin of zero for the pair

Cooper Electron Pairs act like single particles (BOSONS)

Since the Cooper Pair has zero spin, the pair is not required to obey

the Pauli exclusion principle

Bosons are particles which have integer spin and their energy

distribution is described by Bose-Einstein statistics

BCS Theory contd.



Cooper pairs condense into a highly ordered ground state

Condensation: At low temperatures, bosons collect into the same

energy state

The pairs retain this ordered structure while moving through the

crystal lattice

Each pair becomes locked into its position with others pairs, and asa result no random scattering of electron pairs may occur

Zero resistivity may be defined as the absence of electron

scattering; hence, the superconductor now demonstrates zero

resistivity

The binding energy of a Cooper pair at absolute zero is about 3KT C

As the temp rises the binding energy is reduced and goes to zero

when T=Tc

. Above T=Tc

a Cooper pair is not bound.

Fi di f BCS h



Findings of BCS theory

The binding energy of Cooper pair gives arise to

energy gap of the order of 10-3 eV

Eg(T = 0) = 3.53 kT C

A li ti



MRI Exploits the high

magnetic fields expelled

by superconducting wires

for medical applications

The wide applicability of

superconductors is due to

Since the superconducting coils are capable of producing very stable,

large magnetic field strengths, they generate high quality images.

Medical Industry

• Diamagnetism

• Zero resistance

• Higher current

Applications

T t ti I d t



Superconductor coils create strong magnetic fields that produce

the effect of levitation by repulsion

As a result, high speeds of up to 500 miles per hour are

possible with only a small consumption of energy

Maglev trains hover above a magnetic field without any

contact with the tracks

Transportation Industry

El t i i d t



High temperature superconductors (HTS) can be used in the

production of more cost effective motors and generators

HTS power cables can carry

two to ten times more power

in equally or smaller sized

cables

Electric power industry

Superconducting cyclotron

(MSU)

R f



References

A. Beiser – “Concepts of Modern Physics”, 6 Ed., Tata

McGraw-Hill (New Delhi, 2003)

Charles Kittel – “Introduction to Solid State Physics”, 7

Ed., John Wiley and Sons (New York, 1996)

www.wikipedia.org

http://hyperphysics.phy-

astr.gsu.edu/hbase/hframe.html

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9. Superconductivity