# Superconductors

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15 Νοε 2013 (πριν από 4 χρόνια και 6 μήνες)

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Superconductors

Presented by Onur KARAGÖZ

Content

Meissner Effect

Quantum Effects

Transition to Zero Resistivity

“Super” conductivity?

Superconductivity
, discovered in 1911 by
Heike Kamerlingh Onnes, is a phenomenon
occurring in certain materials at extremely low
temperatures.

It was not yet discovered whether the
resistance remains 0, or it is exactly 0 due to
experimental results. So we name it “super”
not perfect conductor.

Meissner Effect

Meissner Effect

http://www.superlife.info/en/book/index.html

http://www.superlife.info/en/book/index.html

The hallmark of superconductivity is expulsion of the
internal B field in an applied magnetic (H) field, unless the
applied field exceeds a critical level.

London Equation

A bulk superconductor is shielded completely from an
external magnetic field by a supercurrent that flows within
the penetration depth (
λ
) at the surface.

m=electron mass

e=electron charge

n
e
=concentration

μ
o
=permeability
in vacuum

London Equation

n
e
, the concentration is given by the following equation:

ρ
=conductor’s
mass density

N
A
number

W
A
=Atomic
weight

Quantum Effects

Cooper Pairs

Flux Quantization

Cooper Pairs

Cooper pairs can have the same energy level.

The mediator that holds the two electrons is a
phonon.

Flux Quantization

Deaver and Fairbank did experiments with a
electroplating tin on a copper wire. They found
magnetic flux quantized in units of

such that the flux through the cylinder was
given by

Related with the Type II superconductors in
the mediated phase that creates vortices.

Transition to Zero Resistivity

Critical

Temperature

Magnetic Field

Current Density

Superconductor Types

Type I (soft)

Type II (hard)

Critical Temperature

Critical Magnetic Field H
c

http://hyperphysics.phy
-
astr.gsu.edu/hbase/solids/scbc.html#c2

Critical Current Density J
c

http://www.users.qwest.net/~csconductor/Experiment_Guide/Critical%20Current%2
0Density
-
1.htm

T
c

H
c

and J
c

of YBCO

BCS Theory

Bardeen, Cooper, and Schrieffer

A key conceptual element in this theory is the
pairing of electrons close to the
Fermi level

into
Cooper pairs

through interaction with the
crystal lattice.

This pairing results from a slight attraction
between the electrons related to lattice
vibrations; the coupling to the lattice is called a
phonon

interaction.

Bandgap

The BCS theory predicts a bandgap of

Ginzburg
-
Landau Theory

Coherence length

is a measure of the
shortest distance over which superconductivity
may be established or destroyed without
excessive cost in energy.

Penetration depth

Types of Superconductors

Type I : Metals and metalloids

Type II: Metal alloys, cuprates etc.

Type I

Always rather pure metallic elements

Easily quenched in magnetic fields less than
~1000 gauss

Must exclude virtually all of an applied
magnetic field to remain superconducting

Type I

http://www.superlife.info/en/book/victor/Image9.jpg

Type I

Nb3Sn

Niobium stannide,
Nb3Sn, is a well
-
established
superconductor of the
A15 (Cr3Si) structure.

A15 structure

http://alpha.mems.duke.edu/aiqin/sdarticle1.pdf

Type II

Alloys or compounds (Niobium and vanadium
are exceptions)

They are able to retaintheir superconductive
characteristics in rather intense magnetic
fields.

Rather than using the energy required to
completely expel magnetic fields, the fields are
confined to an internal array of normal
-
state
flux tubes called"vortices" since they are
surrounded by a circulating supercurrent.

They are capable of carrying relatively large
current densities.

Type II

Three
critical
magnetic
fields

H
c1

H
c2

H
c3

http://www.superlife.info/en/book/victor/Image10.jpg

YBCO

YBa
2
Cu
3
O
7
-
x

was discovered to have a Tc of
92

K in 1987.

This was the first time that superconductivity
had been observed at temperatures which
could be conveniently attained with liquid
nitrogen, and so created great excitement at
the prospect of low
-
cost applications of
superconductivity.

YBCO

There are two
CuO layers.

CuO
2
layers are
responsible for
the
superconductivity

http://cst
-
www.nrl.navy.mil/lattice/struk.picts/hightc/1212c.s.png

YBCO

The only known stable four
-
element compound with a
T
c
above 77 K.

Includes neither toxic
elements nor volatile
compounds

Easy to make single
-
phase
YBCO

Less anisotropic than other
HTS materials, carries higher
current densities at higher
magnetic fields

http://www.tkk.fi/Units/AES/projects/prlaser/ybco.jpg

BSCCO

(Bismuth strontium
calcium copper oxide)

Bi
2
Sr
2
CuO
x

BSCCO can have 1, 2, or
3 CuO planes, with
Tc

increasing with the
number of planes.

Bismuth can also be
replaced with thallium or
mercury, which results in
the highest
Tc

material
known (142K).

MgB
2

MgB
2

Magnesium diboride, MgB2, was first reported
to be superconducting in 2001.

It is superconducting at a temperature of 38
-
40

K and it is an intermetallic material.

Why MgB
2
?

Cost

Lower anisotropy unlike cuprates

Larger coherence lenghts

Transparency of the grain boundaries to current flow

References

Solid State Physics, J.R. Hook & H.E. Hall,Wiley,2000

Superconductivity, J.B. Ketterson & S.N. Song, Cambridge,1999

Superconductivity Fundamentals and Applications, W. Buckel & R.
Kleiner, Wiley,2004

http://alpha.mems.duke.edu/aiqin/sdarticle1.pdf

http://www.ewh.ieee.org/tc/csc/News/MgB2Feb2002.html

http://www.tkk.fi/Units/AES/projects/prlaser/material.htm

http://hyperphysics.phy
-
astr.gsu.edu/hbase/solids/supcon.html#c1

http://www.msm.cam.ac.uk/ascg/materials/mgb2.php

http://hoffman.physics.harvard.edu/research/SCmaterials.php

http://www.superconductors.org/INdex.htm

http://www.futurescience.com/manual/sc1000.html#C

http://www.superlife.info/en/book/index.html