Superconductors: Basic Concepts
Daniel Shantsev
AMCS group
Department of Physics
University of Oslo
• History
• Superconducting materials
• Properties
• Understanding
• Applications
Research School Seminar
February 6, 2006
Discovery of Superconductivity
Discovered by Kamerlingh Onnes
in 1911 during first low temperature
measurements to liquefy helium
Whilst measuring the resistivity of
“pure” Hg he noticed that the electrical
resistance dropped to zero at 4.2K
How small is zero?
A lead ring carrying a current of several hundred
ampères was kept cooled for a period of 2.5
years with no measurable change in the current
1913
The superconducting elements
Li
Be
0.026
Na
K
Transition temperatures (K)
Critical magnetic fields at absolute zero (mT)
Mg
Ca
Sc
Ti
0.39
10
Rb
Cs
Sr
Ba
Y
La
6.0
110
Zr
V
Cr
Mn
Fe
Fe Co
C
N
O
F
Ne
Al
Si
P
S
Cl
Ar
Ge
As
Se
Br
Kr
I
Xe
At
Rn
1.14
10
Ni
Cu
Zn
Ga
0.875 1.091
(iron)
5.3
5.1
Tc=1K
Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
(at 20GPa)
9.5
0.92 7.77
0.51 0.03
0.56
3.4
3.72
5.38
142
Nb
0.546
(Niobium)
4.7
198
9.5
141
HfTc=9K
Ta W
Re
Os
Ir
1.4
20
0.655
16.5
0.14
1.9
0.12
B
4.483 0.012
0.1
c 83
H =0.2T
7
5
3
Pt
Au
29.3
30
Hg
Tl
Pb
4.153
41
2.39
17
7.19
80
Bi
Po
Transition temperatures (K) and critical fields are generally low
Metals with the highest conductivities are not superconductors
The magnetic 3d elements are not superconducting
...or so we thought until 2001
Superconducting transition temperature (K)
Superconductivity in alloys and oxides
HgBa2Ca2Cu3O9
(under pressure)
160
Highest Tc
140
HgBa2Ca2Cu3O9
120
TlBaCaCuO
138 K
(at normal pressure)
BiCaSrCuO
100
YBa2Cu3O7
Liquid Nitrogen
temperature (77K)
80
60
MgB2
(LaBa)CuO
40
20
1987
Hg Pb Nb
1910
NbC
1930
NbN
Nb3Sn
Nb3Ge
V3Si
1950
1970
1990
General properties
• Zero resistance at T<Tc
(Kamerlingh Onnes, 1911)
Ideal conductor
(the resistive state is restored
in a magnetic field or at high transport currents)
• Magnetic field is excluded from
a superconductor
(Meissner & Ochsenfeld, 1933)
Ideal diamagnet
Superconductivity – Quantum phenomenon at macroscale
Quantization of magnetic flux
Deaver & Fairbank, 1961
B
Long hollow cylinder
2
the magnetic flux through a superconducting ring
is an integer multiple of a flux quantum
6
BCS Theory
Bardeen
Cooper
Schriffer
1972
(1) Electrons combine in Cooper pairs
due to interactions with phonons
x
(2) All Cooper pairs (bosons) condense
into one quantum state separated by an
energy gap from excited states
Metal:
many individual electrons
Superconductor: all electrons move coherently
Experimental evidence for BCS
Ivar Giaver
(UiO)
direct experimental
evidence of the existence
of the energy gap
1973
From the Nobel lecture,
http://nobelprize.org/physics/laureates/1973/
N
S
Superconductivity – Quantum phenomenon at macroscale
Quantization of magnetic flux
Deaver & Fairbank, 1961
B
2
BCS:
All Cooper pairs are desribed by
one wave function:
 =| | ei
 dx = 2 /0 = 2k
B. Josephson
Josephson effect
S
I
1973
What is the resistance of the junction?
S
For small currents, the junction is a
superconductor!
V
I = Ic sin (1 - 2)
Supercurrent
Phase of the wave function
Josephson interferometer
Most sensitive magnetometer – SQUID
(superconducting quantum interference device)
SQUID sensitivity
Heart fields
Brains fields
10-14 T
10-10 T
10-13 T
Magnetic
field
Hc
Normal state
Vortex lattice
Type I
A. A. Abrikosov
Meissner state
Temperature
Hc2
Tc
Normal state
Mixed state
(vortex matter)
Hc1
2003
(published 1957)
Type II
Meissner state
Temperature
Tc
Vortex
normal core
x
Coherence length
J
x
B(r)
London penetration depth
l
l
Flux quantum:
 B dA
superconductor
= h/2e = 0
l
x<l
type II
NS interface

x>l
type I
NS interface

12
Ginzburg-Landau Theory
V. L. Ginzburg,
L. D. Landau
2003
Order parameter?
a  T-Tc
Ginzburg-Landau functional:
13
High-current Cables
~100 times better than Cu
In May of 2001
some 150,000 residents of Copenhagen
began receiving their electricity through
high-Tc superconducting material
(30 meters long cable).
Magnetic Resonance Imaging (MRI)
• 75 million MRI scans per year
• Higher magnetic field means higher sensitivity
Magnetoencephalography
Measuring tiny magnetic fields
in the human brain
• Electric generators made with superconducting wire
• Superconducting Magnetic Energy Storage System
• Superconductor-based transformers and fault limiters
• Infrared sensors
• Magnetic shielding devices
• Ultra-high-performance filters
• etc
Most high energy accelerators now use superconducting magnets. The proton
accelerator at Fermilab uses 774 superconducting magnets (7 meter long tubular
magnets which generate a field of 4.5 Tesla) in a ring of circumference 6.2 km.
The coils are made of NbSn3 or NbTi embedded in form of fine filaments
(20 mm diameter) in a copper matrix
Image
from
BNL
Superconducting magnet designed for the Alpha Magnetic Spectrometer
at the International Space Station
to help look for dark matter, missing matter & antimatter
Image
from
U.Geneva
Levitation: MagLev Trains
Miyazaki Maglev Test Track, 40 km
• No friction
• Super-high speed
• Safety
• Noiseless
581 km/h
Vortex pinning
Record
trapped field:
17 Tesla
Field
distribution
Ba
f
J
Jc
Lorentz force:
f = JB
presintered
123-pellet
• The maximal field in the magnets,
• The maximal current in the cables
are determined by vortex pinning
=> it’s important to study vortices
Top-seeded melt-growth
Superconductivity Lab @ UiO
Magneto-optical
imaging
Åge Olsen:
Observation of what Vortices do
NbSe2 field-cooled to 4.3 K
Sanyalak
Niratisairak:
Characterization
of MO-films
10 mm
Jørn Inge Vestgården:
Calculation of Vortex distributions