Superconductors: Basic ConceptsSuperconductors: Basic Concepts
Daniel ShantsevAMCS group
Department of Physics
University of Oslo
• History
• Superconducting materials
• Properties
• Understanding
• Applications
Research School Seminar February 6, 2006
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
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
19131913
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
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)
19871987
Highest Tc
138 K(at normal pressure)
MgB2MgB2
General propertiesGeneral properties
Ideal conductor
• Zero resistance at T<Tc (Kamerlingh Onnes, 1911)
• Magnetic field is excluded from a superconductor (Meissner & Ochsenfeld, 1933)
Ideal diamagnet
(the resistive state is restored in a magnetic field or at high transport currents)
6
Quantization of magnetic flux
Long hollow cylinder
Superconductivity – Quantum phenomenon at macroscale
Deaver & Fairbank, 1961
the magnetic flux through a superconducting ring is an integer multiple of a flux quantum
+B
2
BCS TheoryBCS TheoryBardeenCooperSchriffer 1972
(1) Electrons combine in Cooper pairs due to interactions with phonons
(2) All Cooper pairs (bosons) condense into one quantum state separated by an energy gap from excited states
Experimental evidence for BCS
Metal: many individual electronsSuperconductor: all electrons move coherently
Ivar Giaver (UiO) 1973
direct experimental evidence of the existence
of the energy gap
From the Nobel lecture,http://nobelprize.org/physics/laureates/1973/
N S
2
Quantization of magnetic flux
Superconductivity – Quantum phenomenon at macroscaleSuperconductivity – Quantum phenomenon at macroscale
Deaver & Fairbank, 1961
+B
=| | ei
BCS: All Cooper pairs are desribed by one wave function:
dx = 2 /0 = 2k
Josephson effectJosephson effect
IS S
V
What is the resistance of the junction?
B. Josephson
1973
For small currents, the junction is a superconductor!
I = Ic sin (1 - 2)
Supercurrent Phase of the wave function
Josephson interferometerJosephson interferometer
Most sensitive magnetometer – SQUID(superconducting quantum interference device)
SQUID sensitivity 10-14 THeart fields 10-10 TBrains fields 10-13 T
Temperature TTcc
Mixed state(vortex matter)
Meissner state
Normal state
HHc1c1
HHc2c2
Type II
Temperature TTcc
Normal state
Meissner state
HHcc
Magneticfield
Type IVortex lattice
A. A. Abrikosov
(published 1957)
20032003
12
VortexVortex
B dA = h/2e = 0 Flux quantum:
J
B(r)
normal core
superconductor
Coherence length
London penetration depth
type II
type I
NS interface NS interface
13
Ginzburg-Landau Theory
Order parameter?
20032003
V. L. Ginzburg, L. D. Landau
a T-Tc
Ginzburg-Landau functional:
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 m diameter) in a copper matrix
Imagefrom BNL
Superconducting magnet designed for the Alpha Magnetic Spectrometer at the International Space Station
to help look for dark matter, missing matter & antimatter
Imagefrom U.Geneva
Miyazaki Maglev Test Track, 40 km
581 km/h
Levitation: MagLev Trains
• No friction• Super-high speed• Safety• Noiseless
presintered123-pellet
Top-seeded melt-growthTop-seeded melt-growth
Ba
J
f
Lorentz force: f =
JB
Jc
Field distribution
Vortex pinningRecord
trapped field: 17 Tesla
• The maximal field in the magnets, • The maximal current in the cables are determined by vortex pinning => it’s important to study vortices
Magneto-optical imaging NbSe2 field-cooled to 4.3 KNbSe2 field-cooled to 4.3 K
10 m
Sanyalak Niratisairak:
Characterization of MO-films
Åge Olsen:Observation of what Vortices do
Jørn Inge Vestgården:Calculation of Vortex distributions
Superconductivity Lab @ UiO