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Superconductivity Tokyo University of Science
May, 2010
Professor Allen HermannDepartment of PhysicsUniversity of ColoradoBoulder, CO 80401 USA
andNanotech Solutions, LLCLexington,KY 40506 USA
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Syllabus for “Superconductivity”, a 7 (1 1/2 hour) lecture series in Low-Temperature Physics I at Tokyo University of Science, 2010
Allen Hermann, Ph.D.
Lecture 1. IntroductionDiscovery, history, and superconducting properties (zero resistance and flux expulsion)Type I and Type II superconductorsLow Tc and High Tc Materials
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Lecture 2.Phenomenology: Superfluids and their propertiesElectrodynamics and the Magnetic Penetration LengthThe London Equations and magnetic effectsFluxoids
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Lecture 3. Phenomenology: Ginsburg-Landau theory and the intermediate state•Landau Theory of Phase Transitions•Ginsburg-Landau Expansion•Coherence Length•The Ginsburg-Landau Equations•Abrikosov Lattice and Flux Pinning
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Lecture 4. Microscopic TheoryThe 2-electron ProblemAnnihilation and Creation Operators Solution of the Schroedinger EquationCooper PairsThe Many Electron Problem- BCS TheorySolution of the Many Particle Schroedinger Equation by the Bogoliubov-Valatin TransformationThe BCS Energy Gap
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Lecture 5. Josephson EffectsPair Tunneling and Weak Links SIS Josephson JunctionsSuperconducting Quantum Interference Devices (SQUIDs)
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Lecture 6. Superconducting Materials and their structuresLow Tc Metals and Alloys Organic superconductors High Tc materials: cuprates, borides, and AsFe superconductors
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Lecture 7. Applications and DevicesLevitationWire applications and Superconducting MagnetsFlux Flow Issues in High Tc, High Jc Wire Electronic devices Using Josephson Junctions and SQUIDSNanotechnology and Superconductivity
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Lecture 1 Introduction
• Discovery, history and superconducting properties (zero resistance, magnetic flux expulsion)
• Type I and Type II superconductors
• Low Tc and High Tc materials
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TYPES OF SUPERCONDUCTORS
There are two types of superconductors, Type I and Type II, according to their
behaviour in a magnetic field
superconducting state
Type I superconductors are pure metals and alloys
Type I
normal state
This transition is abrupt
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Type II
superconducting normal state is gradual
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WHAT IS SUPERCONDUCTIVITY??
For some materials, the resistivity vanishes at some low temperature: they become superconducting.
Superconductivity is the ability of certain materials to conduct electrical current with no resistance. Thus, superconductors can carry large amounts of current with little or no loss of energy.
Type I superconductors: pure metals, have low critical field
Type II superconductors: primarily of alloys or intermetallic compounds.
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High Temperature Superconductivity
CuO2 plane
Copper-oxide compounds
1986: J.G. Bednorz & K.A. Müller
La2-xBaxCuO4 Tc =35 K
AFSC
T
x
TN
Tc
T*
Doped antiferromagneticMott insulator
under optimally overdoped
spin gap
strangemetal
Tc up to 133K Schilling & Ott ‘93
Are they unconventional superconductors?Not ordinary metals!
Generic Phase Diagram
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Record TC versus Year Discovered
0
20
40
60
80
100
120
140
160
180
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year
TC (
K)
Hg
NbNNb3Ge
La-Ba-Cu-O
La-Sr-Cu-O
YBa2Cu3O7
Bi2Sr2Ca2Cu3O8
Tl-Ba-Ca-Cu-O
HgBa2Ca2Cu2O8
HgBa2Ca2Cu2O8 Pressure
1986
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Hg0.8Tl0.2Ba2Ca2Cu3O8.33 138 K (record-holder)
HgBa2Ca2Cu3O8 133-135 K
HgBa2CuO4+ 94-98 K
Tl2Ba2Ca2Cu3O10
TlBa2Ca2Cu3O9+
TlBa2Ca3Cu4O11
127 K
123 K
112 K
Ca1-xSrxCuO2 110 K
Highest-Tc 4-element compound
YBa2Cu3O7+ 93 K
La1.85Sr0.15CuO4 40 K
La1.85Ba.15CuO4 35 K
First HTS discovered - 1986
(Nd,Ce)2CuO4 35 K
SOME HIGH Tc SUPERCONDUCTORS
Chemical formula Tc
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APPLICATIONS:SuperconductingMagnetic Levitation
The track are walls with a continuous series of vertical coils of wire mounted inside. The wire in these coils is not a superconductor.
As the train passes each coil, the motion of the superconducting magnet on the train induces a current in these coils, making them electromagnets.
The electromagnets on the train and outside produce forces that levitate the train and keep it centered above the track. In addition, a wave of electric current sweeps down these outside coils and propels the train forward.
The Yamanashi MLX01MagLev Train
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A superconductor displaying the MEISSNER EFFECT
Superconductors have electronic and magnetic properties. That is, they have a negative susceptibility, and acquire a polarization OPPOSITE to an applied magnetic field. This is the reason that superconducting materials and magnets repel one another.
If the temperature increases the sample will lose its superconductivity and the magnet cannot float on the superconductor.
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