lecture 1 introduction tus 2013
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Superconductivity Tokyo University of Science
Sept.-Oct.2013
Professor Allen Hermann Department of Physics University of Colorado Boulder, CO 80401 USA
Syllabus for “Superconductivity”, an 8 (1 1/2 hour) lecture series at Tokyo University of Science, 2013
Allen Hermann, Ph.D.
Lecture 1. Introduction Discovery, history, and superconducting properties (zero resistance and flux expulsion) Type I and Type II superconductors Low Tc and High Tc Materials Course References
Lecture 2.Phenomenology: Superfluids and their properties Electrodynamics and the Magnetic Penetration Length
The London Equations and magnetic effects Fluxoids
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
Lecture 4. Microscopic Theory The 2-electron Problem
Annihilation and Creation Operators Solution of the Schroedinger Equation
Cooper Pairs The Many Electron Problem- BCS Theory
Solution of the Many Particle Schroedinger Equation by the Bogoliubov-Valatin Transformation
The BCS Energy Gap
Lecture 5. Josephson Effects Pair Tunneling and Weak Links SIS Josephson Junctions Superconducting Quantum Interference Devices (SQUIDs)
Lecture 6. Superconducting Materials and their structures Low Tc Metals and Alloys Organic superconductors High Tc materials: cuprates, borides, and AsFe superconductors
Lecture 7. The pseudogap
•Hole Doping and the Phase Diagram
•Strange Metals •Experimental Probes •Current Pseudogap Theories •Pseudogap in BEC?
Lecture 8. Applications and Devices Levitation
Wire applications and Superconducting Magnets Flux Flow Issues in High Tc, High Jc Wire Electronic devices Using Josephson Junctions and SQUIDS
Nanotechnology and Superconductivity
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
• Course references
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
Type II
superconducting normal state is gradual
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.
High Temperature Superconductivity
CuO2 plane
Copper-oxide compounds
1986: J.G. Bednorz & K.A. Müller
La2-xBaxCuO4 Tc =35 K
AF SC
T
x
TN
Tc
T*
Doped antiferromagnetic Mott insulator
under optimally over doped
spin gap
strange metal
Tc up to 133K Schilling & Ott ‘93
Are they unconventional superconductors? Not ordinary metals!
Generic Phase Diagram
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
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
APPLICATIONS: Superconducting Magnetic 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
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.
1. London theory - rigidity to macroscopic perturbations implies a “condensate” (1935,1950)
2. Ginzburg-Landau (Y) theory - order parameter for condensate (1950) 3. Isotope effect (Maxwell, Serin & Reynolds, Frohlich, 1950)
4. Cooper pairs (1956)
5. Bardeen-Cooper-Schrieffer (BCS) microscopic theory (1957)
6. Type-II superconductors (Abrikosov vortices, 1957)
7. Connection of BCS to Ginzburg-Landau (Gorkov, 1958)
8. Strong coupling superconductivity (Eliashberg, Nambu, Anderson, Schrieffer, Wilkins, Scalapino …, 1960-1963)
9. p-wave superfluidity in 3He (Osheroff, Richardson, Lee, 1972; Leggett, 1972)
10. Heavy Fermion Superconductivity (Steglich, 1979)
11. High Temperature Superconductivity (Bednorz & Muller, 1986)
12. Iron Arsenides (Hosono, 2008)
A (Very) Short History of Superconductivity
Course references 1) Introduction to Superconductivity, M. Tinkham, McGraw Hill 1996 2) Principles of Superconductive Devices and Circuits, T. Van Duzer and C. W. Turner, Elsevier, 1981 3) Introduction to Solid state Physics, C. Kittel, Wiley, 1976 4) Superconductivity of Metals and Cuprates, J.R. Waldram, IoP, 1996 5) Many on-line sources including T. Orlando, B. Chapler, M. Rice, I. Guerts, M. Cross, N. Kopnin, and others
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