1. Superconductivity
Tokyo University of Science
Sept.-Oct.2013
Professor Allen Hermann
Department of Physics
University of Colorado
Boulder, CO 80401 USA
2. 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
3. Lecture 2.Phenomenology: Superfluids and their properties
Electrodynamics and the Magnetic Penetration Length
The London Equations and magnetic effects
Fluxoids
4. 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
5. 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
7. Lecture 6. Superconducting Materials and their structures
Low Tc Metals and Alloys
Organic superconductors
High Tc materials: cuprates, borides, and AsFe superconductors
8. Lecture 7. The pseudogap
•Hole Doping and the Phase Diagram
•Strange Metals
•Experimental Probes
•Current Pseudogap Theories
•Pseudogap in BEC?
9. 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
10. 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
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26. 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
28. 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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53. 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
59. 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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64. 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
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67. 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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70. 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
71. 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
