1. Superconductivity
Tokyo University of Science
May, 2010
Professor Allen Hermann
Department of Physics
University of Colorado
Boulder, CO 80401 USA
and
Nanotech Solutions, LLC
Lexington,KY 40506 USA
allen.hermann@colorado.edu

2. 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. Introduction
Discovery, history, and superconducting properties (zero resistance and
flux expulsion)
Type I and Type II superconductors
Low Tc and High Tc Materials

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

6. Lecture 5. Josephson Effects
Pair Tunneling and Weak Links
SIS Josephson Junctions
Superconducting Quantum Interference Devices (SQUIDs)

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. 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

9. 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

25. TYPES OF SUPERCONDUCTORS
There are two types of superconductors, Type I and Type II, according to their
behaviour in a magnetic field
Type I
superconducting state
normal state
This transition is abrupt
Type I superconductors are pure metals and alloys

26. Type II
superconducting normal state is gradual

27. 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

52. High Temperature Superconductivity
1986: J.G. Bednorz & K.A. Müller Tc up to 133K Schilling & Ott ‘93
Doped antiferromagnetic
Mott insulator
Generic Phase Diagram
Copper-oxide compounds T TN
T*
strange
La2-xBaxCuO4 Tc =35 K metal
spin gap
AF Tc
SC
CuO2 plane under optimally over x
doped
Are they unconventional superconductors?
Not ordinary metals!

55. Record TC versus Year Discovered
180
HgBa2Ca2Cu2O8 Pressure
160
HgBa2Ca2Cu2O8
140
Tl-Ba-Ca-Cu-O
120
Bi2Sr2Ca2Cu3O8
TC (K)
100
YBa2Cu3O7
80
60
La-Sr-Cu-O
40
NbN La-Ba-Cu-O
20 Nb3Ge
Hg
0 1986
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year

58. SOME HIGH Tc SUPERCONDUCTORS
Chemical formula Tc
Hg0.8Tl0.2Ba2Ca2Cu3O8.33 138 K (record-holder)
HgBa2Ca2Cu3O8 133-135 K
HgBa2CuO4+ 94-98 K
Tl2Ba2Ca2Cu3O10 127 K
TlBa2Ca2Cu3O9+  123 K
TlBa2Ca3Cu4O11 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

62. 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

65. 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.