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