Superconductors: Basic ConceptsSuperconductors: Basic Concepts

Daniel ShantsevAMCS group

Department of Physics

University of Oslo

• History

• Superconducting materials

• Properties

• Understanding

• Applications

Research School Seminar February 6, 2006

Discovery of SuperconductivityDiscovery of Superconductivity

Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K

Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium

How small is zero?A lead ring carrying a current of several hundred ampères was kept cooled for a period of 2.5 years with no measurable change in the current

19131913

The superconducting elementsThe superconducting elements

Li Be0.026

B C N O F Ne

Na Mg Al1.1410

Si P S Cl Ar

K Ca Sc Ti0.3910

V5.38142

Cr Mn Fe Co Ni Cu Zn0.875

5.3

Ga1.091

5.1

Ge As Se Br Kr

Rb Sr Y Zr0.546

4.7

Nb9.5198

Mo0.929.5

Tc7.77141

Ru0.51

7

Rh0.03

5

Pd Ag Cd0.56

3

In3.429.3

Sn3.7230

Sb Te I Xe

Cs Ba La6.0110

Hf0.12

Ta4.483

83

W0.012

0.1

Re1.420

Os0.65516.5

Ir0.141.9

Pt Au Hg4.153

41

Tl2.3917

Pb7.1980

Bi Po At Rn

Transition temperatures (K)Critical magnetic fields at absolute zero (mT)

Transition temperatures (K) and critical fields are generally low

Metals with the highest conductivities are not superconductors

The magnetic 3d elements are not superconducting

Nb(Niobium)

Tc=9KHc=0.2T

Fe(iron)Tc=1K

(at 20GPa)

Fe(iron)Tc=1K

(at 20GPa)

...or so we thought until 2001

1910 1930 1950 1970 1990

20

40

60

80

100

120

140

160

Su

per

con

du

ctin

g t

ran

siti

on

tem

per

atu

re (

K)

Superconductivity in alloys and oxidesSuperconductivity in alloys and oxides

Hg Pb NbNbCNbC NbNNbN

V3SiV3Si

Nb3SnNb3Sn Nb3GeNb3Ge

(LaBa)CuO(LaBa)CuO

YBa2Cu3O7YBa2Cu3O7

BiCaSrCuOBiCaSrCuO

TlBaCaCuOTlBaCaCuO

HgBa2Ca2Cu3O9HgBa2Ca2Cu3O9

HgBa2Ca2Cu3O9

(under pressure)

HgBa2Ca2Cu3O9

(under pressure)

Liquid Nitrogen temperature (77K)

19871987

Highest Tc

138 K(at normal pressure)

MgB2MgB2

General propertiesGeneral properties

Ideal conductor

• Zero resistance at T<Tc (Kamerlingh Onnes, 1911)

• Magnetic field is excluded from a superconductor (Meissner & Ochsenfeld, 1933)

Ideal diamagnet

(the resistive state is restored in a magnetic field or at high transport currents)

6

Quantization of magnetic flux

Long hollow cylinder

Superconductivity – Quantum phenomenon at macroscale

Deaver & Fairbank, 1961

the magnetic flux through a superconducting ring is an integer multiple of a flux quantum

+B

2

BCS TheoryBCS TheoryBardeenCooperSchriffer 1972

(1) Electrons combine in Cooper pairs due to interactions with phonons

(2) All Cooper pairs (bosons) condense into one quantum state separated by an energy gap from excited states

Experimental evidence for BCS

Metal: many individual electronsSuperconductor: all electrons move coherently

Ivar Giaver (UiO) 1973

direct experimental evidence of the existence

of the energy gap

From the Nobel lecture,http://nobelprize.org/physics/laureates/1973/

N S

2

Quantization of magnetic flux

Superconductivity – Quantum phenomenon at macroscaleSuperconductivity – Quantum phenomenon at macroscale

Deaver & Fairbank, 1961

+B

=| | ei

BCS: All Cooper pairs are desribed by one wave function:

dx = 2 /0 = 2k

Josephson effectJosephson effect

IS S

V

What is the resistance of the junction?

B. Josephson

1973

For small currents, the junction is a superconductor!

I = Ic sin (1 - 2)

Supercurrent Phase of the wave function

Josephson interferometerJosephson interferometer

Most sensitive magnetometer – SQUID(superconducting quantum interference device)

SQUID sensitivity 10-14 THeart fields 10-10 TBrains fields 10-13 T

Temperature TTcc

Mixed state(vortex matter)

Meissner state

Normal state

HHc1c1

HHc2c2

Type II

Temperature TTcc

Normal state

Meissner state

HHcc

Magneticfield

Type IVortex lattice

A. A. Abrikosov

(published 1957)

20032003

12

VortexVortex

B dA = h/2e = 0 Flux quantum:

J

B(r)

normal core

superconductor

Coherence length

London penetration depth

type II

type I

NS interface NS interface

13

Ginzburg-Landau Theory

Order parameter?

20032003

V. L. Ginzburg, L. D. Landau

a T-Tc

Ginzburg-Landau functional:

High-current Cables

~100 times better than Cu In May of 2001 some 150,000 residents of Copenhagen began receiving their electricity through

high-Tc superconducting material (30 meters long cable).

Magnetic Resonance Imaging (MRI)

• 75 million MRI scans per year • Higher magnetic field means higher sensitivity

Magnetoencephalography

Measuring tiny magnetic fields in the human brain

• Electric generators made with superconducting wire • Superconducting Magnetic Energy Storage System • Superconductor-based transformers and fault limiters• Infrared sensors • Magnetic shielding devices • Ultra-high-performance filters• etc

Most high energy accelerators now use superconducting magnets. The proton accelerator at Fermilab uses 774 superconducting magnets (7 meter long tubular magnets which generate a field of 4.5 Tesla) in a ring of circumference 6.2 km.

The coils are made of NbSn3 or NbTi embedded in form of fine filaments (20 m diameter) in a copper matrix

Imagefrom BNL

Superconducting magnet designed for the Alpha Magnetic Spectrometer at the International Space Station

to help look for dark matter, missing matter & antimatter

Imagefrom U.Geneva

Miyazaki Maglev Test Track, 40 km

581 km/h

Levitation: MagLev Trains

• No friction• Super-high speed• Safety• Noiseless

presintered123-pellet

Top-seeded melt-growthTop-seeded melt-growth

Ba

J

f

Lorentz force: f =

JB

Jc

Field distribution

Vortex pinningRecord

trapped field: 17 Tesla

• The maximal field in the magnets, • The maximal current in the cables are determined by vortex pinning => it’s important to study vortices

Magneto-optical imaging NbSe2 field-cooled to 4.3 KNbSe2 field-cooled to 4.3 K

10 m

Sanyalak Niratisairak:

Characterization of MO-films

Åge Olsen:Observation of what Vortices do

Jørn Inge Vestgården:Calculation of Vortex distributions

Superconductivity Lab @ UiO