CH 8 _ M A Islam_Superconductors

Superconductivity

M A Islam

EEE, IIUC

1911: discovery 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

In 1912 he found that the resistive

state is restored in a magnetic field or

at high transport currents

1913 M A Islam, EEE, IIUC

Superconductors

Aluminum 1.2K

Tin 3.7K

Mercury 4.2K

Niobium 9.3K

Niobium-Tin

17.9K

Tl-Ba-Cu-oxide

125K

Metal Critical

T(K)

A superconductor is a metal that allows a current to pass through it with no loss

due to heat dissipation.

Typical values for the critical temperature range

from mK to 100K

Using Superconductors we can preserve a

wavefunction because the fact that the current

wavefunction is not perturbed by its journey through the

metal means that it will stay in a given state.

The current can be seen as a wavefunction, and is thus

A probability distribution of different current values, this

implies that clockwise and counter clockwise. It is this

view of the current that enables us to create qubits from

a simple loop of superconductor.

M A Islam, EEE, IIUC


The superconducting elements Li Be

0.026

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 Zn0.8755.3

Ga1.091

5.1

Ge As Se Br Kr

Rb Sr Y Zr0.5464.7

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

W0.0120.1

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=9K

Hc=0.2T

Fe (iron)

Tc=1K

(at 20GPa)

...or so we thought until 2001


Type I Superconductors

Type I superconductors are sometimes called "soft" superconductors while the

Type II are "hard", maintaining the superconducting state to higher temperatures

and magnetic fields.

In Type I superconductors transition from normal state to superconducting state occurs instantly i.e. at exactly it's critical/transition temperature Tc:

This type of superconductors "repel" magnetic field lines fully, i.e. no magnetic field line could penetrate through in this type of superconductors:

As you can see no magnetic field line penetrates

though this type of superconductor

The pure metals which exhibit zero resistivity at low temperatures and have the property of

excluding magnetic fields from the interior of the superconductor (Meissner effect).


In Type II superconductors transition from a

normal state to a superconducting state

occurs "slowly" i.e. as you decrease

temperature from it's critical temperature

superconducting properties increase:

Superconductors made from alloys are called Type II superconductors. Besides being

mechanically harder than Type I superconductors, they exhibit much higher critical

magnetic fields. Type II superconductors such as niobium-titanium (NbTi) are used in the

construction of high field superconducting magnets.

As you can see on image, there is small curve

which approaches zero resistance after critical

temperature Tc.

The Common and most popular example of Type II

superconductor is YBCO superconductor, which

critical temperature is 90K. Also some magnetic

field lines can penetrate though in this type of

superconductors allowing Flux Pinning which is

also know as Quantum Locking .

As you can see on image, some magnetic field lines can

penetrate though this type of superconductors, thus

resulting aforementioned Flux pinning. Using this it is

possible to say that this type of superconductors aren't

ideal superconductors.

Type II Superconductors


http://en.wikipedia.org/wiki/Flux_pinning



There are few differences between Type I and Type II

superconductors, first of them it transition of superconducting

state, second is magnetic field lines. Also there are few more

differences between them, for example Type I

superconductors always have lower critical temperature than

the most of Type II superconductors, also There is theory

(BCS Theory) which explains only type I superconductors but

can't explain type II superconductors (i.e. High temperature

superconductivity)

Differences between Type I and Type II


http://en.wikipedia.org/wiki/BCS_theory



The magnetic field strength B just outside the surface of the wire is μ0I / 2 a.

It follows that if the current flowing in a superconducting wire is increased,

eventually the field strength at the surface of the wire will exceed Bc and the

sample will revert to its normal state. The maximum current that a wire can carry

with zero resistance is known as its critical current, and for a long straight wire

the critical current Ic is given by Ic = 2 aBc / μ0. A current greater than Ic will

cause the wire to revert to its normal state. This critical current is proportional to

the radius of the wire.The magnetic field strength B just outside the surface of

the wire is μ0I / 2a. It follows that if the current flowing in a superconducting wire

is increased, eventually the field strength at the surface of the wire will exceed

Bc and the sample will revert to its normal state. The maximum current that a

wire can carry with zero resistance is known as its critical current, and for a long

straight wire the critical current Ic is given by Ic = 2aBc / μ0. A current greater

than Ic will cause the wire to revert to its normal state. This critical current is

proportional to the radius of the wire.

The critical current density = Ic / a2, the current flows only in a thin surface layer.

Critical current density


Superconductors II -When a metal is cooled to the critical temperature, electrons in the metal form Cooper Pairs.

-Cooper Pairs are electrons which exchange phonons and become bound together.

-As long as kT < binding energy, then a current can flow without dissipation.

-The BCS theory of Superconductivity states that bound photons have slightly lower

energy, which prevents lattice collisions and thus eliminates resistance.

-Bound electrons behave like bosons. Their wavefunctions don’t obey

Pauli exclusion rule and thus they can all occupy the same quantum state.


Cooper Pairs -Cooper pairs can tunnel together through the insulating layer of Josephson Junction.

-This process is identical to that of quantum barrier

penetration in quantum mechanics.

-Because of the superconducting nature (no

resistance) and the fact that Cooper pairs

can jointly tunnel through an insulator we can

maintain a quantum current through the Josephson Junction without an applied voltage.

-Thus a Josephson Junction can be used as a very sensitive voltage, current or

flux detector.

-A changing magnetic field induces a current to flow in a ring of metal, this effect

can be used to detect flux quanta. Radio Astronomy uses these devices frequently.


Josephson Junction Devices -There are three primary Josephson Junction devices.

-The Cooper Pair box is the most basic device. We can envision it as a

system with easily split levels, and use the degenerate lowest energy levels as a qubit.

-Similarly to the Cooper Pair box we can use inductors to adjust,

a Josephson Junction, until the potential represented by the

potential well is a degenerate double well. We can then use symmetric and anti-

symmetric wavefunctions and their associated eigenvalues as |0> and |1>.


Josephson Junction Devices II

A current-biased Josephson Junction employs

creates a “washboard” shaped potential.

Splitting in the wells indicates allows us to use

the lowest two levels as qubit states.

The higher energy state |1> can be detected because the tunneling probability

under a microwave probe will be 500 times as probable to induce a transition.

Creates a detectable voltage by “going downhill.” Thus we can know the state.


Why Josephson Junctions? • Microscopic implementations:

– based on electron spins, nuclei spins, or other microscopic properties

– (+)decohere slowly as naturally distinguishable from environment

– (+)single ions can be manipulated with high precision

– (-)hard to apply to many qubits

– (-)difficult to implement with devices

• Macroscopic Implementations: Solid State - Semiconductors: quantum dots, single donor systems

- Superconductors: Josephson Junctions:

- more success so far

- Josephson tunnel junction is “the only non-dissipative, strongly non-linear circuit element available at low temperature “


Benefits of Josephson Junctions

- Low temperatures of superconductor: - no dissipation of energyno resistanceno electron-electron

interactions(due to energy gap of Cooper pairs)

- low noise levels

- Precise manipulation of qubits possible

- Scalable theoretically for large numbers of qubits

- Efficient use of resources: circuit implementation using existing integrated circuit fabrication technology

- Nonlinear Circuit Element - Needed for quantum signal processing

- “easy” to analyze electrodynamics of circuit

Current versus flux across

Josephson Junction M A Islam, EEE, IIUC

London Theory – 1

• Newton’s law (inertial response) for applied electric field

SJdt

dE 2en

m

s

en

J

dt

dmeE

s

S svdt

dmF

sss evnJ

dt

dJ

m

Een Ss 2

dt

Jd

m

Een Ss

2

dt

Jd

dt

Bd

m

en Ss

2

02

B

m

enJ

dt

d sS

Supercurrent density is

Bm

enJ s

S

2

We know B = 0 inside superconductors

Faraday’s law

Fritz & Heinz London, (1935)


London Theory – 2

SJdt

dE 2en

m

s

Bm

enJ s

S

2

London Equations

t

EJB

000

JB

0

Bm

enBB s

2

0

2

Bm

enB s

2

0

2

Ampere’s law

=0; Gauss’s law for electrostatics


Conductors in a Magnetic Field

Apply field

Perfect (metallic) conductor Superconductor Normal metal

Cool Cool

Field off

Apply field

Apply field


Meissner-Oschenfeld Effect

Superconductor

Cool Apply

field

• B = 0 perfect diamagnetism: cM = -1

• Field expulsion unexpected; not

discovered for 20 years.

HHM

MHB

c

0)(0

B/0

H

-M

H Hc Hc

Ideal conductor! Ideal diamagnetic!


The Meissner (and Ochsenfeld) Effect

superconductors push out magnetic fields

- and keep them out with constantly- flowing resistance-less currents

this „diamagnetic‟ property is more fundamental than zero resistance

T > Tc T < Tc

htt

p:/

/ww

w.p

hysi

cs.u

bc.

ca/~

ou

trea

ch/p

hys4

20/p

420_96/b

ruce

/yb

co.h

tml


The dream - “Tomorrow‟s Superconducting World”

350 mph levitated Intercity trains

Underground rapid transit: Heathrow to Gatwick in 10

minutes

Computing: 1000 times faster supercomputers

Cargo-carrying

submarines, all-electric US Navy

Energy Saving: power lines

electric motors transformers

Medical Diagnostics: Magnetic Resonance Imaging SQUID:

Brain activity Heart function

Information Technology: much faster, wider band

communications

magnetically launched space shuttle


Some of these dreams are already reality…

Japanese levitating train has superconducting magnets onboard

Superconducting power cable installed in Denmark

SQUID measure-ment of neuro-

magnetic signals

(nuclear) magnetic resonance imaging of the brain, in the field from a superconducting magnet

ww

w.rtri.o

r.jp/rd

/maglev

/htm

l/english

/maglev

_fra

me_

E.h

tml

ww

w.l

an

l.g

ov/q

uart

erly

/q_

spri

ng

03

/meg

_h

elm

et.s

htm

l

htt

p:/

/ww

w.b

esto

fjes

se.c

om

/pro

ject

s

/in

du

st/p

roje

ct1.h

tml


Uses of SC magnets


Scientific and industrial NMR facilities

900 MHz superconductive

NMR installation. It is used

For pharmacological

investigations of various

bio-macromolecules.

Yokohama City University


Medical NMR tomography equipment


Criogenic high frequency filters for wireless communications


Transmission Lines

• 15% of generated

electricity is dissipated in

transmission lines

• Potential 100-fold

increase in capacity

• BNL Prototype: 1000

MW transported in a

diameter of 40 cm

Pirelli Cables & Systems M A Islam, EEE, IIUC

Telecommunications

• Superconductors are used as efficient filters in cellular telephone towers (now 700 worldwide) • Separate signals of individual phone calls. • Because of electrical resistance, conventional interference filters eat away part of the signal.

Conductus Clearsite system


Other Uses of

Superconductivity

• Fault current limiters

• Electric motors

• Electric generators

• Petaflop computers (thousand trillion floating point operations per second)


Merits & Demerits

Trade off between:

Cost Saving and Cost Increase

Zero resistance, no

energy lost, novel

uses…

Need refrigeration,

fabrication costs….

Thank You

Documents

CH 8 _ M A Islam_Superconductors