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
1913M 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 Al
1.14
10
Si P S Cl Ar
K Ca Sc Ti
0.39
10
V
5.38
142
Cr Mn Fe Co Ni Cu Zn
0.875
5.3
Ga
1.091
5.1
Ge As Se Br Kr
Rb Sr Y Zr
0.546
4.7
Nb
9.5
198
Mo
0.92
9.5
Tc
7.77
141
Ru
0.51
7
Rh
0.03
5
Pd Ag Cd
0.56
3
In
3.4
29.3
Sn
3.72
30
Sb Te I Xe
Cs Ba La
6.0
110
Hf
0.12
Ta
4.483
83
W
0.012
0.1
Re
1.4
20
Os
0.655
16.5
Ir
0.14
1.9
Pt Au Hg
4.153
41
Tl
2.39
17
Pb
7.19
80
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

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

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 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 energyno resistanceno 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

London Theory – 1
• Newton’s law (inertial response) for applied electric field
 SJ
dt
d
E  2
en
m
s







en
J
dt
d
meE
s
S
 sv
dt
d
mF 
sss evnJ 
dt
dJ
m
Een Ss

2
dt
Jd
m
Een Ss





2
dt
Jd
dt
Bd
m
en Ss




2
0
2






 B
m
en
J
dt
d s
S

Supercurrent density is
B
m
en
J s
S
 2

We know B = 0 inside superconductors
Faraday’s law
Fritz & Heinz London, (1935)

London Theory – 2
 SJ
dt
d
E  2
en
m
s

B
m
en
J s
S
 2

London Equations
t
E
JB





000 
JB 

0
  B
m
en
BB s
 2
0
2

B
m
en
B s
 2
0
2

Ampere’s
law
=0; Gauss’s law
for electrostatics

Conductors in a Magnetic Field
Apply
field
Perfect (metallic) conductor SuperconductorNormal 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
HHc 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
http://www.physics.ubc.ca/~outreach/phys420/p420_96/bruce/ybco.html

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
www.rtri.or.jp/rd/maglev/html/english/maglev_frame_E.html
www.lanl.gov/quarterly/q_spring03/meg_helmet.shtml
http://www.bestofjesse.com/projects
/indust/project1.html

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

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….

CH 8 _ M A Islam_Superconductors

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CH 8 _ M A Islam_Superconductors