Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Superconductivity
Superconductivity
The Nobel Prize in Physics (HeikeKamerlingh Onnesthe Netherlands 1913"for his
investigations on the properties of matter at low temperatures which led, interalia, to the
production of liquid helium")
“As has been said, the experiment left no doubt that, as far as accuracy of
measurement went, the resistance disappeared. At the same time, however, something
unexpected occurred. The disappearance did not take place gradually but (compare
Fig. 17) abruptly. From 1/500 the resistance at 4.2oK drop to a millionth part. At the
lowest temperature, 1.5oK, it could be established that the resistance had become less
than a thousand-millionth part of that at normal temperature .Thus the mercury at
4.2oK has entered a new state, which, owing to its particular electrical properties, can
be called the state of superconductivity.”((Heike Kamerlingh Onnes,Nobel Lecture ))
Some materials exhibit zero resistivity below a critical temperature, TC. The critical
temperature is lower in the presence of a magnetic field, and goes to zero for magnetic
fields above a critical field, BC.
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Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Normal Metal vs superconductor
.
What is a Superconductor?
“A Superconductor has ZERO electrical resistance below a certain critical
temperature. Once set in motion, a persistent electric current will flow in the
superconducting loop forever without any power loss.”
Magnetic Flux expulsion
A Superconductor exclude any magnetic fields that come near it.
How “Cool” are Superconductors?
Below 77 Kelvin(-200 ºC):
•Some Copper Oxide Ceramics superconductor
Below 4 Kelvin(-270 ºC):
2
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
•Some Pure Metals e.g. Lead, Mercury, Niobium superconductor
Liquid Heluem Keeping at 4Ks Liquid Nitrogen Keeping at 77 K
1. Definition of superconductivity
The superconducting state differs qualitatively from the normal (nonsuperconducting)
state in 3 major respects:
(a) d.c. conductivity (in zero magnetic fields & for small enough current) effectively
infinite (seen either in voltage-drop experiments, or in persistence of current in
rings)
(b) simply connected sample expels weak magnetic field (Meissner effect): perfect
diamagnet, i.e. B = 0. [convention for H, B later]
(c) Peltier coefficient* vanishes, i.e. electrical current not accompanied by heat
current (contrary to usual behavior in normal phase).
_________
These three phenomena set in essentially discontinuously at a critical temperature Tc
which may be anything from ~1 mK to ~25K (higher for HTS, etc.) For most
elements & alloys, Tc ~ a few K. (Note: this is ~3-4 orders of magnitude below TF
and ~1-2 below θD)
2. Occurrence
Superconductivity appears to occur only in materials which in the normal phase (i.e.
above Tc) are metals or (occasionally, under extreme conditions) semiconductors: There
3
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
is no clear case in which, as T is lowered, the system goes from an insulating to a S
state†. In the case of the classic superconductors, N state is almost always a metal.
Many intermetallic compounds, e.g. Nb3, Sn, V3, Ga, often with high Tc (~20K).
Critical temperature
Superconductors are in the superconducting state only below a certain temperature, the
critical temperature Tc. Materials are divided into low-Tc or low-temperature
superconductors, with a Tc below about 30 K, and high-Tc or high-temperature
superconductors (HTSC), with higher Tc's. The highest critical temperature of a
compound at normal pressure is currently about 135 K(at 2010 175 K). The known
HTSC's are typically ceramic-like compounds composed of three to five elements,
almost all containing oxygen and copper, while low-Tc materials with some few
exceptions are elements and metal-alloys.
Meissner effect
A superconductor has zero resistance, so there can be no electric field or emf since
that would produce an infinite current. So there can be no changing magnetic fields in
a superconductor. It is observed that the magnetic field is not only constant,
the magnetic field is zero in a superconductor.
In the superconducting state, current is (except in certain cases) conducted without
resistance. If a material with this property of perfect conductivity is exposed to a
magnetic field, persistent screening currents at the surface will be induced to
screen out the magnetic field, since E = 0 in the superconductor and, according to
the Faraday law of induction,
so that the enclosed fl ux is kept constant (or zero if initially zero). However,
superconductivity is not the same as perfect conductivity. Superconductors that are
placed in a (weak enough) magnetic field at T > Tc and then cooled down to below
Tc expel the magnetic field, so that B is always zero in the bulk. Since
B = µ°(H+M)
this is corresponds to perfect diamagnetism with
χ = M/H = -1.
4
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
A Superconductor is more than a perfect conductor, it is a Perfect Diamagnetism
Perfect Conductor R=0
Perfect Diamagnet B=0
Critical field, type-I, type-II
Just as the temperature cannot be too high for superconductivity to occur, too
strong magnetic fields also destroy superconductivity by making the regular,
normal state energetically favorable.
The superconductors are classified into two groups depending on their behavior in
magnetic fields. All bulk superconductors display the Meissner effect at low
enough magnetic fields. For type-I superconductors, the Meissner state remains
(for favorable geometries) up to a critical field Hc (T), where superconductivity
suddenly disappears.
For type-II superconductors, the Meissner state only remains up to a lower critical
field Hc1, above which magnetic field partially penetrates the superconductor,
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Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
until the field reaches an upper critical field Hc2, where the transition to the normal
state is finally occurring.
4. Magnetic behavior of superconducting phase
For a given material, the magnetic behavior is in general a function of the shape of
the sample: the simplest case to analyze is a (large) long cylinder parallel to the
external field. In this case, there are 2 types of behavior, type-I and type-II. Most pure
elemental superconductors are type-I (exception: pure Nb): compounds and alloys
tend to be type-II, and this is the case for virtually all the highest-Tc materials.
Type-I: At any given T < Tc(0), if we gradually raise H, system remains perfectly
superconducting up to a definite critical field Hc(T), at which point it goes over
discontinuously (by a first-order transition) to the normal phase and readmits the
magnetic field completely. In terms of the B(H) relation*:
*It is conventional in the theory of superconductivity to define H as the field due to
external sources, and B as the total local field averaged over a few atomic
distances. Thus, B = μoH + M where M is the average magnetization due to
macroscopic circulating currents. (Atomic-scale variations usually not considered).
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Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Vortex, mixed state
When magnetic field starts to penetrate type-II superconductors at Hc1, this
happens because it becomes energetically favorable to let certain parts of the
system become normal, instead of just increasing the screening currents and
associated kinetic energy. In type-I superconductors the
boundaries between normal and superconducting states have positive energy, so
that such surfaces are avoided. In type-II superconductors, however, this energy is
negative, and the flux penetrating in the so called mixed state between Hc1 and
Hc2 is divided into the smallest possible bundles, i.e., the flux quantum. The
resulting thin filaments of flux are called vortices, the name coming from the
screening currents surrounding them.
Although the superconductor in the mixed state is still in its superconducting state,
it may not always conduct current without resistance. This is because moving
vortices induce electrical fields that may drive currents in their normal cores.
Type-I Superconductor
Type I superconductors exhibit the Meissner Effect up to their critical field, Bc, above
which the superconductivity and the exclusion of applied magnetic fields abruptly
stops.
7
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Type-II Superconductor
Type II superconductors exhibit superconductivity and the exclusion of applied
magnetic fields up to their lower critical field, BC1. Above this field, the material still
exhibits superconductivity, but the supercurrents can exclude only part of the applied
magnetic field.
A superconductor in an external magnetic field will have supercurrents which cancel
out the magnetic field inside the material, that is, it will be a perfect diamagnet.
There is an energy cost to producing the supercurrents.
If the applied field is sufficiently large (B>BC), the energy cost is too high and the
superconductivity is destroyed.
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Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
A current-carrying type II superconductor in the mixed state When a current is applied
to a type II superconductor (blue rectangular box) in the mixed state, the magnetic
vortices (blue cylinders) feel a force (Lorentz force) that pushes the vortices at right
angles to the current flow. This movement dissipates energy and produces resistance
[from D. J. Bishop et al., Scientific American, 48 (Feb. 1993)].
Cooper pairs, energy gap BSC Theory
Electrons in the superconducting state can form Cooper pairs. Such a pair of
coupled electrons takes the character of a boson, which condenses into a ground
state, described by a macroscopic wave function. The condensation is enabled
through an attraction between the normally repulsive electrons, usually mediated
through electron-phonon interaction. This attraction gives rise to a pair-binding
energy of a few meV.
When many Cooper pairs are allowed to form in the superconducting state, the
pairing opens a gap 2Δ in the normal electron density of states around the Fermi
energy. This gap prevents small excitations such as scattering, and thus leads to
superconductivity. The presence of a common, macroscopic wave function
prevents the destruction of an individual pair wave function without
destroying the entired paired state, to a high energy cost.
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Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Tunneling, Josephson effect
Tunneling through a thin insulator from a metal to a superconductor . It is found
that there is a potential threshold V = Δ /e before a tunneling current flows.
Tunneling between two superconductors can occur with single electrons, but also
with paired electrons if the barrier is thin. Such Cooper pair tunneling is described
by the Josephson effects. In the DC Josephson effect, a supercurrent may flow
across the junction in the absence of any applied electrical field. In the presence of
a magnetic field the tunneling current is given by
I=I°
where is the total magnetic flux in the junction. In the AC Josephson effect, an
oscillatory supercurrent of frequency
ωJ =
is induced by applying a DC voltage V .
Superconducting Quantum Interference Device (SQUID)
A small magnetic field produces a phase difference in the two currents and
interference effects.
10
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
London equations
The first London equation describes the relation between supercurrent and
electrical field,
js =
E
where js = -nsevs is the supercurrent and ns is the density of superconducting
electrons.
The second London equation desctibes the relation between supercurrent and
magnetic field,
E
Together with the Maxwell equation, this equation gives
B = µ°j
where
B=
B
Where
=
is the London penetration depth. it is the depth to which, in the Meissner phase, an
EM field penetrates into the surface of the superconductor. To be more exact, the
field does exist inside a surface region with the thickness 10-5 to10-6 cm where
persistent screening currents flow.
BCS Theory ( Bardeen, Cooper, Schrieffer )
Isotope effect: MαT constant
This indicates that lattice vibrations are important to superconductivity.
11
2011
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Theory: At low temperatures electrons pair up. The attractive interaction comes from
the fact that an electron moving through the lattice attracts the positive ions and so
produces a traveling distortion of the lattice, a phonon. This traveling local increase in
the positive charge density is attractive to another electron. So there is an attraction
between two electrons mediated by the vibrations of the lattice, phonons. At low
enough temperatures, this attractive force is larger than the Coulomb repulsion and a
bound state is formed, a Cooper pair.
The electrons that form a pair have opposite spins and opposite linear momenta!
Together the pair forms a boson and so all pairs can be in the same energy state.
The BCS theory is a microscopic theory of superconductivity, describing how to
approximate the macroscopic quantum state of the system of attractively
interacting electrons. In its simplest form, it relates the zero-temperature energy
gap with Tc, according to
and gives an estimate of Tc,
Tc
where is the Debye frequency, N0 = g( F )/2 is the density of states for one spin
direction, and V0 is an effective coupling / attractive interaction parameter.
The energy to break up the pair is called the superconducting energy gap, Eg.
As the temperature is increased, more and more pairs get broken up. The unpaired
electrons decrease the binding energy of the remaining pairs, i.e. they decrease the
energy gap.
12
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
High TC Superconductors
Type II superconductors with high critical temperatures and high critical fields.
All have copper and oxygen and are in the perovskite structure.
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2011
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Yttrium atoms are yellow, Barium atoms are purple, Copper atoms are blue and
Oxygen atoms are red.
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Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Superconducting elements (at ambient pressure): Superconducting critical temperature Tc,
crystallographic structure (FCC= face centered cubic; BCC=body centered cubic,
HEX=hexagonal,
TET=tetragonal,
RC=orthorhombic,
RHL=rhombohedral)
and
thermodynamic critical magnetic field Hc (at T=0).
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Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Superconductor Application
first type of application is straightforward: superconductors with zero resistance are ideal
current leads, capable of withstanding extreme current densities1 ~106-107 A/cm2, which
should be compared to the current carrying capability “ampacity” of commercial Cu and Al
cables, corresponding to the maximum current density of ~200-300 A/cm2.
16
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Filamentary composite wires
• for reasons that will be described later,
superconducting materials are always
used in combination with a good
normal conductor such as copper
• to ensure intimate mixing between the
two, the superconductor is made in the
form of fine filaments embedded in a
matrix of copper
• typical dimensions are:
• wire diameter 0.3 - 1.0mm
• filament diameter 10 - 60mm
• for electromagnetic reasons, the
composite wires are twisted so that the
filaments look like a rope (see Lecture
3 on filamentary conductors and
cables)
Martin Wilson Lecture 1 slide 7
Superconducting Magnets for Accelerators JUAS February 2003
The second type of application is less trivial and is due to macroscopic phase coherence of
superconductors, which allows observation of quantum mechanical behavior even in
macroscopic objects and thus allows fabrication of novel quantum electronic devices using
conventional microfabrication techniques.
Historically superconductor technology was first utilized in purely performance-driven
sectors i.e. in science, research and technological development (RTD), and in military
17
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
applications. In a next phase, medical applications where competition from nonsuperconducting devices is weak, were opened up. Almost all of today’s superconducting
products still use LTS materials. So far, these markets are mostly for magnets ranging from
small magnets for university research to enormous systems for large laboratory facilities.
The biggest current market is for magnets used in medical diagnosis, Magnetic Resonance
Imaging (MRI). As can be seen in the graph, both fields, RTD and MRI, together account for
most of today’s overall market…”. Fig. below shows the example of main applications of
conventional, low temperature superconductors (LTS) in MRI and scientific project in Large
Hardon Collider.
18
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
19
Dr. Akram Raheem Jabur
Assistant Professor
2011
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Examples of new large scale applications using High Temperature Superconductors .First two
rows: Overview of today’s application of HTS cables for high power lines and Fault Current
Limiters at the power stations. Bottom-left: a prototype of 10 MW HTS transformer. Bottomright: Application of HTS motors in military ship engines.
•Magnetic Levitation allows trains to “float” on strong superconducting magnets (MAGLEV
in Japan, 1997)
traditional high-magnet applications, today new electronic applications are emerging where
superconductors are used in telecommunication, super-sensitivity devices and detectors, highfrequency resonators, mixers, and other cryoelectronic components based on superconducting
tunnel junctions. New large scale applications based on high temperature superconductors
(HTS) are also being
developed. Those new,
World's largest: CMS superconducting solenoid
highly
cost-competitive
commercial
applications
are noted in Fig. 1.1 as
“new electronic” and “new
large scale” applications.
New applications started
very recently, from about
2003. Several scientific and
technological
breakthroughs are staying
CMS solenoid
behind
those
new
4T at 20,000A
applications: First of all,
6 m diameter 12.5m long
stored energy 27000MJ
reliable HTS cables were
made, which outperform
Superconducting Accelerators: Cockroft Institute June 2006
normal Cu cables by ~150
times1, and operate in
Martin Wilson Lecture 1 slide 29
20
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
liquid nitrogen, which is cheap-enough in production and easy-enough in operation.
A SQUID (Superconducting Quantum Interference Device) is the most sensitive
magnetometer. (sensitive to 100 billion times weaker than the Earth’s magnetic field).
•Offers exponential improvement in speed and memory over existing computers •Capable
of reversible computation
•e.g. Can factorize a 250-digit number in seconds while an ordinary computer will take
800 000 years! Current Research focuses on Quantum Computation using
Superconductors.
Examples of new electronic applications of superconductors. Top row: liquid nitrogen cooled
HTS filters for telecommunication provide a dramatic enhancement in performance and
capacity of the telephone line without introduction of new stations. Middle-left: Application
of superconducting SQUID sensors for non-destructive testing of multilayered metallic
constructions. Middle-right: Superconducting Hot Electron Bolometer (HEB) mixer at the
Hershel Space Observatory. Bottom-left: a prototype of a Rapid Single Flux Quantum
microprocessor. Botom-right: Superconducting qubit- the basic element of quantum
computer.
Current research areas in superconductivity, which may lead in future to new applications of
superconducting materials include development of super-sensitive sensors of various kind,
THz frequency generators and detectors, metrology applications, development of
superconducting digital electronics, memory elements and super-computers, as well as
development of principally new quantum electronic devices for quantum informatics and
quantum computing, or devices operating with charge or spin of a single electron.
21
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Such a rapid development requires proper education in the area of superconductivity, which
is today offered by many universities.
22
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
Dr. Akram Raheem Jabur
Assistant Professor
2011
Application of low-Tc superconducting cables for high field persistent magnets. Bottom-left
panel: in Magnet Resonance Imaging (MRI) for medical diagnostics. This is the main
industrial application today. Top-right panel in the research and development area: Large
Hardon Collider (LHC), which in total contains over 1600 superconducting magnets
weighing up to 27 tonnes each. Approximately
96 tonnes of liquid Helium is needed to keep them at the operating temperature,
making the LHC the largest cryogenic facility at liquid helium temperature.
23
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
24
Dr. Akram Raheem Jabur
Assistant Professor
2011
Electronic and Magnetic Materials
Class: 4th year
University of Technology
Materials Engineering Department
25
Dr. Akram Raheem Jabur
Assistant Professor
2011