Prof. THARWAT G. ABDEL- MALIK
Department of Physics , Faculty of Science University of Minia
P426:-INTRODUCTION TO CONDENSED MATTER PHYSICS
SOLID STATE PHYSICS
SUPERCONDUCTIVITY
Prof. Dr. THARWAT G. ABDEL-MALIK EMERITUS PROFESSOR
P426:-INTRODUCTION TO CONDENSED MATTER PHYSICS
SUPER CONDUCTIVITY
LECTURER NUMBER FIVE (15-SLIDES) e-mail:[email protected]
Discovery of the Superconductor
Superconductivity was first discovered in 1911 when mercury was cooled to approximately 4 degrees Kelvin by Dutch physicist Heike Kamerlingh Onnes, which earned him the 1913 Nobel Prize in physics. In the years since, this field has greatly expanded and many other forms of superconductors have been discovered, including Type 2 superconductors in the 1930s.
A superconductor is an element or metallic alloy which, when cooled below a certain threshold temperature, the material dramatically loses all electrical resistance. In principle, superconductors can allow electric current to flow without any energy loss (although, in practice, an ideal superconductor is very hard to produce). This type of current is called a supercurrent.
The threshold temperature below which a material transitions into a
superconductor state is designated as Tc, which stands for critical temperature.
Not all materials turn into superconductors, and the materials that do each have their own value of Tc.
Discovery of the Superconductor
Superconductivity was discovered on 1911 by Heike Kamerlingh Onnes ,who was studying the resistance of the solids mercury at cryogenic temperatures using the
recently –discovered liquids helium as a refrigerant.
At the temperature of 4.2 K, he observed that the resistance suddenly
disappeared . In subsequence decades, superconductivity was found in several other materials.
Critical Temperature
The temperature at which electrical is zero is called the Critical temperature (TC)
The Cooling of the material can be achieved using liquid hellium for even more lower temperature.
Type I superconductors act as conductors at room temperature, but when
cooled below Tc, the molecular motion within the material reduces enough that the flow of current can move unimpeded.
Type 2 superconductors are not particularly good conductors at room
temperature, the transition to a superconductor state is more gradual than Type 1 superconductors. The mechanism and physical basis for this change in state is not, at present, fully understood. Type 2 superconductors are typically metallic compounds and alloys.
The basic theory of superconductivity, BCS Theory, earned the scientists—
John Bardeen, Leon Cooper, and John Schrieffer—the 1972 Nobel Prize in physics. A portion of the 1973 Nobel Prize in physics went to Brian Josephson, also for work with superconductivity.
Superconductor
Types of Superconductors
In January 1986, Karl Muller and Johannes Bednorz made a discovery that
revolutionized how scientists thought of superconductors. Prior to this point, the understanding was that superconductivity manifested only when cooled to near absolute zero , but using an oxide of barium, lanthanum, and copper, they found that it became a superconductor at approximately 40 degrees Kelvin. This
initiated a race to discover materials that functioned as superconductors at much higher temperatures.
In the decades since, the highest temperatures that had been reached were about 133 degrees Kelvin (though you could get up to 164 degrees Kelvin if you applied a high pressure). In August 2015, a paper published in the journal
Nature reported the discovery of superconductivity at a temperature of 203 degrees Kelvin when under high pressure.
Superconductors are used in a variety of applications, but most notably
within the structure of the Large Hadron Collider. The tunnels that contain the beams of charged particles are surrounded by tubes containing powerful superconductors.
The supercurrents that flow through the superconductors generate an intense magnetic field, through electromagnetic induction , that can be used to
accelerate and direct the team as desired.
In addition, superconductors exhibit the Meissner effect in which they cancel all magnetic flux inside the material, becoming perfectly diamagnetic (discovered in 1933). In this case, the magnetic field lines actually travel around the cooled
superconductor. It is this property of superconductors which is frequently used in magnetic levitation experiments, such as the quantum locking seen in quantum levitation. In other words, if Back to the Future style hover boards ever become a reality. In a less mundane application, superconductors play a role in modern
advancements in magnetic levitation trains , which provide a powerful possibility for high-speed public transport that is based on electricity (which can be generated using renewable energy) in contrast to non-renewable current options like airplanes, cars, and coal-powered trains.
Applications of Superconductors
The Meissner Effect In 1920 The Meissner discover not only did
superconductors exhibit zero resistance but also
spontaneous expel all magnetic flux when cooled through the superconducting transition, that is they are also perfect diamagnets. We call this Meissner effect.
The limit of external magnetic field strength at which a superconductor can exclude the field is known as the critical field strength, Hc.
A Cooper pair is the name given to electrons that are bound together in a certain manner first described by Leon Cooper. In normal superconductors, the attraction is due to the electron interaction.
The Cooper Pair state forms the basis of the BCS theory of superconductivity
BCS-COOPER PAIRS
Formation of cooper pairs
Cooper pairs are formed by an attractive force between electrons from the exchange of phonons.
The energy of phonon is usually less than 0.1eV
What is a type I and a type II superconductor?
The difference between type I and type II superconductors can be found in their magnetic behaviour.
A type I superconductor keeps out the whole magnetic field until a critical
applied field Hc reached. Above that field a type I superconductor is no longer in its superconducting state.
A type II superconductor will only keep the whole magnetic field out until a first critical field Hc1 is reached. Then vortices start to appear. A vortex is a magnetic flux quantum that penetrates the superconductor. Where the vortex appears the superconducting order parameter drops to zero. In this region the metal is no longer a superconductor. Around the vortex a current starts to
circulate. Even though the vortices have formed, the rest of the metal stays superconducting.
If the field is increased to the second critical field Hc2 the metal stops to be superconducting. Hc2 is usually a lot bigger than Hc that's why type II
superconductors are typically used for superconducting magnets.
Figure 1 shows the difference in the magnetic behavior of type I and type II super-conductors. As
)
0
( H E B
means that the whole field is kept out. If not the whole field is kept out any more.
H M
M H
B B x e
Z
) /
0
exp(
In a type II superconductor the coherence length is shorter than the
penetration depth. Then it is energetically favorable for vortices to form.
Draw the magnetic field and current density around a vortex
Fig.2.Superconducting order parameter, amplitude of magnetic field and current circulating around flux quantum
In a type I superconductor the coherence length (length over which superconductivity changes) is bigger than the penetration depth
Figure 2 shows what happens in the region of a vortex. At the vortex there is one magnetic flux quantum ( ) that enters the superconductor.
Around the vortex superconducting currents are trying to keep the field out.
The magnetic field decreases exponentially from the center of the vortex. In the center of the vortex the superconducting order parameter goes to zero. This means that in this region the metal is no longer a superconductor.
You can also see that the coherence length is shorter than the penetration depth λ. As explained above, this defines a type II superconductor and makes the formation of vortices favorable.
Explain flux quantization
The equation for a super current can be calculated from the imaginary part of the Schrödinger equation for a charged particle in an electric and magnetic field. This is the equation for the current density the number of cooper pairs, so half of the number of electrons and is the phase..
) 2 2 (
e A
m n J e
e
cp
ncp is the number of cooper pairs, so half of the number of electrons and is the phase.
2 15
0 2 10
2 Tm
e
h
Path through the superconducting ring
We now integrate both sides of the equation along the dotted path
We can then use Stokes' theorem to get ) 3 2 (
dl e A
l
d
) 4 2 (
2
2
d l e A d s e B d s e
S S
We now take a superconducting ring, which is thicker than the penetration depth. If you choose a path through the middle of the ring (the distance to any edge should be bigger than the penetration depth) there should be no field and
no current along the path. So and therefore and 2 0
e A
e A
2
0 J
.
where S is the area enclosed by the dotted path and is the magnetic flux.
On the left you can see a circular integral over a phase. When you integrate over a ring like this the phase should be the same after one lap as when you started (except for a factor of 2, or a multiple of 2). So you get
) 5 2 (
2
d l n e
where n is a whole number positive or negative. We can transfer the negative sign into the n and get
) 6 2 (
2
0
n e
So the magnetic flux in a superconductor can only appear in whole number portions of the superconducting flux quantum and
therefore is quantized:
0
) 7
0
(
n
And the flux quantum equals:
) 8 ( Tm
10
2.0679 2
2
2
-15 20
