Superconductors expel magnetic fields below a critical temperature due to the Meissner effect. Quantum levitation occurs when a type-II superconductor is placed above a magnet. Magnetic flux tubes form and become pinned inside the superconductor, locking it in place against gravity. As the superconductor moves, energy increases due to the shifting flux tubes, creating a drag force that resists movement and provides stable levitation. Potential applications include frictionless trains and devices that could simulate weightlessness.

1. QUANTUM LEVITATION
(Superconductors)
Presented By : ABHIK DEBNATH
15PH40002

2. •Definitions
•Concepts associated with
Superconductors
•Description of Quantum locking
•Applications and Future of
Superconductors
OUTLINE

3. IT ALL STARTS WITH SUPERCONDUCTIVITY!
Superconductivity is a phenomenon of exactly zero electrical resistance and
expulsion of magnetic flux fields occurring in certain materials when cooled below
a characteristic critical temperature. It was discovered by Dutch physicist H.K.
Onnes on April 8, 1911. Like ferromagnetism and atomic spectral lines,
superconductivity is a quantum mechanical phenomenon. It is characterized by
the Meissner effect, the complete ejection of magnetic field lines from the interior of
the superconductor as it transitions into the superconducting state. The occurrence of
the Meissner effect indicates that superconductivity cannot be understood simply as
the idealization of perfect conductivity in classical physics.
What is a Superconductor made of?
Almost any material, if cooled enough, can be made into a superconductor. Even
many materials which are insulators at room temperature can be superconductors
when cooled to extremely low temperatures.
Elements : Al, Sn, Hg, Pb
Alloys : Mercury or Yttrium based
Organics : Carbon nanotubes
Ceramics : LBCO, YBCO, TBCCO
Resistance vs. absolute
temperature curve by
Onnes which marked the
discovery of
superconductivity.

4. Classification of Superconductors
 By their magnetic properties:
Type I superconductors: those having just one critical field, Hc, and changing abruptly from
one state to the other when it is reached.
Type II superconductors: having two critical fields, Hc1 and Hc2, being a perfect
superconductor under the lower critical field (Hc1) and leaving completely the superconducting
state above the upper critical field (Hc2), being in a mixed state when between the critical fields.
 By their critical temperature:
Low-temperature superconductors, or LTS: those whose critical temperature is below 30 K.
High-temperature superconductors, or HTS: those whose critical temperature is above 30 K.
Nowadays, 77 K is used as the split to emphasize whether or not we can cool the sample
with liquid nitrogen (whose boiling point is 77K), which is much more feasible than liquid
helium(the alternative to achieve the temperatures needed to get low-temperature
superconductors).
 By material:
Superconductor material classes include chemical elements(e.g. mercury or lead), alloys (such
as niobium-titanium, germanium-niobium, and niobium nitride), ceramics
(YBCO and magnesium diboride), superconducting pnictides (like fluorine-doped LaOFeAs)
or organic superconductors (fullerenes and carbon nanotubes; though perhaps these examples
should be included among the chemical elements, as they are composed entirely of carbon).

5. Expulsion of magnetic fields – The Meissner Effect:
The magnetic properties of superconductors are as dramatic as their complete
lack of resistance. In 1933, Hans Meissner and Robert Ochsenfeld studied the
magnetic behaviour of superconductors and found that when certain ones are
cooled below their critical temperatures, they have an interesting property of
expelling a magnetic field. They discovered that a superconductor will not allow
a magnetic field to penetrate its interior. It achieves this by producing a
“magnetic mirror” surface currents which produce a magnetic field that exactly
counters the external field. The phenomenon of the expulsion of magnetic fields
from the interior of a superconductor is known as the Meissner effect.
A good comparison to electricity is that a good conductor expels static electric
fields by moving charges to its surface. In effect, the surface charges produce an
electric field that exactly cancels the externally applied field inside the
conductor. In a similar manner, a superconductor expels magnetic fields by
forming surface currents. At ordinary temperatures, these currents decay almost
instantaneously due to the finite resistivity of the conductor. However, when
cooling the superconductors below Tc, persistent surface currents are induced
and produce a magnetic field that exactly cancels the externally applied field
inside the superconductor.
Superconductor in the presence of an
external magnetic field. (a) At temperatures
above Tc, the field lines penetrate the
sample because it is in its normal state. (b)
When the rod is cooled to T<Tc and
becomes superconducting, magnetic flux is
excluded from its interior by the induction
of surface currents.

6. The Meissner effect was given a phenomenological explanation by London
brothers, who showed that the electromagnetic free energy in a superconductor
is minimized provided:
𝛁 𝟐 𝐇 = 𝛌−𝟐 𝐇
where H is the magnetic field and λ is the London penetration depth.
This equation, which is known as the London equation, predicts that the
magnetic field in a superconductor decays exponentially from whatever value it
possesses at the surface.
In a weak applied field, a superconductor "expels" nearly all magnetic flux. It
does this by setting up electric currents near its surface. The magnetic field of
these surface currents cancels the applied magnetic field within the bulk of the
superconductor. As the field expulsion, or cancellation, does not change with
time, the currents producing this effect (called persistent currents) do not decay
with time. Therefore, the conductivity can be thought of as infinite: a
superconductor.
Near the surface, within the London penetration depth, the magnetic field is not
completely cancelled. Each superconducting material has its own
characteristic penetration depth.

7. Superconductors in the Meissner state exhibit perfect Diamagnetism, or superdiamagnetism, meaning that the total
magnetic field is very close to zero deep inside them (many penetration depths from the surface). This means that
their magnetic susceptibility is -1. Diamagnetics are defined by the generation of a spontaneous magnetization of a
material which directly opposes the direction of an applied field. However, the fundamental origins of diamagnetism in
superconductors and normal materials are very different. In normal materials diamagnetism arises as a direct result of
the orbital spin of electrons about the nuclei of an atom induced electromagnetically by the application of an applied
field. In superconductors the illusion of perfect diamagnetism arises from persistent screening currents which flow to
oppose the applied field (the Meissner effect); not solely the orbital spin.
In superconducting state, the magnetic induction inside the specimen is given by,
Where H is the external field and M is the magnetization produced inside the specimen.
According to Meissner effect, the magnetic induction B = 0 inside the bulk superconductor. Therefore,
This is an important result which can’t be derived from simple definition of superconductivity as a medium of zero
resistivity. Accordingly if 𝛒 tends to zero while the current J is held finite, then from Ohm’s law E = J𝛒 , E must be
zero. Further from Maxwell’s equation,
We obtain
𝐝𝐁
𝐝𝐭
= 0 and hence B = constant, i.e. the flux passing through the specimen can’t change on cooling through
the transition. The Meissner effect contradicts the result and suggests that perfect Diamagnetism is an essential property
of defining the superconducting state. They are:
E = 0 (from zero resistivity) and B = 0 (from Meissner effect)
𝐁 = 𝛍 𝟎(𝐇 + 𝐌
𝛍 𝟎 𝐇 + 𝐌 = 𝟎 or 𝐌 = −𝐇 hence, 𝛘 =
𝐌
𝐇
= −1
𝛁 × 𝐄 = −
𝐝𝐁
𝐝𝐭

8. Transition to Quantum Levitation
What is Quantum levitation?
Quantum levitation is the ability of a superconductor to
perfectly match the magnetic fields surrounding it. Because of
the zero resistance properties of superconductors we get an
effect known as quantum levitation. This phenomenon creates a
magnetic locking effect between the superconductor and the
magnetic field, thus allowing the superconductor to levitate.
This isn’t a magic or an illusion. This is real science.
The phenomenon of quantum levitation is composed of two
different effects that occur simultaneously:
1. The Meissner Effect.
2. Quantum Locking/Flux Pinning.

9. What is Quantum Locking/Flux Pinning?
Flux pinning is the phenomenon where a superconductor is pinned in space
above a magnet. The superconductor must be a type-II superconductor
because type-I superconductors cannot be penetrated by magnetic fields. The
act of magnetic penetration is what makes flux pinning possible. At higher
magnetic fields (above Hc1 and below Hc2) the superconductor allows
magnetic flux to enter in quantized packets surrounded by a superconducting
current vortex (Quantum vortex). These sites of penetration are known as
flux tubes. The number of flux tubes per unit area is proportional to the
magnetic field with a constant of proportionality equal to the magnetic flux
quantum. On a simple 76 mm diameter, 1-micrometer thick disk, next to a
magnetic field of 350 Oe, there are approximately 100 billion flux tubes that
hold 70,000 times the superconductor's weight. At lower temperatures the
flux tubes are pinned in place and cannot move. This pinning is what holds
the superconductor in place thereby allowing it to levitate. This phenomenon
is closely related to the Meissner effect, though with one crucial difference
— the Meissner effect shields the superconductor from all magnetic fields
causing repulsion, unlike the pinned state of the superconductor disk which
pins flux, and the superconductor in place.
Flux Pinning: Flux Tube diagram

10. How does this make it levitate?
When a superconductor is placed on a magnetic track, the effect is that the superconductor
remains above the track, essentially being pushed away by the strong magnetic field right
at the track's surface. There is a limit to how far above the track it can be pushed, of course,
since the power of the magnetic repulsion has to counteract the force of gravity.
A disk of a type-I superconductor will demonstrate the Meissner effect in its most extreme
version, which is called "perfect diamagnetism," and will not contain any magnetic fields
inside the material. It'll levitate, as it tries to avoid any contact with the magnetic field. The
problem with this is that the levitation isn't stable. The levitating object won't normally stay
in place. (This same process has been able to levitate superconductors within a concave,
bowl-shaped lead magnet, in which the magnetism is pushing equally on all sides.)
In order to be useful, the levitation needs to be a bit more stable. That's where quantum
locking comes into play.
What are these flux tubes?
One of the key elements of the quantum locking process is the existence of these flux
tubes, called a "vortex". If a superconductor is very thin, or if the superconductor is a type-
II superconductor, it costs the superconductor less energy to allow some of the magnetic
field to penetrate the superconductor. That's why the flux vortices form, in regions where
the magnetic field is able to, in effect, "slip through" the superconductor.
Flux vortices can also form in type-II superconductors, even if the superconductor material
isn't quite so thin. The type-II superconductor can be designed to enhance this effect, called
"enhanced flux pinning."
The partial penetration of a magnetic field is
in the form of a regular array of normal
conducting regions (shown as the dark
regions in Figure). These normal regions
allow the penetration of the magnetic field in
the form of thin filaments. The vortices are so
named because each is a “vortex” or swirl of
electrical current. One can view a vortex as a
cylindrical swirl of current surrounding a
core that allows some flux to penetrate the
interior of the superconductors.

11. How do flux tubes lead to quantum locking?
When the field penetrates into the superconductor in the form of a flux
tube, it essentially turns off the superconductor in that narrow region.
Picture each tube as a tiny non-superconductor region within the middle of
the superconductor. If the superconductor moves, the flux vortices will
move. Remember two things, though:
 The flux vortices are magnetic fields.
 The superconductor will create currents to counter magnetic fields (i.e.
the Meissner effect).
The very superconductor material itself will create a force to inhibit any
sort of motion in relation to the magnetic field. If you tilt the
superconductor, for example, you will "lock" or "trap" it into that position.
It'll go around a whole track with the same tilt angle. This process of
locking the superconductor in place by height and orientation reduces any
undesirable wobble.
You're able to re-orient the superconductor within the magnetic field
because your hand can apply far more force and energy than what the field
is exerting.
If the levitator moves from its position, the vortices’ positions will shift
from their original location and the energy will increase. This energy
change is translated to a drag force that resists any movements.
Magnetic Flux is QUANTIZED inside the
superconductor, i.e. Magnetic flux enclosed in a
superconductor is in integral multiples of
FLUXONS.

12. Quantum Levitation Vs. Magnetic Levitation
Magnetic Levitation (Non-zero Potential)
 This is based on the repulsive nature of the magnetic
fields.
 Conductive property of the superconductors are used
(Electro-magnets).
 Type-1 as well as Type-2 superconductors may be
used.
 Low stability.
 Lift lesser loads in comparison.
 Electromagnets required on both rails and the train as
well.
Quantum Levitation (Zero Potential)
 Based on the quantum locking principle.
 Diamagnetic property of superconductors are used.
 Only occurs in Type-2 superconductors.
 High stability, multiple vehicles on the same track
at same time is possible.
 Can lift very high loads.
 Electromagnets required on the rail only.

13. Quantum Levitation in action.

14. Future Applications

15. 1. Gravity Loophole
As superconductor locks a particle above and below its surface, it
can be used anywhere to create an environment without gravity.
2. Frictionless Bearings
A lot of energy is wasted in bearing friction even though the
contact area is too small .It is because of the perpendicular force.
But in case of quantum levitation the bearing remains suspended
in mid air.
3. Quantum Levitation Trains
Quantum levitating trains are far more stable and practical . They
require lesser magnetic field to operate and also can carry heavy
loads in comparison. Instead of using fossil fuels, the magnetic
field created by the electrified coils in the guide way walls and
the track combine to propel the train.
4. Lossless Electrical Machines
Generally Electrical machines faces a lot of losses like Hysteresis
loss, Eddy current loss, Copper loss , Friction and windage
losses. With the help of HTS power cables copper losses have
already been minimized. But this quantum levitation will help us
in minimizing the windage and friction losses. This will also help
in minimizing the leakage flux to zero.

16. 5. Hover Board
Hover board is the future of magnetic levitation , short distance
and effort less travel can be possible using the magnetically
levitated hover board.
6. 3D Cell Cultures
Cells grown in flat Petri dishes are not always the most accurate
models for three-dimensional human bodies. To over come this
we are using Quantum Levitation.
7. Studying Weightlessness
Being weightless can have serious health consequences for
astronauts. For every month that an astronaut spends in zero
gravity, he loses one to two percent of his bone density and
weaken the immune system. To understanding how the body
reacts to weightlessness we can use magnetic levitation.

18. From the properties of quantum
levitation we get to know, how
quantum levitation is advantageous
compared to magnetic levitation.
Future application shows the
pollution free and fast mode
transportation, efficient generation of
electricity, and many more future
application are based on principle of
quantum levitation.
CONCLUSION

19. Thank you!