Lecture: April 13, 2020

SUMMARY OF LAST LECTURES:

So far we have talked about quantum effects for microscopic objects: electrons, atoms....

As we discussed in the last lecture, the ultimate theory of quantum physics is the quantum field

theory ( QFT ). It describes everything that can be described within the rules of quantum physics,

including creation and annihilation of particles. Particles are “quanta” of the field and this field can

describe interaction between a particle and electromagnetic field. We discussed that electron, due

to its charge and spin ( magnetic moment) is a complex thing as it can emit and absorb photons and

photons can create electron-positron pair. All possibilities are beautifully described by Feynman

diagrams, where each diagram describes a probable event and we have to add all the diagrams to

obtain the net probability. The good news is, more complex the Feynman diagram, smaller the

probability of its occurrence and therefore typically one or few diagrams are enough to obtain

good agreement with the experiments. Here are such diagrams that represent compton scattering.

We now move on to quantum effects that occur at macroscopic level- quantum effects visible

to naked eyes.

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Macroscopic Quantum Phenomenon

• (1) Superconductivity

• (2) Quantization of Resistance : Quantum Hall Effect

• (3) Bose Einstein Condensation

• Lasers

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Superconductivity

Superconductivity is a phenomenon occurring in some materials when cooled below a

critical temperature with two key characteristics

(1) Exactly zero electrical resistance and

(2) Expulsion of magnetic fields

It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911 in Leiden

Applications:

Two important applications are in MRI and particle accelerators. This is because

superconductors give us very powerful electromagnets.

(1) Superconducting magnet: An electromagnet made from coils of superconducting wire.

They must be cooled to very low temperatures during operation. In its superconducting state

the wire has no electrical resistance and therefore can conduct much larger electric currents

than ordinary wire, creating intense magnetic fields. Superconducting magnets can produce

greater magnetic fields than all but the strongest non-superconducting electromagnets and can

be cheaper to operate because no energy is dissipated as heat in the windings. The most widely

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used application for superconductors is an MRI machine commonly found in hospitals. Only a

superconductive system could allow the energy required to generate a magnetic field that powers

an MRI, which can be anywhere from 2,500 times to 10,000 times the strength of Earths magnetic

field, to be economical.

(2) Another important application is in particle accelerators, like the kind used in CERN

Large Hadron Collider (LHC) or its proposed Future Circular Collider.

If the MRI machine sounds powerful, the LHC is an absolute beast. Sending trillions of

particles around 27km of tunnels at speeds close to the speed of light, keeping the particle beam

stable and moving along the precise path requires a magnetic field of immense power, more than

100,000 times the Earths magnetic field. This requires an enormous amount of energy, the kind

that superconducting coils can provide.

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The Future of Superconductivity

There is a lot we do not know about superconductive materials, and we are developing new

applications for superconductors every day.

The key is to develop superconductors that are superconducting at room temperature.

Possible Revolutionary Applications

(1) The hope is to one day use superconductivity in power transmissions, which would

dramatically reduce energy costs around the world.

(2) Mag-lev trains, which use superconductivity to hover a train car above the rail, thereby

eliminating friction that might slow a train down, may be the future of transportation.

(3) Who knows? Maybe one day we will have electronics that utilize superconductors to give us

smartphones that only need to be charged once a month or more.

With the rapid advances in our technology, we will all likely to see superconductivity in our

lives as a regular feature sooner rather than later.

UNDERSTANDING SUPERCONDUCTIVITY at microscopic level

Why some materials become superconductors ??

The complete microscopic theory of superconductivity was finally proposed in 1957 by

Bardeen, Cooper and Schrieffer, known as the BCS theory. It is puely quantum phenomena that

cannot be explained within classical theory. In short, superconductivity is due to formation of

Cooper pairs , pairs of electrons. That is, two electrons somehow pair up. Unlike electrons,

Cooper pairs are bosons. For this work, the authors were awarded the Nobel Prize in 1972.

Nobel Prizes:

(1) Heike Kamerlingh Onnes (1913): Experimental Discovery of Superconductivity: About 4

degrees Kelvin (-452 degrees Fahrenheit, -268 degrees Celsius)

(2) John Bardeen, Leon N. Cooper, and J. Robert Schrieffer (1972), “for their jointly developed

theory of superconductivity, usually called the BCS-theory”

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(3) Georg Bednorz and Alex Miller : 1987 - High Temperature Superconductivity: 30 degrees

Kelvin

( Latest : about 134 degrees K

QUANTUM HALL EFFECT

Resistance R of some sheets of material, in a magnetic field assumes quantized values that

depend on charge of the electron and Planck constant.

Conductance = 1Resistance

= ne2

h, n = 1, 2, 3....

• Why is the resistance quantized

• Why is this quantization observed with extreme precision ( better than one part in billion )

• Why is the conductivity independent of geometry of the sample and impurities in the sample

?

Nobel Prizes:

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(1) Von Klitzing in 1980 who was at that time Heisenberg fellow at universiity of Wrzburg

(2) Robert Laughlin, 1990 ( For theoretical work on fractional quantum Hall effect )

(3) David Thouless for theoretical explanation of Quantum Hall Effect.

This mysterious phenomenon was explained by David Thouless described theoretically, using

TOPOLOGY and was awarded Nobel prize in 2016.

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