Superconductivity

Experiments:

Lectures:

Lecture notes:

Media:

Transition into superconductivity can be seen as a phase transition, which happens to be a second-order phase transition.

andor.oxinst.com/learning/view/article/measuring-resistance-of-a-superconducting-sample-with-a-dry-cryostat Not a video, but well done, by Oxford Instruments.

TODO!!! Even this is hard to find! A clean and minimal one! Why! All we can find are shittly levitating YBCO samples in liquid nitrogen! Maybe because liquid helium is expensive?

We know that superfluidity happens more easily in bosons, and so electrons joins in Cooper pairs to form bosons, making a superfluid of Cooper pairs!

Isn't that awesome!

As of 2020, basically means "liquid nitrogen temperature", which is much cheaper than liquid helium.

The dream of course being room temperature and pressure superconductor.

LK-99:

Upside: superconducting above 92K, which is above the 77K of liquid nitrogen, and therefore much much cheaper to obtain and maintain than liquid helium.

Downside: it is brittle, so how do you make wires out of it? Still, can already be used in certain circuits, e.g. high temperature SQUID devices.

Discovered in 1988, the first high-temperature superconductor which did not contain a rare-earth element.

Superconductivity is one of the key advances of 21st century technology:

Bibliography:

As of 2023 the most important ones economicaly were:The main application is Magnetic resonance imaging. Both of these are have to be Liquid helium, i.e. they are not "high-temperature superconductor" which is a pain. One big strength they have is that they are metallic, and therefore can made into wires, which is crucial to be able to make electromagnetic coils out of them.

TODO, come on, Internet!

Bibliography.

No, see: superconductor I-V curve.

Bibliography:

Main theory to explain Type I superconductors very successfully.

TODO can someone please just give the final predictions of BCS, and how they compare to experiments, first of all? Then derive them.

High level concepts:

Discrete quantum effect observed in superconductors with a small insulating layer, a device known as a Josephson junction.

To understand the behaviour effect, it is important to look at the Josephson equations consider the following Josephson effect regimes separately:

A good summary from Wikipedia by physicist Andrew Whitaker:

at a junction of two superconductors, a current will flow even if there is no drop in voltage; that when there is a voltage drop, the current should oscillate at a frequency related to the drop in voltage; and that there is a dependence on any magnetic field

Bibliography:

Some golden notes at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:

We were all - Josephson, Pippard and myself, as well as various other people who also habitually sat at the Mond tea and participated in the discussions of the next few weeks - very much puzzled by the meaning of the fact that the current depends on the phase

As part of the course Anderson had introduced the concept of broken symmetry in superconductors. Josephson "was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally."

This is what happens when you apply a DC voltage across a Josephson junction.

It is called "AC effect" because when we apply a DC voltage, it produces an alternating current on the device.

By looking at the Josephson equations, we see that $V(t)=k$ a positive constant, then $\phi$ just increases linearly without bound.

Therefore, from the first equation: we see that the current will just vary sinusoidally between $\pm I_c$.

This meas that we can use a Josephson junction as a perfect voltage to frequency converter.

Wikipedia mentions that this frequency is $484GHz/mV$, so it is very very high, so we are not able to view individual points of the sine curve separately with our instruments.

Also it is likely not going to be very useful for many practical applications in this mode.

An I-V curve can also be seen at: Figure "Electron microscope image of a Josephson junction its I-V curve".

If you shine microwave radiation on a Josephson junction, it produces a fixed average voltage that depends only on the frequency of the microwave. TODO how is that done more preciesely? How to you produce and inject microwaves into the thing?

It acts therefore as a perfect frequency to voltage converter.

The Wiki page gives the formula: en.wikipedia.org/wiki/Josephson_effect#The_inverse_AC_Josephson_effect You get several sinusoidal harmonics, so the output is not a perfect sine. But the infinite sum of the harmonics has a fixed average voltage value.

And en.wikipedia.org/wiki/Josephson_voltage_standard#Josephson_effect mentions that the effect is independent of the junction material, physical dimension or temperature.

All of the above, compounded with the fact that we are able to generate microwaves with extremely precise frequency with an atomic clock, makes this phenomenon perfect as a Volt standard, the Josephson voltage standard.

TODO understand how/why it works better.

Two equations derived from first principles by Brian Josephson that characterize the device, somewhat like an I-V curve: where:

Note how these equations are not a typical I-V curve, as they are not an instantaneous dependency between voltage and current: the history of the voltage matters! Or in other words, the system has an internal state, represented by the Josephson phase at a given point in time.

To understand them better, it is important to look at some important cases separately:

Maximum current that can flow across a Josephson junction, as can be directly seen from the Josephson equations.

Is a fixed characteristic value of the physical construction of the junction.

A function $\mathbb{R}\to \mathbb{R}$ defined by the second of the Josephson equations plus initial conditions.

It represents an internal state of the junction.

A device that exhibits the Josephson effect.

The inverse of the magnetic flux quantum.

As mentioned in True Genius: The Life and Science of John Bardeen page 224, the idea of symmetry breaking was a major motivation in Josephson's study of the Josephson effect.

The most practical/precise volt standard.

It motivated the definition of the ampere in the 2019 redefinition of the SI base units

Quick NIST article about it: www.nist.gov/news-events/news/2013/04/primary-voltage-standard-whole-world (archive)

The wiki page en.wikipedia.org/wiki/Josephson_voltage_standard contains amazing schematics of the device, apparently made by the US Government.

Can be used as a very precise magnetometer.

There are high temperature yttrium barium copper oxide ones that work on liquid nitrogen.

Two parallel Josephson junctions.

In Ciro's ASCII art circuit diagram notation: