Ciro Santilli distinctly remembers being taught that at basic electrical engineering school during Ciro Santilli's undergrad studies at the University of São Paulo.
It really allows you to do alternating current calculations much as you'd do DC calculations with resistors, quite poweful. It must have been all the rage in the 1950s.
The basis of 1970-20XX computers, gotta understand them I guess?
- "An introduction to superconductivity" by Alfred Leitner originally published in 1965, source: www.alfredleitner.com/
- Isotope effect on the critical temperature. hyperphysics.phy-astr.gsu.edu/hbase/Solids/coop.html mentions that:
If electrical conduction in mercury were purely electronic, there should be no dependence upon the nuclear masses. This dependence of the critical temperature for superconductivity upon isotopic mass was the first direct evidence for interaction between the electrons and the lattice. This supported the BCS Theory of lattice coupling of electron pairs.
- Actually goes into the equations.Notably, youtu.be/O_zjGYvP4Ps?t=3278 describes extremely briefly an experimental setup that more directly observes pair condensation.
- Cool CNRS video showing the condensed wave function, and mentioning that "every pair moves at the same speed". To change the speed of one pair, you need to change the speed of all others. That's why there's not energy loss.
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.
Isn't that awesome!
The dream of course being room temperature and pressure superconductor.
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.
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!
No, see: superconductor I-V curve.
- physics.stackexchange.com/questions/62664/how-can-ohms-law-be-correct-if-superconductors-have-0-resistivity on Physics Stack Exchange
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:
- the wave functions of pairs of electrons (fermions) get together to form bosons. This is a phase transition effect, thus the specific sudden transition temperature.
- the pairs form a Bose-Einstein condensate
- once this new state is reached, all pairs are somehow entangled into one big wave function, and you so individual lattice imperfections can't move just one single electron off trajectory and make it lose energy
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
In 1962 Brian Josephson published his inaugural paper predicting the effect as Section "Possible new effects in superconductive tunnelling (1963, Prediction of the Josephson effect)".
In 1963 Philip W. Anderson and John M. Rowell published their paper that first observed the effect as Section "Possible new effects in superconductive tunnelling (1963, Prediction of the Josephson effect)".
Some golden notes can be found at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:
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."
The inaugural that predicted the Josephson effect.
Published on Physics Letters, then a new journal, before they split into Physics Letters A and Physics Letters B. True Genius: The Life and Science of John Bardeen mentions that this choice was made rather than the more prestigious Physical Review Letters because they were not yet so confident about the results.
Paywalled by Elsevier as of 2023 at: www.sciencedirect.com/science/article/abs/pii/0031916362913690
Paywalled by the American Physical Society as of 2023 at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.10.230
TODO understand the graphs in detail.
A reconstruction of their circuit in Ciro's ASCII art circuit diagram notation TODO:
There are not details of the physical construction of course. Reproducibility lol.
By looking at the Josephson equations, we see that a positive constant, then just increases linearly without bound.
Therefore, from the first equation: .
This meas that we can use a Josephson junction as a perfect voltage to frequency converter.
Wikipedia mentions that this frequency is , 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.
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:
Is a fixed characteristic value of the physical construction of the junction.
A function 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.
TODO is there any relationship between this and the Josephson effect?
Experimental observation published as Experimental Evidence for Quantized Flux in Superconducting Cylinders.
This appears to happen to any superconducting loop, because the superconducting wave function has to be continuous.
Paywalled at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.7.43
The first published experimental observation of the magnetic flux quantum.
The paper that follows it in the journal is also of interest, "Theoretical Considerations Concerning Quantized Magnetic Flux In Superconducting Cylinders" by N. Byers and C. N. Yang, it starts:
In a recent experiment, the magnetic flux through a superconducting ring has been found to be quantized in units of ch/2e. Quantization in twice this unit has been briefly discussed by London' and by Onsager. ' Onsager' has also considered the possibility of quantization in units ch/2e due to pairs of electrons forming quasi-bosons.So there was some previous confusion about the flux quantum due to the presence of Cooper pairs or not.
Dumping the fitures at: archive.org/details/experimental-evidence-for-quantized-flux-in-superconducting-cylinders One day we can also dump the paper scans when it goes into the public domain in 2056! Public domain scientific paper by year.
The inverse of the magnetic flux quantum.
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)
Can be used as a very precise magnetometer.
Two parallel Josephson junctions.
In Ciro's ASCII art circuit diagram notation:
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