If you adda bit of impurities to certain materials, at low temperatures of a few Kelvin their resistivity actually starts increasing if you go below a certain critical temperature.
Most notable example: gallium arsenide, see also: gallium arsenide vs silicon.
An important class of semiconductors, e.g. there is a dedicated III-V lab at: École Polytechnique: www.3-5lab.fr/contactus.php
Experiments:
- "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.
20. Fermi gases, BEC-BCS crossover by Wolfgang Ketterle (2014)
Source. Part of the "Atomic and Optical Physics" series, uploaded by MIT OpenCourseWare.Actually goes into the equations.
Notably, youtu.be/O_zjGYvP4Ps?t=3278 describes extremely briefly an experimental setup that more directly observes pair condensation.
The Map of Superconductivity by Domain of Science
. Source. Lacking as usual, but this one is particularly good as the author used to work on the area as he mentions in the video.Lecture notes:
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?
First 10T Tape Coil by Mark Benz
. Source. Dr. Mark Benz describes the first commercially sold superconducting magnet made by him and colleagues in 1965. The 10 Tesla magnet was made at GE Schenectady and they sold magnets to research facilities world wide before the team formed Intermagnetics General. IGC and Carl Rosner went on to pioneer MRI technology.
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.
- Nb-Ti: the most widely used one. Used e.g. to create the magnetic fields of the Large Hadron Collider Up to 15 T.
- Nb-Sn: more expensive than Nb-Ti, but can reach up to 30 T.
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
In 1962 Brian Josephson published his inaugural paper predicting the effect as Section "Possible new effects in superconductive tunnelling".
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".
Some golden notes can be found at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:
Probable observation of the Josephson superconducting tunneling effect by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Paper by Philip W. Anderson and John M. Rowell that first (?) experimentally observed the Josephson effect.
Paywalled by the American Physical Society as of 2023 at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.10.230
They used tin-oxide-lead tunnel at 1.5 K. TODO oxide of what? Why two different metals? They say that both films are 200 nm thick, so maybe it is:
-----+------+------+-----
... Sn | SnO2 | PbO2 | Pb ...
-----+------+------------
100nm 100nmA reconstruction of their circuit in Ciro's ASCII art circuit diagram notation TODO:
DC---R_10---X---GThere are not details of the physical construction of course. Reproducibility lol.
Two equations derived from first principles by Brian Josephson that characterize the device, somewhat like an I-V curve:where:
- : Josephson current
- : the Josephson phase, a function defined by the second equation plus initial conditions
- : input voltage of the system
- : current across the junction, determined by the input voltage
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:
- AC Josephson effect: V is a fixed DC voltage
Experimental Evidence for Quantized Flux in Superconducting Cylinders by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Paywalled at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.7.43
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:So there was some previous confusion about the flux quantum due to the presence of Cooper pairs or not.
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.
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.
Figure 1 of Experimental Evidence for Quantized Flux in Superconducting Cylinders
. The legend reads:(Upper) Trapped flux in cylinder No. 1 as a function of magnetic field in which the cylinder was cooled below the superconducting transition. temperature. The open circles are individual data points. The solid circles represent th, e average value of all data points at a particular value of applied field including all the points plotted and additional data which could not be plotted due to severe overlapping of points. Approximately two hundred data points are represented. The lines are drawn at multiples of hc/2e.(Lower) Net flux in cylinder No. 1 before turning off the applied field in which it was cooled as a function of the applied field. Open and solid circles have the same significance as above. The lower line is the diamagnetic calibration to which all runs have been normalized. The other lines are translated vertically by successive steps of hc/2e.
Figure 2 of Experimental Evidence for Quantized Flux in Superconducting Cylinders
. The legend reads:(Upper) Trapped flux in cylinder No. 2 as a function of magnetic field in which the cylinder was cooled below the superconducting transition temperature. The circles and triangles indicate points for oppositely directed applied fields. Lines are drawn at multiples of hc/2e.(Lower) Net flux in cylinder No. 2 before turning off the applied field as a function of the applied field. The circles and triangles are points for oppositely directed applied fields. The lower line is the diamagnetic calibration to which all runs have The other been normalized. lines are translated vertically by successive steps of hc/2e.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
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