Incoming links: Phase transition
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
Condensed matter physics is one of the best examples of emergence. We start with a bunch of small elements which we understand fully at the required level (atoms, electrons, quantum mechanics) but then there are complex properties that show up when we put a bunch of them together.
Includes fun things like:
As of 2020, this is the other "fundamental branch of physics" besides to particle physics/nuclear physics.
Condensed matter is basically chemistry but without reactions: you study a fixed state of matter, not a reaction in which compositions change with time.
Just like in chemistry, you end up getting some very well defined substance properties due to the incredibly large number of atoms.
Just like chemistry, the ultimate goal is to do de-novo computational chemistry to predict those properties.
And just like chemistry, what we can actually is actually very limited in part due to the exponential nature of quantum mechanics.
Also since chemistry involves reactions, chemistry puts a huge focus on liquids and solutions, which is the simplest state of matter to do reactions in.
Condensed matter however can put a lot more emphasis on solids than chemistry, notably because solids are what we generally want in end products, no one likes stuff leaking right?
But it also studies liquids, e.g. notably superfluidity.
One thing condensed matter is particularly obsessed with is the fascinating phenomena of phase transition.
What Is Condensed matter physics? by Erica Calman
. Source. Cute. Overview of the main fields of physics research. Quick mention of his field, quantum wells, but not enough details.A charismatic, perfect-English-accent (Received Pronunciation) physicist from University of Cambridge, specializing in quantum field theory.
He has done several "vulgarization" lectures, some of which could be better called undergrad appetizers rather, a notable example being Video "Quantum Fields: The Real Building Blocks of the Universe by David Tong (2017)" for the prestigious Royal Institution, but remains a hardcore researcher: scholar.google.com/citations?hl=en&user=felFiY4AAAAJ&view_op=list_works&sortby=pubdate. Lots of open access publications BTW, so kudos.
The amount of lecture notes on his website looks really impressive: www.damtp.cam.ac.uk/user/tong/teaching.html, he looks like a good educator.
David has also shown some interest in applications of high energy mathematical ideas to condensed matter, e.g. links between the renormalization group and phase transition phenomena. TODO there was a YouTube video about that, find it and link here.
Ciro Santilli wonders if his family is of East Asian, origin and if he can still speak any east asian languages. "Tong" is of course a transcription of several major Chinese surnames and from looks he could be mixed blood, but as mentioned at www.ancestry.co.uk/name-origin?surname=tong it can also be an English "metonymic occupational name for a maker or user of tongs". After staring at his picture for a while Ciro is going with the maker of tongs theory initially.
Toy model of matter that exhibits phase transition in dimension 2 and greater. It does not provide numerically exact results by itself, but can serve as a tool to theorize existing and new phase transitions.
Each point in the lattice has two possible states: TODO insert image.
As mentioned at: stanford.edu/~jeffjar/statmech/intro4.html some systems which can be seen as modelled by it include:
- the spins direction (up or down) of atoms in a magnet, which can undergo phase transitions depending on temperature as that characterized by the Curie temperature and an externally applied magnetic fieldNeighboring spins like to align, which lowers the total system energy.
- the type of atom at a lattice point in a 2-metal alloy, e.g. Fe-C (e.g. steel). TODO: intuition for the neighbour interaction? What likes to be with what? And aren't different phases in different crystal structures?
Also has some funky relations to renormalization TODO.
Bibliography:
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.
Superconductivity and Quantum Mechanics at the Macro-Scale - 1 of 2 by Steven Kivelson (2016)
Source. For the Stanford Institute for Theoretical Physics. Gives a reasonable basis overview, but does not go into the meat of BCS it at the end.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:
Media:
- 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.
Transition into superconductivity can be seen as a phase transition, which happens to be a second-order phase transition.
As mentioned on the introduction, the main objective of the course is to try predict qualitative properties of materials, notably the existence of certain phase transitions, starting from first principle toy models.
Key phenomena covered include: