AI-assisted research in superconductors

What is a cooper pair?

In condensed matter physics, a Cooper pair is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper[1]. The electrons in a Cooper pair have opposite spins and are loosely bound at absolute temperatures due to electron-lattice interactions[3]. Although Cooper pairing is a quantum effect, the reason for the pairing can be seen from a simplified classical explanation. An electron in a metal normally behaves as a free particle. The electron is repelled from other electrons due to their negative charge, but it also attracts the positive ions that make up the rigid lattice of the metal. This attraction can cause a passing electron to attract the lattice, causing a slight ripple toward its path. Another electron passing by will be attracted to this ripple, and the two electrons can then form a Cooper pair[2].

The paired electrons are not actually in close proximity to each other, but are instead paired over several hundred nanometers. This allows multiple Cooper pairs to occupy the same space, overlap, and form a collective condensate. The binding energy of Cooper pairs is quite low, of a magnitude 10^-3 eV[3]. The total spin of a Cooper pair is integer (0 or 1), even though electrons have a spin of 1/2, making them fermions[1]. The distance between the electrons in a pair is referred to as the coherence length, which is large compared with the mean separation between electrons in a metal[4].

Citations: [1] https://en.wikipedia.org/wiki/Cooper_pair [2] http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/coop.html [3] https://www.scienceabc.com/pure-sciences/what-are-cooper-pairs-how-are-they-responsible-for-superconductivity.html [4] https://www.doitpoms.ac.uk/tlplib/superconductivity/cooper.php [5] https://www.merriam-webster.com/dictionary/Cooper pair [6] https://physicsworld.com/a/superconductor-reveals-new-state-of-matter-involving-pairs-of-cooper-pairs/

What is the propagation time of signal across a superconductor?

I could not find a specific answer to the question "What is the propagation time of signal across a superconductor" in the search results. However, I found some information related to the propagation of signals in superconductors:

The velocity of propagation in superconductors is set by the dielectric (insulator) materials that the majority of the electric field is in, as well as the [insulator's] geometry[2].
A study reports a method to simulate the propagation of picosecond pulses in superconducting passive transmission lines (PTLs) [3][4].
Another study calculates the longitudinal propagation inside the aluminum-stabilized superconductor of the ATLAS model coil using the time information between two pickup coil signals[5].
A study provides evidence for the propagation of superconducting coherence via chiral quantum-Hall edge channels[6].

In summary, the propagation time of signals across a superconductor is not directly addressed in the search results. However, the velocity of propagation in superconductors is influenced by the dielectric materials and geometry, and there are studies that simulate the propagation of signals in superconducting transmission lines and provide evidence for the propagation of superconducting coherence.

Citations: [1] https://physics.stackexchange.com/questions/69667/what-is-the-rc-time-constant-in-a-superconductor [2] https://www.reddit.com/r/askscience/comments/mlq3t0/how_fast_are_electrons_moving_in_superconductors/ [3] https://iopscience.iop.org/article/10.1088/1361-6668/ac5783/ampdf [4] https://iopscience.iop.org/article/10.1088/1361-6668/ac5783/meta [5] https://cds.cern.ch/record/725946/files/cer-002439517.pdf [6] https://www.nature.com/articles/s41598-017-11209-w

explain superconducting coherence

Superconducting coherence refers to the phenomenon where the electrons in a superconductor behave collectively as a single entity, known as the superconducting condensate. This coherence arises due to the formation of Cooper pairs, which are pairs of electrons that are bound together by lattice vibrations. The superconducting coherence length is a measure of the size of a Cooper pair, which is of the order of cm[6]. The coherence length depends on temperature and is related to the phase rigidity of the superconducting condensate[1]. It is one of two parameters in the Ginzburg-Landau theory of superconductivity[6]. The propagation of superconducting coherence has been observed via chiral quantum-Hall edge channels[3].

Citations: [1] https://physics.stackexchange.com/questions/375143/what-is-superconducting-coherence-length [2] http://web.mit.edu/6.763/www/FT03/PSfiles/CH-117_(KAD-TPO_revised)_corrected_1.pdf [3] https://www.nature.com/articles/s41598-017-11209-w [4] http://cmms.triumf.ca/theses/Sonier/PhD/node10.html [5] http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/chrlen.html [6] https://en.wikipedia.org/wiki/Superconducting_coherence_length

how does the coherence length affect the behavior of a superconductor