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The key to the BCS theory is the pairing of electrons. ing to the BCS theory, electrons in a superconductor pair up to form what are known as Cooper pairs.
The BCS theory reproduces the isotope effect, which is the experimental observation that for a given superconducting material, the critical temperature is inversely proportional to the square-root of the mass of the isotope used in the material.
The BCS theory relies on the assumption that supercon- ductivity arises when the attractive Cooper pair interac- tion dominates over the repulsive Coulomb force (2). A Cooper pair is a weak electron-electron bound pair medi- 1 Page 2 ated by a phonon interaction.
Superconductivity was discovered on April 8, 1911, by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently produced liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared.
The superconductor categories covered include type-I, type-II, bulk, hard, soft, oxide, fermions, organic, iron, Lanthanide-based superconductors, high temperature superconductors and superconducting metamaterials.

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BCS theory states that electrons in a superconductor form tightly bound pairs (known as Cooper pairs) which travel together through the material. If an electron interacts with an atom in the material, this interaction is seen by the second electron of the Cooper pair through the coupling between them.
18.3 Microscopic BCS theory. The mean-field assumption made by BCS is that due to the presence of many different. numbers of Cooper pairs in the groundstate VBCS) the pair operator ckck has a. finite groundstate expectation value (cc) 0, and its fluctuations around this. average value are small.
Cooper Pairs - BCS Theory Supercurrent Carriers Mathematically, because the Cooper pair is more stable than a single electron within the lattice, it experiences less resistance (although the superconducting state cannot be made up entirely of Cooper pairs as this would lead to the collapse of the state).