View source for Bardeen–Cooper–Schrieffer Theory

== Introduction ==
The Bardeen–Cooper–Schrieffer (BCS) theory is a fundamental theory in the field of [[Condensed Matter Physics|condensed matter physics]] that explains the phenomenon of [[Superconductivity|superconductivity]]. Proposed by John Bardeen, Leon Cooper, and John Robert Schrieffer in 1957, the BCS theory is the first microscopic theory of superconductivity and provides a comprehensive understanding of the behavior of superconducting materials.

[[Image:Detail-37405.jpg|thumb|center|A superconducting material in a laboratory setting.|class=only_on_mobile]]
[[Image:Detail-37406.jpg|thumb|center|A superconducting material in a laboratory setting.|class=only_on_desktop]]

== Theoretical Background ==
The BCS theory is built upon the earlier works of several physicists, including the [[London Equations|London brothers]], [[Maxwell's Equations|Maxwell]], and [[Quantum Mechanics|quantum mechanics]]. The theory is a quantum mechanical description of superconductivity, and as such, it uses the principles of quantum mechanics and statistical mechanics.

== BCS Pairing Mechanism ==
The central concept of the BCS theory is the pairing of electrons, known as [[Cooper Pair|Cooper pairs]]. According to the theory, in a superconductor, electrons form pairs that move through the lattice of positive ions in the material without scattering off impurities and defects, which is why superconductors have zero electrical resistance.

== Energy Gap and Critical Temperature ==
The BCS theory also explains the existence of an energy gap in the density of states of a superconductor, and how this gap depends on the temperature. The theory predicts that the energy gap closes at a critical temperature, above which the superconductor transitions to a normal state.

== Experimental Verification ==
The predictions of the BCS theory have been confirmed by numerous experiments. The most direct verification of the BCS theory is the measurement of the energy gap and its temperature dependence, which agree with the theoretical predictions.

== Limitations and Extensions of BCS Theory ==
While the BCS theory successfully explains many aspects of superconductivity, it has its limitations. For instance, it cannot explain high-temperature superconductivity. However, extensions of the BCS theory, such as the [[BCS-BEC Crossover|BCS-BEC crossover]], have been proposed to address these limitations.

== Impact on Science and Technology ==
The BCS theory has had a profound impact on the fields of condensed matter physics and materials science. It has also found applications in various technologies, including [[Magnetic Resonance Imaging|MRI]] and [[Quantum Computing|quantum computing]].

== See Also ==
* [[Quantum Field Theory]]
* [[Fermi Surface]]
* [[Second Quantization]]

[[Category:Physics]]
[[Category:Superconductivity]]
[[Category:Theoretical Physics]]

== References ==