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BCS Theory
BCS theory, or the Bardeen-Cooper-Schrieffer theory, is a foundational theory in the field of condensed matter physics describing the behavior of a system of electrons that are generally bound together in a lattice structure. Developed in 1957 by American physicists John Bardeen, Leon Cooper and John Schrieffer, BCS theory focused on how electrons interact with each other in a lattice structure in response to a temperature drop. The interactions, when temperature drops, create electron pairs known as Cooper Pairing. Through this pairing, the angular momentum of the electrons pairs becomes bound together and forms a superconductive state.
The BCS theory makes several fundamental assumptions about how electrons interact with each other. The theory assumes that the force of attraction between electrons is given by the average of the Coulomb force, rather than the instantaneous force given by the point charges of the lattice structure. Additionally, the theory assumes that electrons form Cooper pairs in a nuclear lattice when the temperature of the object is lower. This simple picture of BCS theory is true for all type of electron pairings and provides the starting point for developing more accurate descriptions of the behavior of electrons in response to different temperatures and other physical conditions.
The most important feature of the BCS theory is its prediction of a so-called “superconductive state” in certain materials at sufficiently low temperatures. Superconductors are materials whose electrical resistance (the measure of how much electrical energy is lost through conducting it through a material) is essentially zero. This property of superconductors has made them useful in a variety of fields, ranging from consumer electronics to medical applications. The behavior of a superconductor was first observed by Dutch physicist Heike Kamerlingh Onnes in 1911, who was awarded the Nobel Prize for his discovery.
The most famous model that arises from the BCS theory is the BCS Hamiltonian, which is essentially the model equation describing the behavior of electrons in a lattice structure in response to a temperature drop. This Hamiltonian was first derived in a paper published in 1957 and then proposed as an explanation for the observed behavior of superconductors by Bardeen, Cooper and Schrieffer. The mathematical predictions of BCS theory were later confirmed experimentally in a classic paper published in 1962 by American physicist John Bardeen and collaborators.
BCS theory is now considered the foundation for the understanding of electron-electron interactions in materials. The theoretical framework of BCS theory has been used to explore a variety of physical phenomena from superconductivity, lattice reconstructions, heat transport, magnetism, nuclear physics and more. In addition, the idea of Cooper Pairing is now central to understanding superconductivity and related phenomena in condensed matter physics. BCS theory has become a cornerstone in the field and continues to be a major area of research that has enhanced our understanding of quantum mechanics and its applications.
