BCS Theory of Superconductivity (Essay Sample)

BCS Theory of Superconductivity
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The discovery of superconductivity dates back in 1911. However, it is until 1957 where three physicists namely, Leon Cooper, John Bardeen and John Robert Schrieffer at last found the right explanation of the theory of superconductivity in metals. They named it according to their surname initials, BCS. The explanations they proposed are; the collective quantum state is formed by electrons and it is composed of the electron pairs of opposite momentum and spin. The remarkable state referred to as a pair condensate gave the explanation of every single acknowledged superconducting property and enabled the prediction of latest ones. It assists in the forecasting of the ‘behavior of characteristic lengths'. Since then, the BCS theory has been proven by many experiments conducted in alloys and metals (COOPER 2011).
Foundation of the BCS Theory This approach base on the assumption that domination of the interaction of the attractive Cooper pair over the repulsive Coulomb force brings rise of the superconductivity. At the start, the theory makes a vital assumption that there exists an attracting force between the electrons where it occurs as a result of Coulomb attraction between the crystal lattice and the electron in Type 1 superconductors. A slight increase of the positive charges in the lattice is a result of an electron where in turn, this boost in positive charge attracts an additional electron. The resulting two electrons are the Cooper pair in BCS theory of superconductivity. Therefore, the interaction between the crystal lattice and the Coulomb forms the Cooper pairs. The theory also explains roughly the need of low temperatures in superconductivity. If the energy required to bind together the electrons is less than the one lattice thermal vibrations trying to part them, the pair will not break apart. Therefore, to allow the formation of Cooper pairs, the lattice thermal wave should be small enough (SAXENA 2012). The three physicists based their theory primary idea on the quantum nature of electrons. Electrons in a metal are like waves where every single particle is independent and trails on its course without merging with the other electrons. In a superconductor, a big collective wave is formed when there is merging of the most of these electrons. In quantum physics, this is a ‘microscopic quantum wave-function'. During the formation of a collective wave, each member is required to move at a similar speed. The diversion of an electron by a flaw in a superconductor can happen if only and at the same time, otherthe members of a collective wave diverts in the exact identical way. The wave will neither slow down nor divert therefore it superconducts. In metals, on the other hand, diversion by a big atom or a flaw is possible to individual electron (ALEXANDROV 2013).
BCS Theory Successes A number of significant theoretical predictions, independent of the interaction information have been derived by BCS. Numerous experiments conducted have confirmed the various successes of the BCS theory. On the critical temperature Tc, dependence of the value of the energy gap Δ at temperature T is predicted by BCS theory. The ratio between the amount of superconducting transition temperature and the value of the energy gap when temperature is zero obtains the universal value without depending on the material. In a proximity to the critical temperature, the relative asymptotes to .This latter relation is of the form recommended the previous year by J. Buckingham rooted in the truth that the second order is the superconducting transition phase. Also in Fairbank, Blevins and Gordy's experimental findings on the ‘absorption of millimeter waves by superconducting tin', the superconducting phase includes a mass gap (ALTOMARE and CHANG 2013). In an approved manner, BCS theory forecasts the Meissner effect, that is, the discharge of the magnetic field from a superconductor and penetration depth variation with temperature. In 1933 article (Ein Neuer Effekt Bei Eintritt der Supraleitfähigkeit) by Robert Ochsenfeld and Walther Meissner, they demonstrated the Meissner effect as in the figure below.Meissner effect illustration
BCS theory also explains the critical magnetic field variation with the temperature. At Fermi level, the theory relates the density of states and transition temperature value to that of critical field when temperature is zero. The graph below explains the critical field (SINGH 2012).Critical field graph Another success of this theory is the reproduction of the isotope effect. It is an experimental observation that states that, ‘The mass of an isotope used in the material is inversely proportional to the critical temperature, for a given superconducting material.' Two groups in 1950 reported the isotope effect and published the results in "Isotope Effect in the Superconductivity of Mercury and Superconductivity of Isotopes of Mercury". The isotope effect proposes that there is a relation between the lattice vibrations and superconductivity (POOLE et al 2014).The superconducting transition temperature is given in terms Debye cut-off energy ED and also in terms of electron-phonon coupling potential V, in simplest form. That is, where N (...