PesWiki.com

Menu

PowerPedia:BCS theory

Lasted edited by Andrew Munsey, updated on June 14, 2016 at 10:10 pm.

  • 23 errors has been found on this page. Administrator will correct this soon.
  • This page has been imported from the old peswiki website. This message will be removed once updated.

BCS theory (named for its creators, There was an error working with the wiki: Code[1], There was an error working with the wiki: Code[2], and There was an error working with the wiki: Code[3]) explains There was an error working with the wiki: Code[4], the ability of certain There was an error working with the wiki: Code[5] effect. It proposes that There was an error working with the wiki: Code[6] can become paired, forming There was an error working with the wiki: Code[11]s. Independently and at the same time, superconductivity phenomenon was explained by There was an error working with the wiki: Code[12] by means of the so-called There was an error working with the wiki: Code[13]s.

History

BCS theory was developed in 1957 by There was an error working with the wiki: Code[7], and There was an error working with the wiki: Code[8], who received the There was an error working with the wiki: Code[14] for Physics in 1972 as a result. In 1986, "There was an error working with the wiki: Code[15]" was discovered (i.e. superconductivity at temperatures considerably above the previous limit of about 30 K up to about 130 K). Today it is believed that at these temperatures other effects are at play these effects are not yet fully understood. (It is possible that these unknown effects also control superconductivity even at low temperatures for some

materials).

General description

In many superconductors, the attractive interaction between electrons (necessary for pairing) is brought about indirectly by the interaction between the electrons and the vibrating crystal lattice (the There was an error working with the wiki: Code[16]s). Roughly speaking the picture is the following:

: An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite "spin", to move into the region of higher positive charge density. The two electrons are then held together with a certain binding energy. If this binding energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electron pair will stick together and resist all kicks, thus not experiencing resistance.

Full description

{| style="width: 222px clear: right border: solid #aaa 1px margin: 1em 1em 1em 1em font-size: 85% line-height:1.5 background: #f9f9f9 padding: 4px spacing: 0px text-align: left float: right"

|

There was an error working with the wiki: Code[1]

There was an error working with the wiki: Code[2]

There was an error working with the wiki: Code[3]

There was an error working with the wiki: Code[4]

There was an error working with the wiki: Code[5]

BCS theory

There was an error working with the wiki: Code[6]

There was an error working with the wiki: Code[7]

|}

BCS theory starts from the assumption that there is some attraction between electrons, which can overcome the There was an error working with the wiki: Code[17]. In most materials (in low temperature superconductors), this attraction is brought about indirectly by the coupling of electrons to the There was an error working with the wiki: Code[18] (as explained above). However, the results of BCS theory do not depend on the origin of the attractive interaction. The original results of BCS (discussed below) described an "s-wave" superconducting state, which is the rule among low-temperature superconductors but is not realized in many "unconventional superconductors", such as the "d-wave" high-temperature superconductors.

Extensions of BCS theory exist to describe these other cases, although they are insufficient to completely describe the observed features of high-temperature superconductivity.

BCS were able to give an approximation for the quantum-mechanical state of the

system of (attractively interacting) electrons inside the metal. This state is

now known as the "BCS state". Whereas in the normal metal electrons move independently, in the BCS state they are bound into "Cooper pairs" by the attractive interaction.

BCS have derived several important theoretical predictions that are independent

of the details of the interaction (the quantitative predictions mentioned below hold only for sufficiently weak attraction between the electrons, which is however fulfilled for many low temperature superconductors

- the so-called "weak-coupling case"). These have been confirmed in numerous experiments:

Since the electrons are bound into Cooper pairs, a finite amount of energy is needed to break these apart into two independent electrons. This means there is an "energy gap" for "single-particle excitation", unlike in the normal metal (where the state of an electron can be changed by adding an arbitrarily small amount of energy). This energy gap is highest at low temperatures but vanishes at the transition temperature when superconductivity ceases to exist. BCS theory correctly predicts the variation of this gap with temperature. It also gives an expression that shows how the gap grows with the strength of the attractive interaction and the (normal phase) single particle There was an error working with the wiki: Code[19] at the There was an error working with the wiki: Code[20]. Furthermore, it describes how the density of states is changed on entering the superconducting state, where there are no electronic states any more at the Fermi energy. The energy gap is most directly observed in tunneling experiments and in reflection of microwaves from the superconductor.

The ratio between the value of the energy gap at zero temperature and the value of the superconducting transition temperature (expressed in energy units) takes the universal value of 3.5, independent of material.

Due to the energy gap, the specific heat of the superconductor is suppressed strongly (There was an error working with the wiki: Code[9]) at low temperatures, there being no thermal excitations left. However, before reaching the transition temperature, the specific heat of the superconductor becomes even higher than that of the normal conductor (measured immediately above the transition) and the ratio of these two values is found to be universally given by 2.5.

BCS theory correctly predicts the There was an error working with the wiki: Code[21], i.e. the expulsion of a Magnetic field from the superconductor and the variation of the penetration depth (the extent of the screening currents flowing below the metal's surface) with temperature.

It also describes the variation of the critical magnetic field (above which the superconductor can no longer expel the field but becomes normalconducting) with temperature. BCS theory relates the value of the critical field at zero temperature to the value of the transition temperature and the density of states at the Fermi energy.

Related

References and external articles

J. Bardeen, L. N. Cooper, and J. R. Schrieffer, "Theory of Superconductivity", Phys. Rev. 108 (5), 1175 (1957).

ScienceDaily: Physicist Discovers Exotic Superconductivity (There was an error working with the wiki: Code[22]) August 17, 2006

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.

An excellent introduction to BCS theory and related areas of There was an error working with the wiki: Code[10] book, Theory of Superconductivity, ISBN 0-7382-0120-0.

See also

There was an error working with the wiki: Code[23]

Comments