Superconductivity and the BCS Theory


by XtremePhysX
Tags: superconductivity, theory
XtremePhysX
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#1
Aug12-12, 12:31 PM
P: 92
Can some one explain to me how superconductivity works exactly? I will type all I know about it so can you guys correct any misconceptions I may have?

Superconductivity is the phenomenon in which a conductor, when cooled sufficiently (past a critical temperature Tc) exhibits negligible resistance. This phenomenon can be explained by the BCS theory, which works well in some scenarios (traditional metallic) but fails miserably at others (ceramics). The BCS theory is based upon the formation of Cooper pairs of electrons. The BCS theory states that when a negatively charged electron travels past positively charged ions in the lattice, the lattice distorts inwards towards the electron. This causes a relative concentration of positive charge following behind the moving electron. This deformation of the lattice causes another electron, with opposite "spin", to move into the region of higher positive charge density.


The parts in Bold, which one is correct?


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. This electron pairing is favoured as it puts the electrons into a lower energy state. As long as T<Tc, the electrons remain paired due to reduced molecular motion.


Electrons are fermions with spin +0.5 and -0.5 so when they combine they form a Boson which is 0, +1 or -1 spin. Below Tc, the Boson becomes a Bose Einstein Condensate which is a new state of matter that doesn't interact with ordinary matter so it passes through the metal lattice unimpeded.


BCS Theory was highly successful in explaining the microscopic and macroscopic properties of some superconductors. It predicted certain properties which were verified later, such as the Meissner effect and heat capacity. For this, Bardeen, Schrieffer and Cooper were awarded the Nobel Prize. However, BCS Theory cannot explain high-temperature ceramic conductivity.
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atyy
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Aug12-12, 08:40 PM
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Quote Quote by XtremePhysX View Post
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. This electron pairing is favoured as it puts the electrons into a lower energy state. As long as T<Tc, the electrons remain paired due to reduced molecular motion.
The superconducting state in which the electrons form Cooper pairs is the ground state of the system. There is an energy "gap" to the excited state, which is not superconducting. The gap depends on temperature, and Tc is the temperature at which the gap becomes zero.

Quote Quote by XtremePhysX View Post
Electrons are fermions with spin +0.5 and -0.5 so when they combine they form a Boson which is 0, +1 or -1 spin. Below Tc, the Boson becomes a Bose Einstein Condensate which is a new state of matter that doesn't interact with ordinary matter so it passes through the metal lattice unimpeded.
In BCS theory, Cooper pairs are weakly bound and far apart. In Bose-Einstein condensation, the paired fermions are tighly bound and close together. Some systems can be made to change smoothly from BCS to BEC, eg. http://jila.colorado.edu/~jin/research/crossover.html .
XtremePhysX
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Aug13-12, 12:37 AM
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I get it now, thank you a lot Mr. atyy.

DrDu
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Aug13-12, 02:05 AM
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Superconductivity and the BCS Theory


Quote Quote by XtremePhysX View Post
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. This electron pairing is favoured as it puts the electrons into a lower energy state. As long as T<Tc, the electrons remain paired due to reduced molecular motion.

It predicted certain properties which were verified later, such as the Meissner effect and heat capacity. For this, Bardeen, Schrieffer and Cooper were awarded the Nobel Prize. However, BCS Theory cannot explain high-temperature ceramic conductivity.
The kicks break up Cooper pairs. However, electronic excitations can only relax by re-combining into a Cooper pair. In a normal metal, the excited states can relax into a state carrying less momentum thus reducing the current.

The Meissner effect and heat capacity where observed long before BCS. However, these observations where neatly fit by the BCS theory. However BCS did not give an explanation for the infinite conductance of superconductors.


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