The BCS state does indeed require weak attraction, and the main interaction between electrons is the repulsive Coulomb interaction. There are three basic ingredients that conspire to make the effective interaction attractive:.
At long distances, the Coulomb repulsion is much weaker than in free space. The interaction is attractive for the same reason that all other scalar boson mediated forces are attractive. The coupling constant is small, and depends on details of the system such as the Fermi momentum and the speed of sound. As a result, a suitable pair wave function can avoid the Coulomb repulsion and be sensitive to the phonon attraction. This is sometimes described as the electron being attracted to the "wake" the lingering lattice distortion of the other electron.
IMHO it's like Thomas said. As for the electron being attracted to the "wake" of the other electron, IMHO you can get the gist of that via a fluid analogy called the Falaco soliton:. The Falaco soliton is a U-tube vorton which is remarkably stable.
You make one by dipping a plate into a pool and stroking it forward whilst lifting it clear. It's something like half a Dirac spinor without the bispinor rotation. A better analogy would be a smoke ring which also had a major axis "steering-wheel" rotation on top of the minor-axis rolling rotation. By the by, Thomson and Tait experimented with smoke rings, see this article.
They also coined the phrase spherical harmonics. Anyway, you can emulate attraction repulsion and annihilation with Falaco solitons by aiming them at one another at various angles. To emulate Coopers pairs you use two plates to create one Falaco soliton closely followed by another. The second soliton swoops through the inside of the first one and overtakes it. The first one then swoops through the inside of the second, and there's a "dosy doe" combined motion.
It doesn't last long, but whilst it does it's reminiscent of dance partners effortlessly swinging each other around. Sign up to join this community. In , Bardeen, Cooper and Schrieffer BCS proposed a theory that explained the microscopic origins of superconductivity, and could quantitatively predict the properties of superconductors. Prior to this, there was Ginzburg-Landau theory, suggested in , which was a macroscopic theory. Mathematically, BCS theory is complex, but relies on an earlier 'discovery' by Cooper , who showed that the ground state of a material is unstable with respect to pairs of 'bound' electrons.
These pairs are known as Cooper pairs and are formed by electron-phonon interactions - an electron in the cation lattice will distort the lattice around it, creating an area of greater positive charge density around itself.
Another electron at some distance in the lattice is then attracted to this charge distortion phonon - the electron-phonon interaction. The electrons are thus indirectly attracted to each other and form a Cooper pair - an attraction between two electrons mediated by the lattice which creates a 'bound' state of the two electrons:. This is demonstrated by the next animation. Up to now we have considered pairs to be correlated over a fairly short distance. In fact the mean separation at which pair correlation becomes effective is between and nm.
This coherence length is large compared with the mean separation between conduction electrons in a metal. Thus Cooper pairs overlap greatly. In between one pair there may be up to 10 7 other electrons which are themselves bound as pairs. Previous Next Cooper pairs In order for electrons to be able to move in some coherent manner and exhibit superconducting properties, there must be some type of interaction between them.
Video of the movement of particles into a depression This analogy can be taken further if we consider the balls to be moving. Video of the movement of particles into and out of a depression Up to now we have considered pairs to be correlated over a fairly short distance.
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