One of the key ideas that pointed out that phonons are the pairing mechanism for BCS superconductors is the isotope effect -why the critical temperature was lower for heavier metal isotopes (elements with the same number of protons but different number of neutrons).
I have read somewhere before a simple explanation on how BCS theory accounts for this. A simple mental picture of the BCS theory is as follows. When electron moves through the lattice made up of positively charge metal ions, it distorts the ion lattice, since it attracts the ions creating a relatively positive region. This region then attracts another electron with the opposite spin and both electrons form what is known as a Cooper pair! Since heavier ions are harder to move, they are less attracted by the electrons. This results smaller binding energy between the Cooper pairs which means lower critical temperature for heavier isotopes.
This is pretty cool, it's always good to have some kind of physical intuition about a problem, before looking deeper. That said, one must keep in mind that oversimplifying a problem can lead to misunderstandings.
ReplyDeleteOne question: what do you mean by "Since heavier ions are harder to move, they are less attracted by the electrons." I don't follow...
Yeah, that's a nice little picture...sort of like springs all pulling on each other
ReplyDeleteHeavier ions being harder to move, I think should be interpreted as ions with more protons (but also more electrons). We have a bigger (positive) charge with heavier ions...
However, there would still only be that same 1 or 2 valence electrons missing in the ion...
I suppose the confusion is that our forces are the Coulomb force (on charges) which wouldn't really be affected by the masses, would it?
By heavier ions I mean ions with the same number of protons but more neutrons(thus heavier) so the Coulomb force would be the same but would be harder to move due to larger mass. I looked around and found a link that might help in imagining the stuff.
ReplyDeletehttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/coop.html
Thanks Joseph.
DeleteIt's interesting to see how all this fits together. (To paraphrase David in more casual terms:)
We have one electron doing it's own little thing. This electron throws it's weight onto the phonons. The phonons disturb each other, eventually reaching another electron.
Then the two electrons sort are synched up with each other without ever really meeting each other.
Surprised phonons gets involved in this.
Ahhhh, I understand now. Also, hyperphysics is great.
ReplyDeleteThe cooper pairs are coupled with phonons, which is why they form this collective state within the crystal. The properties of the phonons are effected by the mass of the ions (among other things), so therefore, the mass of the ions affects the formation of cooper pairs, and thus superconductivity. Wicked!
This might seem like an obvious question, but why does the ion attract an electron of opposite spin? If the classical picture is of a distortion of the ion lattice, surely this coulomb potential shouldn't differentiate between an electron's spin? Especially seeing as the cooper pairing can be at large distances in real space.
ReplyDeleteActually, just doing a bit of reading it seems that the cooper pair's spin can be either 0 or 1, corresponding to either opposite spins, or two positive half spins. But not two negative half spins? Is there any reason behind that?