nbo10 said:
To Entropy's question, hopefully ZZ can chime in here. This is something me and my advisor have debated. The cooper pairs lifetime is infinite, you can break a pair and form quasiparticles by exciting the system. But the reason they form is that the bound state have a lower energy than the normal state.
JMD
I could have "chimed in" a lot sooner than this, but each time I formulated something to say, I started thinking of all the exceptions to the "rule" and gave up. So I will state the caveat to what I will say below by stating that this is the "naive" version as applied to conventional superconductors (but with some examples taken from high-Tc superconductors).
While it is somewhat true that below Tc, the Cooper pairs have an "infinite" lifetime, we need to be careful on what we mean here. It is true that if you fix the temperature to a value below Tc, the SUPERFLUID DENSITY remains constant at an equilibrium value. It means that the density of Cooper pairs remains constant. However, it doesn'tmean that each Cooper pair remains in the same state forever. This is due to two factors:
(1) the indistinguishibility of each Cooper pair. You can't tag one Cooper pair and follow it around. Remember, these are bosons, and when you say that, it implies the indistinguishibility of quantum statistics has already kicked in. So we can't say that THAT particular cooper pair has an infinite lifetime, because you don't have the ability to pick out a cooper pair.
(2) In the BCS formulation, there is nothing preventing one cooper pair being scattered out of a particular (k1_up, -k1_down) state, and 2 electrons from the Fermi sea coming in and taking over. In other words, it is perfectly "legal" for a continuous scattering in and out of Cooper pair states. All it requires is that at a fix T, the density of cooper pairs reaches an equilibrium.
Now, the quasiparticles are a different matter completely. Let me first say that there is a HUGE amount of background info that one needs to understand what a "quasiparticle" is. The relevant information is contained within Landau's Fermi Liquid theory. In a superconductor, the quasiparticle is a single-particle excitation in the NORMAL state, i.e. not in a condensed Cooper pair. In fact, to be exact, the quasiparticles are the ones that form the Cooper pairs, not the bare electrons or holes.
In a conventional superconductor, when you break a cooper pair, you form two quasiparticles. This is because the normal state of a conventional superconductor can be accurately described as a Fermi liquid. Unfortunately, this breaks down in high-Tc superconductors, especially in the optimally doped and underdoped regime. The normal state of these materials have no "well-defined" quasiparticles. This then is the impetus for many theorists to argue that conventional BCS theory will not work for high-Tc superconductors because the material we are studying starts off as being "strange", i.e. non-Fermi Liquid.
Now, this would fine and dandy, except the damn thing throws us another curve. The ARPES spectra in my avatar is from a highly overdoped Bi2212 high-Tc material (Tc ~ 51K). We found that while the underdoped and optimally doped compounds behave in a non-Fermi Liquid manner, the overdoped ones start to show Fermi Liquid-like characteristics! It starts to show well-defined quasiparticle in the normal state. If all these observations are true, then we have to reconcile the fact that this thing has two wildly different characteristics. We have to figure out if the boundary between these two are simply a gradual crossover, or a distinct phase transition.
I hope this illustrates my claim in another thread on why we should not delve into high-Tc materials or else we'll go mad! :)
Zz. [who got out of studying high-Tc superconductors 3 years ago]
So if you're looking for more technical info, I can't help