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vanhees71
vanhees71 is offline
#5
Mar7-12, 11:35 PM
Sci Advisor
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I think there has come up some misunderstanding in this thread on the term "heavy electron". It has nothing to do with free elementary particles. Indeed there are three generations of leptons (and quarks), and indeed the other charged leptons are the muons and the tau leptons, but that's not what's meant when a condensed-matter physicist talks about "heavy electrons".

"Heavy electrons" are socalled quasi particles. The idea of quasi particles is a very clever concept, invented by Lev D. Landau in his work on liquid helium. Nowadays quasi particles are used to describe a lot of phenomena in condensed-matter physics. It's a rather complicated matter, involving (non-relativistic) quantum-field theory, which is a particularly useful way to describe many-particle systems.

As an example take a piece of metal, and we try to describe on a microscopical level conductivity. It's very complicated to describe the phenomenon by using the complete wave function of the zillions of electrons and atomic nuclei making up this piece of metal. Instead, as a first apparoximation, one considers the atomic nuclei with the part of electrons which is bound to them (the valence electrons) as fixed on their lattice points and staying at rest while the rest of electrons are relatively free to move over the metal (conduction electrons). These conduction electrons can be described, further simplifying the picture, as a Fermi gas of quasifree electrons, building a Fermi sea. Really "active" in the sense of making up an electric current when we put a voltage at the metal, are electrons excited by this disturbance above the Fermi sea, and at not too high temperatures (and considering the large Fermi energy of conduction electrons in a metal room temperature is quite low, and the Fermi gas is highly degenerate, i.e., it really behaves very much like a quantum gas of Fermions rather than a classical gas obeying Boltzmann statistics!) you can consider these "excitations" as a view "particles" moving in the vacuum.

However, in reality these electrons feel a lot of forces from the positive ion background and the other electrons around them. Thus when they move they also disturb all these other particles, and this collective effects can be taken into account to a certain extent by the idea that an electron in this environment behaves like an electron with a somewhat different (usually a larger) mass than a free electron. In heavy-fermion materials this "effective mass" of these quasiparticles are pretty much larger than the mass of a free electron. Otherwise it still has the same properties of the electron (e.g., it's effective charge stays one negative elementary charge).

At further sophistication one can also take into account that the lattice made up of the ions is not totally rigid but vibrates. Also these vibrations have to be described by quantum theory. As long as one has pretty small disturbances from the equilibrium limit of a rigid lattice one can describe this by a set of harmonic oscillators, each of which corresponding to a certain normal mode of vibrations. Note that these are indeed vibrations of the macroscopic piece of metal as a whole, but from a quantum theoretical point of view, again these collective excitations can be effectively described as another kind of quasiparticles called phonons (from the greek word for "sound" since these vibrations are nothing else as sound waves propagating in the metal). These quasiparticles behave like a gas of bosons and can also interact with the moving "quasielectrons" with there effective mass, and often these interactions can be described with perturbation theory using Feynman diagrams pretty much as in elementary-particle physics, of course with somewhat adapted rules for the non-relativistic many-body situation we are dealing with here. In this picture the phonons are pretty analogous to, e.g., the photons in QED which describe the electromagnetic interaction between charged particles.

Sometimes it happens that the effective interaction between the quasielectrons, mediated by the phonons becomes attractive, and then really interesting things happen! One can show that such an effectively attractive interaction between fermions leads to the effect that quasielectrons with opposite momenta tend to build pairs, which form again a completely different kind of quasiparticles, the Cooper pairs (named after the inventors of this description of superconductivity, Bardeen, Cooper and Shriever). It's just energetically more favorable for the quasielectrons to form these pairs and behave collectively as another kind of quasiparticles. Now two fermions make up a boson, and it takes energy to break the Cooper pairs appart! This makes an energy gap between the ground state consisting of Cooper pairs to the next excited state. Thus for not too large distrubances, the Cooper pairs feel no friction, because it takes this minimal amount of energy to excite the next higher state. This explains the most striking feature of superconductors, namely that they have 0 electric resistance (up to a certain critical current running through them).

Nowadays there's a whole plethora of pretty "exotic" quasiparticles investigated in solid-state physics. E.g., certain materials, forming what's been dubbed "spin ice", have quasiparticle excitations behaving like magnetic monopoles. Note that these are not really elementary magnetica monopoles which up to date have never been discovered, but rather extended collective modes in this kind of solids.

Another rich field of research is graphene, having quasiparticle excitations behaving like massless Dirac fermions in two dimensions.

Quasiparticles are a very far reaching concept in theoretical condensed matter physics, but one should not think of those as real elementary particles in free space but as effective descriptions of very complicated collective (quantum) motions in matter.