# Electron mass in a Kondo lattice

1. Jun 16, 2012

### SW VandeCarr

I'm not a physicist, but I always thought that the rest mass of the electron was a physical constant and its apparent mass was only affected by relativistic effects. This abstract discusses heavy electrons in a Kondo lattice. In what sense are these electrons "heavy"? At low temperatures, they apparently behave as "fast" electrons, which I would think would only be "massive" in a relativistic sense. There seems to be something else going on here. Can someone explain? Thanks.

http://www.nature.com/nature/journal/v486/n7402/full/nature11204.html

Last edited by a moderator: May 6, 2017
2. Jun 17, 2012

### M Quack

In a crystal the electrons interact very strongly. As a result you cannot move a single electron without affecting a whole bunch of others. The net effect is that the physics is best described by "elementary excitations" and "quasi-particles". The best example is a hole, which behaves pretty much like a positron, but really is just a missing electron in an otherwise full band.

If you have a band that is mostly empty, then you get quasiparticles that look just like electrons but with an effective mass that is given by the curvature of the band. In common usage, they are just referred to as electrons.

In Heavy Fermion systems, the conduction bands can be nearly flat. This gives rise to electron-like quasiparticles with a very high effective mass.

This is derived from E=p^2/2m where E is the energy ,p = \hbar k is the momentum and m is the effective mass. If the band is flat then E is small even for large k, and thus m has to be large.

3. Jun 17, 2012

### SW VandeCarr

Thanks M Quack for the clear explanation. These are clearly different from free electrons and seem to be composites if I can use that word. I'm wondering if these are in any way similar to condensates at very low temperatures where a single wave function can describe a number of particles.

4. Jun 17, 2012

### M Quack

Yes, similar in principle but different in the details. For crystals you also have to find many-electron wave functions that describe all electrons at the same time.

5. Jun 17, 2012

### nucl34rgg

The dispersion relation can be used to convert the energy of a hole or electron in the conduction band of a semiconductor to an effective mass. You basically Taylor expand about the wavenumber value that gives the energy minimum of the conduction band. Then you take the second order term, and define $m^{*}=\frac{\hbar^{2}}{1}\frac{1}{\frac{ \partial ^{2}E}{\partial k^{2}}}$ to be the effective mass. It's a mathematical way to say that the electrons or holes in the lattice behave like a free gas of electrons or holes would if each particle had an effective mass corresponding to their value for $m^{*}$.

Last edited by a moderator: May 6, 2017
6. Jun 17, 2012

### SW VandeCarr

Thank you both for your explanations.