Electron mass in a Kondo lattice

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    Electron Lattice Mass
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Discussion Overview

The discussion centers around the concept of "heavy electrons" in a Kondo lattice, exploring the nature of electron mass in this context. Participants examine the implications of effective mass, quasiparticles, and the behavior of electrons at low temperatures, with references to theoretical frameworks and mathematical formulations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the nature of "heavy" electrons, suggesting that while the rest mass of an electron is a constant, its apparent mass may be influenced by relativistic effects.
  • Another participant explains that in a crystal, strong interactions among electrons lead to the concept of quasiparticles, which can exhibit an effective mass influenced by the curvature of the energy band.
  • A participant notes that in Heavy Fermion systems, the conduction bands can be nearly flat, resulting in electron-like quasiparticles with a high effective mass.
  • There is a discussion about the similarity between heavy electrons and condensates at low temperatures, with one participant suggesting they may be composites.
  • Another participant clarifies that while there are similarities, the details differ, emphasizing the need for many-electron wave functions in crystals.
  • A mathematical approach to defining effective mass through the dispersion relation is presented, involving Taylor expansion around the energy minimum of the conduction band.

Areas of Agreement / Disagreement

Participants express various viewpoints on the nature of heavy electrons and quasiparticles, with no consensus reached on the precise implications or definitions. The discussion remains exploratory and open-ended.

Contextual Notes

Participants reference complex interactions and mathematical formulations without resolving the underlying assumptions or dependencies on specific definitions of effective mass and quasiparticles.

SW VandeCarr
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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
 
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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.
 
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.
 
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.
 
SW VandeCarr said:
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

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 [itex]m^{*}=\frac{\hbar^{2}}{1}\frac{1}{\frac{ \partial ^{2}E}{\partial k^{2}}}[/itex] 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 [itex]m^{*}[/itex].
 
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Thank you both for your explanations.
 

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