Talk:Crystal momentum

Form of article

I think that the article should explain the relation of crystal momentum to the electron-phonon interaction as well as the translational symmetry in the Hamiltonian. I want to remove the extensive use of real in quotation marks. WilliamDParker 16:49, 10 November 2006 (UTC)

Units of crystal momentum

The crystal momentum is given by $\hbar \mathbf {k}$. The quantity $\mathbf {k}$ denotes the wave vector. --132.199.98.122 16:18, 19 March 2007 (UTC)

Rewrite

Recently rewrote the article. Mostly this was for my own edification and understanding of the topic so clarifications would be welcome. A few notes: The first couple sentences are basically the same. Later on I wasn’t entirely convinced that the problem of finite momentum leading to electrons shooting out the sides of a crystal defines a real difference between regular and crystal momentum, so I canned the idea in the rewrite. I moved the old second paragraph under the “origins” section. Most of the rest of the previous article is reworked under “physical significance” which I was trying to write as a section that addresses how one might be able to think about crystal momentum intuitively. Pictures would be nice to add. I also removed the flags. Csmallw (talk) 05:31, 27 July 2008 (UTC)

Perhaps a proof of the theorem d/dt(p_crystal)=F_ext is in order, since it is so often used? There is a very short and formal proof (due to Herbert Kroemer) in Charles Kittel, 'Introduction to Solid State Physics' 7th Edition, Appendix E, P. 646. --Philipralph (talk) 02:38, 14 June 2010 (UTC)

Relation to conductivity -wrong statement

it does NOT follow from the finiteness of v_k that any crystal should be a conductor as the article now says. Insulators are such NOT because they scatter electrons strongly. Group velocities can be both positive and negative, and in a fully occupied band the two exactly cancel each other. 71.137.237.162 (talk) 03:31, 23 December 2010 (UTC)

How about "...any crystal structure containing any conduction-band electrons or valence-band holes should be a perfect conductor..."? Do you think that would that be OK?

Actually, I think maybe even that is oversimplified. It's a "perfect conductor" insofar as it sustains a lossless current, but it's not a "perfect conductor" insofar as the current cannot be arbitrarily large. (Each electron can only travel as fast as the slope of the band of course.) Maybe instead of the term "perfect conductor", we could say something more specific like "can sustain a nonzero current perpetually, even with no applied voltage".

What do you think? :-) --Steve (talk) 13:35, 23 December 2010 (UTC)

I also think that this should be changed. At first I thought only deleting this sentence would be okay, but the conductance story goes further. Yes, a perfect crystal could sustain a nonzero current, even without applied voltage, and this holds even for an insulator: you just inject an electron into an unoccupied high-lying band, and it will come out on the other side, as it will not be scattered. This is then just a very non-equilibrium situation. But I would propose to remove the whole idea of perfect conductance, as this is not relevant to the crystal momentum. It could be relevant for a quantum-mechanical discussion of conductivity. Seattle Jörg (talk) 15:02, 27 September 2012 (UTC)

I rewrote the section, hope that helps :-) I decided that the discussion of "perfect conductor" added nothing but distraction; better to describe directly what really happens. --Steve (talk) 14:05, 28 September 2012 (UTC)

Article needs extension

I think this article is not quite correct or too narrow: So in the first sentence it is said that crystal momentum refers to electrons. However, crystal momentum is also defined for phonons and magnons in crystal and is especially important for the description of their interaction. It would also be appropriate to derive it from more fundamental symmetries, namely the permutation symmetry of identical nuclei. This can be found e.g. in the appendices of the book by Ashcroft & Mermin. — Preceding unsigned comment added by 79.251.31.200 (talk) 06:28, 8 October 2014 (UTC)

I second that strongly. Crystal momentum is not only also defined for phonons and magnons, I would even say that the crystal momentum is as little specific to electrons as momentum is specific to automobiles: both have it, but they have also other quantities (energy for instance), and also other entities have momentum and crystal momentum, respectively. Fundamentally, momentum is a conserved quantity under specific circumstances if you have continuous translation symmetry of space, and crystal momentum is just the same but under the weaker assumption of discrete translation symmetry of space (that is, crystal symmetry). Because the assumption is weaker, a given momentum implies a crystal momentum but not the other way around. As you have momentum conservation in collisions between free electrons, you have crystal momentum conservation in collisions between electrons in a crystal potential and so on. I would say that all of this article apart from the three-sentence introduction should actually be incorporated in Bloch electrons. Seattle Jörg (talk) 07:57, 13 July 2018 (UTC)