Working with atomic (?) units in solid state physics

I'm having some troubles understanding the units used in solid state physics paper. In the paper I read

$\Lambda a \sim 1$

where $\Lambda$ is a momentum cutoff and $a$ is the lattice spacing of a crystal. Questions:

1) What kind of units are customarily used in solid state physics scientific articles? Can I be confident that they are atomic units?

2) The aforementioned equation is not (strictly speaking) dimensionally correct. If this was particle physics, I would say that one could set the speed of light and the Planck constant to 1 and make the equation correct. However in a low energy treatment in solid state physics, I don't see the point in using the speed of light or the Planck constant, and making the physics of the system dependent upon these quantities.

• Notice that you only need to set $\hbar$ to be one. The equation means that you're near the edge of the Brillouin zone. Feb 5 '12 at 18:43
• I'm confused by all this talk about Planck's constant "disappearing" (see the only answer as of this comment) or not being important in solid state. I think it's actually extremely unlikely to see a totally classical treatment of a solid state topic in a journal article published in the last 50-odd years. We just set $\hbar=1$.
– wsc
Feb 5 '12 at 19:54
• @wsc: I did not say the Planck constant was not important, I said that it (formally) "disappears" in the formulas, as you just replace it with 1, which you don't write explicitly. If you wish, you can restore the Planck constant in the formulas, using dimensional analysis. So you don't change any physics when you choose a system of units where the Plank constant equals unity. Feb 5 '12 at 20:59
• @akhmeteli: ah, sorry for my misunderstanding, the way it was worded made me think you meant it vanished identically from many formulas (and thus that there are results in solid state that are insensitive to the value of $\hbar$. And there are of course beautiful fully classical results in solid state! Just not at the level of most modern topics.)
– wsc
Feb 5 '12 at 21:11