# Distinguish electron-like and hole-like orbits in reciprocal space, with reference to the Brillouin Zones

So I have a solid state and thermodynamic exam next week and I've been going through some of the previous exams from years gone by to prepare. I came across this question "Distinguish electron-like and hole-like orbits in reciprocal space, with reference to the Brillouin Zones of squarium by sketching an example of each type." Apologies if this seems simple, solid state physics is not a strong point. Any help at all would be great! Also, what is squarium? I can't find anything in my notes on it and I'm wondering if it is simply referring to some sort of 2D square layout on which to sketch on. Thanks :)

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Squarium... yeah maybe it's just the square lattice? –  Lagerbaer May 9 at 21:02
Wow that was a quick reply! Yea i'm thinking that must be the case. Thanks very much :) any ideas about the distinguishing between electron-like and hole-like orbits in reciprocal space? I can't understand how a hole could have an orbit –  Carson1091 May 9 at 21:19

The reason for these names is that we are thinking of applying a perpendicular magnetic field $B_z$. In that case we have $$\frac{\partial k}{\partial t} = v_k \times B_z,$$ where the group velocity $v_k = \nabla_k E(k)$. Since $v_k$ is pointed in the opposite direction of $k$ in holelike orbits, the electrons orbits in the "wrong direction". That is it orbits in the direction that, naively, a positively charged particle would orbit in. Hence it is called holelike.