Band structure analysis

[Palak]

Respected Sir,
I have a band structure of 1D nanowire of lead  along Γ-X-Γ-K-X , but actually the wire is relaxed along Z. Then how I defend that the X that appear in between is simply a point in the Brillioun Zone along Z-direction. Is there any method for calculating the coordinates for the special points Z, X and K for tetragonal supercell.

With Highest Regards!

[Anders Blom]

If the system truly is 1D, and for the sake of argument periodic along Z, then the only band structure that makes sense is from k=(0,0,0) to k=(0,0,pi/c) where c is the cell length in Z. The first point is Gamma, I usually call the other point Z for obvious reasons.

Now, you indicate that you are using the SimpleTetragonal class for your wire, and I assume it's aligned then such that it's periodic in Z with the C-vector = (0,0,c). In that case, the standard notation is such that the band structure should indeed be computed along G-Z.

You mention, however, K and X. The only crystal class where both these appear as symmetry points in the standard notation is FaceCenteredCubic, and that doesn't make sense for your 1D wire. In fact, ATK would only appear these points as input for the FCC lattice.