I am writing to seek guidance on calculating the Chern number for a 3D ferromagnetic semiconductor material. I intend to determine whether that material is a 3D Chern insulator or not. After reviewing the available resources, I've come across WannierTools as a potential tool for this task where you can use the following input values to perform chern calculation

Chern_3D_calc = T
NumOccpuied = 88  ! No. of occupied wannier bands
Nk1 = 41    ! No. of slices of the k points for WCCs
Nk2 = 41    ! No. of slices of the k points for WCCs

Now, my primary question is whether I can proceed with these input values and, subsequently, read the output file to determine the Chern number, similar to the process used for finding the Z2 number for 3D topological insulators. I would greatly appreciate a detailed explanation of it. Your expertise in this matter would be invaluable to me.

  • $\begingroup$ What do you mean by a 3D Chern insulator? The Chern number is typically defined only in 2D (but may be generalized to even dimensions). I'm aware of a notion of a 3D Chern insulator where one considers individual Chern numbers on lower-dimensional surfaces, but then there wouldn't be a single Chern number as you imply here. $\endgroup$
    – Anyon
    Sep 26, 2023 at 21:36


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