In OpenMX Ver. 3.9, a postprocessing code 'calB' is supported to calculate the Chern number and Berry curvature of bands using overlap matrix elements between KohnSham orbitals at neighboring kpoints by the FukuiHatsugaiSuzuki method [81,85]. The functionality is compatible with only the noncollinear calculations. To acknowledge in any publications by using the functionality, the citation of the reference [84] would be appreciated.
The Chern number is a topological invariant being an integer number,
which characterizes the topology of bands for any materials.
In systems having a finite Chern number , the anomalous Hall conductivity defined by

As shown in Fig. 73, the Berry curvature can be calculated in each 'plaquette'
(plaquette means meshed area in Brillouin zone) on a regular mesh
introduced in the first Brillouin zone by the following formula: