All codes compute the flatness ratios and Chern number of the bands as a function of model parameters. The model under consideration is the "simplified model" from the paper, i.e. Eq. (3) with Green's function (4) where all terms are neglected except the ones varying as 1/r^3.

In the case of simple triangular lattice (dipolar_triangular.py) the only parameter is the rescaled magnetic field B_0. The code produces just a single file triangular.pdf with the plot of Chern number of the lowest band and flatness ratios of both band.

In the case of square lattice with basis (dipolar_square.py; two atoms per unit cell) and triangular lattice with basis (dipolar_triangular_V.py; three atoms per unit cell) there are two parameters: the rescaledmagnetic field B_0 and the rescaled onsite potential V_0 on one of the atoms in the unit cell. The codes produce a separate file with a map of flatness ratio and Chern number for each band.

In the case of models with more than two bands, the flatness ratio of a given band is the smaller one of two flatness ratios, computed using the gap above and below the band. Negative flatness ratio means a negative gap, i.e. the bands overlap on the energy axis. Note that the Chern number result is not meaningful if there are band crossings.

The codes need pythtb library. They can be run by typing
python dipolar_<lattice>.py
in the command line.

