This is an extention package of PythTB, a package used to simulate crystal structures using the tight-binding approximation. See http://physics.rutgers.edu/pythtb/.

pcn.py

This script contains routine c_l(my_model,n_occ) which calculates the partial Chern number C(l) for each orbital l of a spinor slab model (extended in two direction and finite in the third) provided the number of occupied bands. The routine assumes dim_k=2 while dim_r=2 (one layer) or 3 (many layers) and C(l) corresponds to the component of the partial Chern vector along the k₁ x k₂ direction.

For the implementation of pcn see:

[1] T. Rauch, T. Olsen, D. Vanderbilt, and I. Souza, "Geometric and nongeometric contributions to the surface anomalous Hall conductivity," Phys. Rev. B 98, 115108 (2018).

[2] N. Varnava and D. Vanderbilt, "Surfaces of axion insulators," arXiv:1809.02853. (please cite this paper if you use this code in a scientific publication)

Demo/pcn_example.py

Example usage of pcn.py for the calculation of the partial Chern number of a spinor slab model of an axion isnulator. After the C(l) list is calculated, the routine plots the pcn density and integrated pcn in a single output PDF.

For the axion insulator model see:

[3] T.L. Hughes, E. Prodan, and B.A. Bernevig, "Inversion-symmetric topological insulators," Phys. Rev. B 83, 245132 (2011).