pengwann.utils.get_spilling_factor

utils.get_spilling_factor(u, num_wann)

Compute the spilling factor for a set of Wannier functions.

Parameters:

undarray of complex

The U matrices that define the Wannier functions in terms of the canonical Bloch states.

num_wannint

The total number of Wannier functions.

Returns:

spilling_factorfloat

The spilling factor.

See also

pengwann.io.read_u

Notes

The spilling factor is calculated as [1][2]

\[S = \frac{1}{N_{k}}\frac{1}{N_{w}}\sum_{nk} 1 - \sum_{\alpha} |\braket{\psi_{nk}|w_{\alpha}}|^{2},\]

where \(N_{k}\) is the total number of k-points, \(N_{w}\) is the total number of Wannier functions, \(n\) labels bands, \(k\) labels k-points and \(\alpha\) labels Wannier functions \(\ket{w_{\alpha}}\).

References

[1]

Daniel Sanchez-Portal, Emilio Artacho, and Jose M Soler. Projection of plane-wave calculations into atomic orbitals. Solid State Commun., 95(10):685–690, 1995. URL: https://www.sciencedirect.com/science/article/pii/003810989500341X, doi:10.1016/0038-1098(95)00341-X.

[2]

Sudipta Kundu, Satadeep Bhattacharjee, Seung-Cheol Lee, and Manish Jain. Population analysis with Wannier orbitals. J. Chem. Phys., 154(10):104111, 03 2021. URL: https://doi.org/10.1063/5.0032605, arXiv:https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/5.0032605/13469861/104111\_1\_online.pdf, doi:10.1063/5.0032605.