PAOFLOW.spectrum.do_Efermi#

Attributes#

`comm`
`rank`

Functions#

E_Fermi(Hksp, data_controller[, parallel])

Find the Fermi energy using a bisection bracketing algorithm.

Module Contents#

PAOFLOW.spectrum.do_Efermi.comm[source]#

PAOFLOW.spectrum.do_Efermi.rank[source]#

PAOFLOW.spectrum.do_Efermi.E_Fermi(Hksp, data_controller, parallel=False)[source]#

Find the Fermi energy using a bisection bracketing algorithm.

Parameters:

Hksp (np.ndarray, shape (nawf, nawf, snktot, nspin) or (nawf, nawf, nk1, nk2, nk3, nspin)) – k-space Hamiltonian distributed over MPI pools. The array is reshaped internally to (nawf, nawf, snktot, nspin) before diagonalisation.
data_controller (DataController) – Object providing data_arrays and data_attributes. Required attributes: insulator, nkpnts, bnd, nelec, dftSO.
parallel (bool, optional) – If True, an MPI reduction is performed across ranks to compute the global Fermi energy. Default is False.

Returns:

Fermi energy in eV.

Return type:

float

Notes

For insulators the Fermi energy is set to the maximum eigenvalue of the highest occupied band, accounting for spin–orbit coupling via dftSO.

For metals, eigenvalues at each local k-point are first computed by diagonalising Hksp. The Fermi energy is then located by bisection: upper and lower bounds \(E_{\text{up}}\) and \(E_{\text{lw}}\) are established such that the integrated occupation at \(E_{\text{up}}\) exceeds nelec and at \(E_{\text{lw}}\) is below nelec. The midpoint is accepted when

\[\left| N(E_F) - N_{\text{elec}} \right| < \epsilon\]

where \(N(E)\) is the smeared electron count computed by intmetpax() with a fixed Gaussian broadening of 0.01 eV, and \(\epsilon = 10^{-10}\). A maximum of 100 iterations is performed.