conductivity

sisl.physics.electron.conductivity(bz, distribution='fermi-dirac', method='ahc', degenerate=1e-05, degenerate_dir=(1, 1, 1), *, eigenstate_kwargs=None)[source]

Electronic conductivity for a given BrillouinZone integral

Currently the only implemented method is the anomalous Hall conductivity (AHC, see [11]) which may be calculated as:

\[\sigma_{\alpha\beta} = \frac{-e^2}{\hbar}\int\,\mathrm d\mathbf k\sum_i f_i\Omega_{i,\alpha\beta}(\mathbf k)\]

where \(\Omega_{i,\alpha\beta}\) and \(f_i\) is the Berry curvature and occupation for state \(i\).

The conductivity will be averaged by the Brillouin zone volume of the parent. See BrillouinZone.volume for details. Hence for 1D the returned unit will be S/Ang, 2D it will be S/Ang^2 and 3D it will be S/Ang^3.

Parameters:

bz (BrillouinZone) – containing the integration grid and has the bz.parent as an instance of Hamiltonian.
distribution (str or func, optional) – distribution used to find occupations
method ({"ahc"}) – “ahc” calculates the dc anomalous Hall conductivity
degenerate (float, optional) – de-couple degenerate states within the given tolerance (in eV)
degenerate_dir ((3,), optional) – along which direction degenerate states are decoupled.
eigenstate_kwargs (dict, optional) – keyword arguments passed directly to the contour.eigenstate method. One should not pass a k or a wrap keyword argument as they are already used.

Returns:

cond – conductivity in units [S/cm^D]. The D is the dimensionality of the system.

Return type:

float