pythtb.WFArray.berry_curvature#

WFArray.berry_curvature(plane=None, state_idx=None, non_abelian=False, return_flux=False)[source]#

Berry curvature tensor using the Fukui-Hatsugai-Suzuki formalism.

The Berry curvature tensor \(\Omega_{\mu\nu}(\mathbf{k})\) is computed using a discretized formula based on the Fukui-Hatsugai-Suzuki (FHS) plaquette-based method [1]. The curvature is approximated from the Berry flux (computed in berry_flux()) by dividing the flux by the (presumed uniform) area of the plaquette in parameter space,

\[\Omega_{\mu\nu}(\mathbf{k}) \approx \frac{\mathcal{F}_{\mu\nu}(\mathbf{k})}{A_{\mu\nu}},\]

where \(A_{\mu\nu}\) is the area (in Cartesian units) of the plaquette in parameter space.

The tensor is either defined is a matrix-valued quantity (non-Abelian case) or as a scalar quantity obtained by tracing over the band indices (Abelian case).

Added in version 2.0.0.

Parameters:

plane(2,) array_like, optional: Array or tuple of two indices defining the axes in the WFArray mesh which the Berry flux is computed over. By default, all directions are considered, and the full Berry flux tensor is returned.
state_idxint or array_like of int, optional: Optional index or array of indices defining the states to be included in the subsequent calculations, typically the indices of bands considered occupied. If not specified, or None, all bands are included.
non_abelianbool, optional: If True then the non-Abelian Berry flux tensor is computed defined as a matrix-valued quantity. If False (default) then the Berry flux is computed as a scalar quantity by tracing over the band indices.
return_fluxbool, optional: If True, the function returns a tuple containing both the Berry curvature and the Berry flux tensors. If False (default), only the Berry curvature tensor is returned.

Returns:

berry_curvnp.ndarray: Berry curvature tensor with shape depending on input parameters.
berry_fluxnp.ndarray, optional: Berry flux tensor with shape depending on input parameters.