pythtb.WFArray.position_matrix#

WFArray.position_matrix(pos_dir, mesh_idx, state_idx=None)[source]#

Position matrix for a given k-point and set of states.

Position operator is defined in reduced coordinates. The returned object \(X\) is

\[X_{m n {\bf k}}^{\alpha} = \langle u_{m {\bf k}} \vert r^{\alpha} \vert u_{n {\bf k}} \rangle\]

Here \(r^{\alpha}\) is the position operator along direction \(\alpha\) that is selected by pos_dir.

This routine can be used to compute the position matrix for a given k-point and set of states (which can be all states, or a specific subset).

Parameters:

pos_dir: int: Direction of the position operator. 0 corresponds to the first non-periodic direction, 1 to the second, and so on.

Changed in version 2.0.0: Renamed from dir to pos_dir to avoid conflict with built-in Python function dir().
mesh_idx: array-like of int: Set of integers specifying the \((k, \lambda)\)-point of interest in the mesh.
state_idx: array-like, optional: List of states to be included. If not specified, all states are included.

Changed in version 2.0.0: Renamed from occ. The band indices are not required to be occupied bands only. The default behavior is to include all bands, and the "all" option has been removed.

Returns:

pos_matnp.ndarray: Position operator matrix \(X_{m n}\) as defined above. This is a square matrix with size determined by number of bands given in evec input array. First index of pos_mat corresponds to bra vector (\(m\)) and second index to ket (\(n\)).