pythtb.TBModel.position_matrix#

TBModel.position_matrix(evecs, pos_dir)[source]#

Position operator matrix elements

Returns matrix elements of the position operator along direction pos_dir for eigenvectors evecs at a single k-point. 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.

Parameters:

evecsnp.ndarray: Eigenvectors for which we are computing matrix elements of the position operator. The shape of this array is evecs[band, orbital] if spinful=False and evecs[band, orbital, spin] if spinful=True.

Changed in version 2.0.0: Parameter evec renamed to evecs to clarify that multiple eigenvectors can be passed at once.
pos_dirint: Direction along which we are computing the center. This integer must not be one of the periodic directions since position operator matrix element in that case is not well defined.

Changed in version 2.0.0: Parameter dir renamed to pos_dir to avoid conflict with built-in function dir().

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 (\(n\)).