Bloch

class sisl.physics.Bloch(*bloch)

Bloch’s theorem object containing unfolding factors and unfolding algorithms

This class is a wrapper for expanding any matrix from a smaller matrix cell into a larger, using Bloch’s theorem. The general idea may be summarized in the following equation:

\[\begin{split}\mathbf M_{k}^N =\frac1N \; \sum_{ \substack{j=0\\ k_j=2\pi\frac{k+j}N } }^{N-1} \quad \begin{bmatrix} 1 & \cdots & e^{i (1-N)k_j} \\ e^{i k_j} & \cdots & e^{i (2-N)k_j} \\ \vdots & \ddots & \vdots \\ e^{i (N-1)k_j} & \cdots & 1 \end{bmatrix} \otimes \mathbf M_{k_j}^1.\end{split}\]

Parameters

bloch(3,) int

Bloch repetitions along each direction

Examples

>>> bloch = Bloch([2, 1, 2])
>>> k_unfold = bloch.unfold_points([0] * 3)
>>> M = [func(*args, k=k) for k in k_unfold]
>>> bloch.unfold(M, k_unfold)

Attributes

bloch

Number of Bloch expansions along each lattice vector

Methods

__init__(self, \*bloch)	Create Bloch object
unfold(self, M, k_unfold)	Unfold the matrix list of matrices M into a corresponding k-point (unfolding k-points are k_unfold)
unfold_points(self, k)	Return a list of k-points to be evaluated for this objects unfolding

property bloch

Number of Bloch expansions along each lattice vector

unfold(self, M, k_unfold)

Unfold the matrix list of matrices M into a corresponding k-point (unfolding k-points are k_unfold)

Parameters

M(*, :, :)

an *-N-M matrix used for unfolding

k_unfold(*, 3) of float

unfolding k-points as returned by Bloch.unfold_points

Returns

M_unfoldunfolded matrix of size M[0].shape * k_unfold.shape[0] ** 2

unfold_points(self, k)

Return a list of k-points to be evaluated for this objects unfolding

The k-point k is with respect to the unfolded geometry. The return list of k points are the k-points required to be sampled in the folded geometry (this.parent).

Parameters

k(3,) of float

k-point evaluation corresponding to the unfolded unit-cell

Returns

k_unfolda list of np.prod(self.bloch) k-points used for the unfolding