sisl.physics.Bloch
- class sisl.physics.Bloch(*bloch)
Bases:
object
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:
\[\begin{split}\mathbf M_{K}^N =\frac1N \; \sum_{ \substack{j=0\\ k_j=\frac{K+j}N } }^{N-1} \quad \begin{bmatrix} 1 & \cdots & e^{i (1-N)k_j} \\ e^{i k_j} & \cdots & e^{i (2-N)k_j} \\ \vdots & \ddots & \vdots \\ e^{i (N-1)k_j} & \cdots & 1 \end{bmatrix} \otimes \mathbf M_{k_j}^1.\end{split}\]- 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)
Methods
unfold
(M, k_unfold)Unfold the matrix list of matrices M into a corresponding k-point (unfolding k-points are k_unfold)
Return a list of k-points to be evaluated for this objects unfolding
Attributes
Number of Bloch expansions along each lattice vector
- __call__(func, k: sisl.typing.KPoint, *args, **kwargs)[source]
Return a functions return values as the Bloch unfolded equivalent according to this object
Calling the
Bloch
object is a shorthand for the manual use of theBloch.unfold_points
andBloch.unfold
methods.This call structure is a shorthand for:
>>> 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)
Notes
The function passed must have a keyword argument
k
.- Parameters:
- Returns:
numpy.ndarray
– unfolded Bloch matrix
- unfold(M, k_unfold: Sequence[sisl.typing.KPoint])[source]
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 unfoldingk_unfold (
(:
,3)
offloat
) – unfolding k-points as returned byBloch.unfold_points
- Returns:
numpy.ndarray
– unfolded matrix of sizeM[0].shape * k_unfold.shape[0] ** 2
- unfold_points(k: sisl.typing.KPoint)[source]
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.
- Parameters:
k (
(3,)
offloat
) – k-point evaluation corresponding to the unfolded unit-cell- Returns:
numpy.ndarray
– a list ofnp.prod(self.bloch)
k-points used for the unfolding
- property bloch
Number of Bloch expansions along each lattice vector