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)

Attributes

__dict__
__doc__
__module__
__weakref__	list of weak references to the object (if defined)
bloch	Number of Bloch expansions along each lattice vector

Methods

__call__(func, k, *args, **kwargs)	Return a functions return values as the Bloch unfolded equivalent according to this object
__delattr__	Implement delattr(self, name).
__dir__	Default dir() implementation.
__eq__	Return self==value.
__format__	Default object formatter.
__ge__	Return self>=value.
__getattribute__	Return getattr(self, name).
__gt__	Return self>value.
__hash__	Return hash(self).
__init__(*bloch)	Create Bloch object
__init_subclass__	This method is called when a class is subclassed.
__le__	Return self<=value.
__len__()	Return unfolded size
__lt__	Return self<value.
__ne__	Return self!=value.
__new__	Create and return a new object.
__reduce__	Helper for pickle.
__reduce_ex__	Helper for pickle.
__repr__	Return repr(self).
__setattr__	Implement setattr(self, name, value).
__sizeof__	Size of object in memory, in bytes.
__str__()	Representation of the Bloch model
__subclasshook__	Abstract classes can override this to customize issubclass().
unfold(M, k_unfold)	Unfold the matrix list of matrices M into a corresponding k-point (unfolding k-points are k_unfold)
unfold_points(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(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

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

Return type

numpy.ndarray

unfold_points(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

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

Return type

k_unfold