BandStructure¶

class sisl.physics.brillouinzone.BandStructure(parent, point, division, name=None)[source]¶

Create a path in the Brillouin zone for plotting band-structures etc.

Parameters:

parent : object or array_like: An object with associated parentcell and parent.rcell or an array of floats which may be turned into a SuperCell
point : array_like of float: a list of points that are the corners of the path
division : int or array_like of int: number of divisions in each segment. If a single integer is passed it is the total number of points on the path (equally separated). If it is an array_like input it must have length one less than point.
name : array_like of str: the associated names of the points on the Brillouin Zone path

Examples

>>> sc = SuperCell(10)
>>> bs = BandStructure(sc, [[0] * 3, [0.5] * 3], 200)
>>> bs = BandStructure(sc, [[0] * 3, [0.5] * 3, [1.] * 3], 200)
>>> bs = BandStructure(sc, [[0] * 3, [0.5] * 3, [1.] * 3], 200, ['Gamma', 'M', 'Gamma'])

Attributes

`cell`
`k`	A list of all k-points (if available)
`rcell`
`weight`	Weight of the k-points in the `BrillouinZone` object

Methods

`__init__`(parent, point, division[, name])	Initialize self.
`asarray`()	Return self with `numpy.ndarray` returned quantities
`asaverage`()	Return self with k-averaged quantities
`aslist`()	Return self with list returned quantities
`asnone`()	Return self with None, this may be done for instance when wrapping the function calls.
`assum`()	Return self with summed quantities
`asyield`()	Return self with yielded quantities
`copy`()	Create a copy of this object
`in_primitive`(k)	Move the k-point into the primitive point(s) ]-0.5 ; 0.5]
`iter`([ret_weight])	An iterator for the k-points and (possibly) the weights
`lineark`([ticks])	A 1D array which corresponds to the delta-k values of the path
`lineartick`()	The tick-marks corresponding to the linear-k values
`param_circle`(sc, N_or_dk, kR, normal, origo)	Create a parameterized k-point list where the k-points are generated on a circle around an origo
`parametrize`(sc, func, N, args, *kwargs)	Generate a new `BrillouinZone` object with k-points parameterized via the function func in N separations
`set_parent`(parent)	Update the parent associated to this object
`tocartesian`(k)	Transfer a k-point in reduced coordinates to the Cartesian coordinates
`toreduced`(k)	Transfer a k-point in Cartesian coordinates to the reduced coordinates
`write`(sile, args, *kwargs)	Writes k-points to a `tableSile`.

asarray()¶

Return self with numpy.ndarray returned quantities

This forces the __call__ routine to return a single array.

See also

asyield: all output returned through an iterator
asaverage: take the average (with k-weights) of the Brillouin zone
assum: return the sum of values in the Brillouin zone
aslist: all output returned as a Python list

Notes

All invocations of sub-methods are added these keyword-only arguments:

eta : bool, optional: if true a progress-bar is created, default false.
wrap : callable, optional: a function that accepts the output of the given routine and post-process it. Defaults to lambda x: x.

Examples

>>> obj = BrillouinZone(...) 
>>> obj.asarray().eigh(eta=True) 

asaverage()¶

Return self with k-averaged quantities

This forces the __call__ routine to return a single k-averaged value.

See also

asarray: all output as a single array
asyield: all output returned through an iterator
assum: return the sum of values in the Brillouin zone
aslist: all output returned as a Python list

Notes

All invocations of sub-methods are added these keyword-only arguments:

eta : bool, optional: if true a progress-bar is created, default false.
wrap : callable, optional: a function that accepts the output of the given routine and post-process it. Defaults to lambda x: x.

Examples

>>> obj = BrillouinZone(Hamiltonian) 
>>> obj.asaverage().DOS(np.linspace(-2, 2, 100)) 

>>> obj = BrillouinZone(Hamiltonian) 
>>> obj.asaverage() 
>>> obj.DOS(np.linspace(-2, 2, 100)) 
>>> obj.PDOS(np.linspace(-2, 2, 100), eta=True) 

aslist()¶

Return self with list returned quantities

This forces the __call__ routine to return a list with returned values.

See also

asarray: all output as a single array
asyield: all output returned through an iterator
assum: return the sum of values in the Brillouin zone
asaverage: take the average (with k-weights) of the Brillouin zone

Notes

All invocations of sub-methods are added these keyword-only arguments:

eta : bool, optional: if true a progress-bar is created, default false.
wrap : callable, optional: a function that accepts the output of the given routine and post-process it. Defaults to lambda x: x.

Examples

>>> obj = BrillouinZone(...) 
>>> def first_ten(es):
...    return es.sub(range(10))
>>> obj.aslist().eigenstate(eta=True, wrap=first_ten) 

asnone()¶

Return self with None, this may be done for instance when wrapping the function calls.

This forces the __call__ routine to return None. This usage is mainly intended when creating custom wrap function calls.

See also

asyield: all output returned through an iterator
asaverage: take the average (with k-weights) of the Brillouin zone
assum: return the sum of values in the Brillouin zone
aslist: all output returned as a Python list

Notes

All invocations of sub-methods are added these keyword-only arguments:

eta : bool, optional: if true a progress-bar is created, default false.
wrap : callable, optional: a function that accepts the output of the given routine and post-process it. Defaults to lambda x: x.

Examples

>>> obj = BrillouinZone(...) 
>>> obj.asnone().eigh(eta=True) 

assum()¶

Return self with summed quantities

This forces the __call__ routine to return all k-point values summed.

See also

asarray: all output as a single array
asyield: all output returned through an iterator
asaverage: take the average (with k-weights) of the Brillouin zone
aslist: all output returned as a Python list

Notes

All invocations of sub-methods are added these keyword-only arguments:

eta : bool, optional: if true a progress-bar is created, default false.
wrap : callable, optional: a function that accepts the output of the given routine and post-process it. Defaults to lambda x: x.

Examples

>>> obj = BrillouinZone(Hamiltonian) 
>>> obj.assum().DOS(np.linspace(-2, 2, 100)) 

>>> obj = BrillouinZone(Hamiltonian) 
>>> obj.assum() 
>>> obj.DOS(np.linspace(-2, 2, 100)) 
>>> obj.PDOS(np.linspace(-2, 2, 100), eta=True) 

asyield()¶

Return self with yielded quantities

This forces the __call__ routine to return a an iterator which may yield the quantities calculated.

See also

asarray: all output as a single array
asaverage: take the average (with k-weights) of the Brillouin zone
assum: return the sum of values in the Brillouin zone
aslist: all output returned as a Python list

Notes

All invocations of sub-methods are added these keyword-only arguments:

eta : bool, optional: if true a progress-bar is created, default false.
wrap : callable, optional: a function that accepts the output of the given routine and post-process it. Defaults to lambda x: x.

Examples

>>> obj = BrillouinZone(Hamiltonian) 
>>> obj.asyield().eigh(eta=True) 

cell¶

copy()¶: Create a copy of this object

static in_primitive(k)¶

Move the k-point into the primitive point(s) ]-0.5 ; 0.5]

Parameters:	k : array_like k-point(s) to move into the primitive cell
Returns:	k : all k-points moved into the primitive cell

iter(ret_weight=False)¶

An iterator for the k-points and (possibly) the weights

Parameters:	ret_weight : bool, optional if true, also yield the weight for the respective k-point
Yields:	kpt : k-point weight : weight of k-point, only if ret_weight is true.

k¶: A list of all k-points (if available)

lineark(ticks=False)[source]¶

A 1D array which corresponds to the delta-k values of the path

This is meant for plotting

Parameters:	ticks : bool, optional if True the ticks for the points are also returned lk, xticks, label_ticks, lk = BandStructure.lineark(True)
Returns:	linear_k : The positions in reciprocal space determined by the distance between points k_tick : Linear k-positions of the points, only returned if ticks is `True` k_label : Labels at k_tick, only returned if ticks is `True`

Examples

>>> p = BandStructure(...) 
>>> eigs = Hamiltonian.eigh(p) 
>>> for i in range(len(Hamiltonian)): 
...     plt.plot(p.lineark(), eigs[:, i]) 

>>> p = BandStructure(...) 
>>> eigs = Hamiltonian.eigh(p) 
>>> lk, kt, kl = p.lineark(True) 
>>> plt.xticks(kt, kl) 
>>> for i in range(len(Hamiltonian)): 
...     plt.plot(lk, eigs[:, i]) 

lineartick()[source]¶

The tick-marks corresponding to the linear-k values

Returns:	linear_k : The positions in reciprocal space determined by the distance between points

See also

lineark: Routine used to calculate the tick-marks.

classmethod param_circle(sc, N_or_dk, kR, normal, origo, loop=False)¶

Create a parameterized k-point list where the k-points are generated on a circle around an origo

The generated circle is a perfect circle in the reciprocal space (Cartesian coordinates). To generate a perfect circle in units of the reciprocal lattice vectors one can generate the circle for a diagonal supercell with side-length \(2\pi\), see example below.

Parameters:

sc : SuperCell, or SuperCellChild: the supercell used to construct the k-points
N_or_dk : int: number of k-points generated using the parameterization (if an integer), otherwise it specifies the discretization length on the circle (in 1/Ang), If the latter case will use less than 4 points a warning will be raised and the number of points increased to 4.
kR : float: radius of the k-point. In 1/Ang
normal : array_like of float: normal vector to determine the circle plane
origo : array_like of float: origo of the circle used to generate the circular parameterization
loop : bool, optional: whether the first and last point are equal

Returns:

BrillouinZone : with the parameterized k-points.

Examples

>>> sc = SuperCell([1, 1, 10, 90, 90, 60])
>>> bz = BrillouinZone.param_circle(sc, 10, 0.05, [0, 0, 1], [1./3, 2./3, 0])

To generate a circular set of k-points in reduced coordinates (reciprocal

>>> sc = SuperCell([1, 1, 10, 90, 90, 60])
>>> bz = BrillouinZone.param_circle(sc, 10, 0.05, [0, 0, 1], [1./3, 2./3, 0])
>>> bz_rec = BrillouinZone.param_circle(2*np.pi, 10, 0.05, [0, 0, 1], [1./3, 2./3, 0])
>>> bz.k[:, :] = bz_rec.k[:, :]

classmethod parametrize(sc, func, N, *args, **kwargs)¶

Generate a new BrillouinZone object with k-points parameterized via the function func in N separations

Generator of a parameterized Brillouin zone object that contains a parameterized k-point list.

Basically this generates a new BrillouinZone object as:

>>> def func(sc, frac):
...    return [frac, 0, 0]
>>> bz = BrillouinZone.parametrize(1, func, 10)
>>> len(bz) == 10
True
>>> np.allclose(bz.k[-1, :], [9./10, 0, 0])
True

Parameters:

sc : SuperCell, or SuperCellChild: the supercell used to construct the k-points
func : callable: method that parameterizes the k-points, must at least accept two arguments, sc (super-cell object containing the unit-cell and reciprocal cell) and frac (current parametrization fraction, between 0 and (N-1)/N. It must return a k-point in 3 dimensions.
N : int: number of k-points generated using the parameterization
args: list of arguments: arguments passed directly to func
kwargs: dictionary of arguments: keyword arguments passed directly to func

rcell¶

set_parent(parent)¶

Update the parent associated to this object

Parameters:	parent : object or array_like an object containing cell vectors

tocartesian(k)¶

Transfer a k-point in reduced coordinates to the Cartesian coordinates

Parameters:	k : list of float k-point in reduced coordinates
Returns:	k : in units of 1/Ang

toreduced(k)¶

Transfer a k-point in Cartesian coordinates to the reduced coordinates

Parameters:	k : list of float k-point in Cartesian coordinates
Returns:	k : in units of reciprocal lattice vectors ]-0.5 ; 0.5] (if k is in the primitive cell)

weight¶: Weight of the k-points in the BrillouinZone object

write(sile, *args, **kwargs)¶

Writes k-points to a tableSile.

This allows one to pass a tableSile or a file-name.