sisl.physics.MonkhorstPack
- class sisl.physics.MonkhorstPack(parent, nkpt, displacement=None, size=None, centered=True, trs=True)
Bases:
BrillouinZone
Create a Monkhorst-Pack grid for the Brillouin zone
- Parameters
parent (object or array_like) – An object with associated parent.cell and parent.rcell or an array of floats which may be turned into a SuperCell
nkpt (array_like of ints) – a list of number of k-points along each cell direction
displacement (float or array_like of float, optional) – the displacement of the evenly spaced grid, a single floating number is the displacement for the 3 directions, else they are the individual displacements
size (float or array_like of float, optional) – the size of the Brillouin zone sampled. This reduces the boundaries of the Brillouin zone around the displacement to the fraction specified. I.e. size must be of values \(]0 ; 1]\). Defaults to the entire BZ. Note that this will also reduce the weights such that the weights are normalized to the entire BZ.
centered (bool, optional) – whether the k-points are \(\Gamma\)-centered (for zero displacement)
trs (bool, optional) – whether time-reversal symmetry exists in the Brillouin zone.
Examples
>>> sc = SuperCell(3.) >>> MonkhorstPack(sc, 10) # 10 x 10 x 10 (with TRS) >>> MonkhorstPack(sc, [10, 5, 5]) # 10 x 5 x 5 (with TRS) >>> MonkhorstPack(sc, [10, 5, 5], trs=False) # 10 x 5 x 5 (without TRS)
Methods
copy
([parent])Create a copy of this object, optionally changing the parent
grid
(n[, displ, size, centered, trs])Create a grid of n points with an offset of displ and sampling size around displ
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
param_circle
(parent, N_or_dk, kR, normal, origin)Create a parameterized k-point list where the k-points are generated on a circle around an origin
parametrize
(parent, func, N, *args, **kwargs)Generate a new
BrillouinZone
object with k-points parameterized via the function func in N separationsreplace
(k, mp[, displacement, as_index, ...])Replace a k-point with a new set of k-points from a Monkhorst-Pack grid
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
volume
([ret_dim, periodic])Calculate the volume of the full Brillouin zone of the parent
write
(sile, *args, **kwargs)Writes k-points to a
tableSile
.Loop over all k-points by applying parent methods for all k.
A list of all k-points (if available)
Weight of the k-points in the
BrillouinZone
object- apply
Loop over all k-points by applying parent methods for all k.
This allows potential for running and collecting various computationally heavy methods from a single point on all k-points.
The
apply
method will dispatch the parent methods through all k-points and passingk
as arguments to the parent methods in a straight-forward manner.For instance to iterate over all eigenvalues of a Hamiltonian
>>> H = Hamiltonian(...) >>> bz = BrillouinZone(H) >>> for ik, eigh in enumerate(bz.apply.eigh()): ... # do something with eigh which corresponds to bz.k[ik]
By default the
apply
method exposes a set of dispatch methods:apply.iter, the default iterator module
apply.average reduced result by averaging (using
BrillouinZone.weight
as the weight per k-point.apply.sum reduced result without weighing
apply.array return a single array with all values; has len equal to number of k-points
apply.none, specialized method that is mainly useful when wrapping methods
apply.list same as apply.array but using Python list as return value
apply.oplist using
sisl.oplist
allows greater flexibility for mathematical operations element wiseapply.datarray if
xarray
is available one can retrieve anxarray.DataArray
instance
Please see Brillouin zone for further examples.
- property cell
- copy(parent=None)[source]
Create a copy of this object, optionally changing the parent
- Parameters
parent (optional) – change the parent
- classmethod grid(n, displ=0.0, size=1.0, centered=True, trs=False)[source]
Create a grid of n points with an offset of displ and sampling size around displ
The \(k\)-points are \(\Gamma\) centered.
- Parameters
n (int) – number of points in the grid. If trs is
True
this may be smaller than ndispl (float, optional) – the displacement of the grid
size (float, optional) – the total size of the Brillouin zone to sample
centered (bool, optional) – if the points are centered
trs (bool, optional) – whether time-reversal-symmetry is applied
- Returns
k (numpy.ndarray) – the list of k-points in the Brillouin zone to be sampled
w (numpy.ndarray) – weights for the k-points
- 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
all k-points moved into the primitive cell
- Return type
- 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.)
- property k
A list of all k-points (if available)
- static param_circle(parent, N_or_dk, kR, normal, origin, loop=False)
Create a parameterized k-point list where the k-points are generated on a circle around an origin
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
parent (SuperCell, or SuperCellChild) – the parent object
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
origin (array_like of float) – origin of the circle used to generate the circular parameterization
loop (bool, optional) – whether the first and last point are equal
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[:, :]
- Returns
with the parameterized k-points.
- Return type
- static parametrize(parent, func, N, *args, **kwargs)
Generate a new
BrillouinZone
object with k-points parameterized via the function func in N separationsGenerator of a parameterized Brillouin zone object that contains a parameterized k-point list.
- Parameters
parent (SuperCell, or SuperCellChild) – the object that the returned object will contain as parent
func (callable) –
method that parameterizes the k-points, must at least accept three arguments, 1.
parent
: object 2.N
: total number of k-points 3.i
: current index of the k-point (starting from 0)the function must return a k-point in 3 dimensions.
N (int or list of int) – number of k-points generated using the parameterization, or a list of integers that will be looped over. In this case arguments
N
andi
in func will be lists accordingly.*args – additional arguments passed directly to func
**kwargs – additional keyword arguments passed directly to func
Examples
Simple linear k-points
>>> def func(sc, N, i): ... return [i/N, 0, 0] >>> bz = BrillouinZone.parametrize(1, func, 10) >>> assert len(bz) == 10 >>> assert np.allclose(bz.k[-1, :], [9./10, 0, 0])
For double looping, say to create your own grid
>>> def func(sc, N, i): ... return [i[0]/N[0], i[1]/N[1], 0] >>> bz = BrillouinZone.parametrize(1, func, [10, 5]) >>> assert len(bz) == 50
- property rcell
- replace(k, mp, displacement=False, as_index=False, check_vol=True)[source]
Replace a k-point with a new set of k-points from a Monkhorst-Pack grid
This method tries to replace an area corresponding to mp.size around the k-point
k
such that the k-points are replaced. This enables one to zoom in on specific points in the Brillouin zone for detailed analysis.- Parameters
k (array_like) – k-point in this object to replace, if as_index is true, it will be regarded as integer positions of the k-points to replace, otherwise the indices of the k-points will be located individually (in chunks of 200 MB).
mp (MonkhorstPack) – object containing the replacement k-points.
displacement (array_like or bool, optional) – the displacment of the mp k-points. Needed for doing lots of replacements due to efficiency. Defaults to not displace anything. The inserted k-points will be mp.k + displacement. If True, it will use
k
as the displacement vector. For multiple k-point replacements each k-point will be replaced my mp with k as the displacement.as_index (bool, optional) – whether
k
is input as reciprocal k-points, or as indices of k-points in this object.check_vol (bool, optional) – whether to check the volume of the replaced k-point(s); by default the volume of each k-point is determined by the original
size
andnkpt
values. However, when doing replacements of k-points these values are not kept for the individual k-points that were replaced, so subsequent replacements of these points will cause errors that effectively are not valid.
Examples
This example creates a zoomed-in view of the \(\Gamma\)-point by replacing it with a 3x3x3 Monkhorst-Pack grid.
>>> sc = SuperCell(1.) >>> mp = MonkhorstPack(sc, [3, 3, 3]) >>> mp.replace([0, 0, 0], MonkhorstPack(sc, [3, 3, 3], size=1./3))
This example creates a zoomed-in view of the \(\Gamma\)-point by replacing it with a 4x4x4 Monkhorst-Pack grid.
>>> sc = SuperCell(1.) >>> mp = MonkhorstPack(sc, [3, 3, 3]) >>> mp.replace([0, 0, 0], MonkhorstPack(sc, [4, 4, 4], size=1./3))
This example creates a zoomed-in view of the \(\Gamma\)-point by replacing it with a 4x4x1 Monkhorst-Pack grid.
>>> sc = SuperCell(1.) >>> mp = MonkhorstPack(sc, [3, 3, 3]) >>> mp.replace([0, 0, 0], MonkhorstPack(sc, [4, 4, 1], size=1./3))
- Raises
SislError – if the size of the replacement
MonkhorstPack
grid is not compatible with the k-point spacing in this object.
- 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
- Returns
in units of 1/Ang
- Return type
- toreduced(k)
Transfer a k-point in Cartesian coordinates to the reduced coordinates
- Parameters
- Returns
in units of reciprocal lattice vectors ]-0.5 ; 0.5] (if k is in the primitive cell)
- Return type
- volume(ret_dim=False, periodic=None)
Calculate the volume of the full Brillouin zone of the parent
This will return the volume depending on the dimensions of the system. Here the dimensions of the system is determined by how many dimensions have auxilliary supercells that can contribute to Brillouin zone integrals. Therefore the returned value will have differing units depending on dimensionality.
- Parameters
- Returns
vol – the volume of the Brillouin zone. Units are Ang^D with D being the dimensionality. For 0D it will return 0.
dimensionality (int) – the dimensionality of the volume
- property weight
Weight of the k-points in the
BrillouinZone
object