MonkhorstPack¶
-
class
sisl.physics.brillouinzone.
MonkhorstPack
(parent, nkpt, displacement=None, size=None, centered=True, trs=True)[source]¶ Create a Monkhorst-Pack grid for the Brillouin zone
- Parameters
- parentobject or array_like
An object with associated parent.cell and parent.rcell or an array of floats which may be turned into a
SuperCell
- nktparray_like of ints
a list of number of k-points along each cell direction
- displacementfloat 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
- sizefloat 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.
- centeredbool, optional
whether the k-points are \(\Gamma\)-centered (for zero displacement)
- trsbool, 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)
Attributes
A list of all k-points (if available)
Weight of the k-points in the
BrillouinZone
objectMethods
__init__
(self, parent, nkpt[, displacement, …])Initialize self.
asarray
(self)Return self with
numpy.ndarray
returned quantitiesasaverage
(self)Return self with k-averaged quantities
asgrid
(self)Return self with Grid quantities
aslist
(self)Return self with list returned quantities
asnone
(self)Return self with None, this may be done for instance when wrapping the function calls.
assum
(self)Return self with summed quantities
asyield
(self)Return self with yielded quantities
call
(self, func, \*args, \*\*kwargs)Call the function func and run as though the function has been called
copy
(self)Create a copy of this object
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
(self[, ret_weight])An iterator for the k-points and (possibly) the weights
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 separationsreplace
(self, k, mp)Replace a k-point with a new set of k-points from a Monkhorst-Pack grid
set_parent
(self, parent)Update the parent associated to this object
tocartesian
(self, k)Transfer a k-point in reduced coordinates to the Cartesian coordinates
toreduced
(self, k)Transfer a k-point in Cartesian coordinates to the reduced coordinates
write
(self, sile, \*args, \*\*kwargs)Writes k-points to a
tableSile
.-
asarray
(self)¶ Return self with
numpy.ndarray
returned quantitiesThis forces the
__call__
routine to return a single array.See also
Notes
All invocations of sub-methods are added these keyword-only arguments:
- etabool, optional
if true a progress-bar is created, default false.
- wrapcallable, 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)
To compute multiple things in one go one should use wrappers to contain the calculation
>>> E = np.linspace(-2, 2, 100) >>> dist = get_distribution('gaussian', smearing=0.1) >>> def wrap(es, parent, k, weight): ... DOS = es.DOS(E, distribution=dist) ... PDOS = es.PDOS(E, distribution=dist) ... occ = es.occupation() ... spin_moment = (es.spin_moment(E, distribution=dist) * occ.reshape(-1, 1)).sum(0) ... return oplist([DOS, PDOS, spin_moment]) >>> bz = BrillouinZone(hamiltonian) >>> DOS, PDOS, spin_moment = bz.asaverage().eigenstate(wrap=wrap)
-
asaverage
(self)¶ Return self with k-averaged quantities
This forces the
__call__
routine to return a single k-averaged value.See also
Notes
All invocations of sub-methods are added these keyword-only arguments:
- etabool, optional
if true a progress-bar is created, default false.
- wrapcallable, 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)
>>> obj = BrillouinZone(Hamiltonian) >>> obj.asaverage() >>> E = np.linspace(-2, 2, 100) >>> def wrap(es): ... return es.DOS(E), es.PDOS(E) >>> DOS, PDOS = obj.eigenstate(wrap=wrap)
-
asgrid
(self)[source]¶ Return self with Grid quantities
This forces the
__call__
routine to return all k-point values in a regular grid.The calculation of values on a grid requires some careful thought before running the calculation as the returned grid may be somewhat difficult to comprehend.
See also
Notes
All invocations of sub-methods are added these keyword-only arguments:
- etabool, optional
if true a progress-bar is created, default false.
- wrapcallable, optional
a function that accepts the output of the given routine and post-process it. Defaults to
lambda x: x
.- data_axisint, optional
the Grid axis to put in the data values in. Has to be specified if the subsequent routine calls return more than 1 data-point per k-point.
- grid_unit{‘b’, ‘Ang’, ‘Bohr’}, optional
for ‘b’ the returned grid will be a cube, otherwise the grid will be the reciprocal lattice vectors (for any other value) and in the given reciprocal unit (‘Ang’ => 1/Ang)
Examples
>>> obj = MonkhorstPack(Hamiltonian, [10, 1, 10]) >>> grid = obj.asgrid().eigh(data_axis=1)
-
aslist
(self)¶ Return self with list returned quantities
This forces the
__call__
routine to return a list with returned values.See also
Notes
All invocations of sub-methods are added these keyword-only arguments:
- etabool, optional
if true a progress-bar is created, default false.
- wrapcallable, 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
(self)¶ Return self with None, this may be done for instance when wrapping the function calls.
This forces the
__call__
routine to returnNone
. This usage is mainly intended when creating custom wrap function calls.See also
Notes
All invocations of sub-methods are added these keyword-only arguments:
- etabool, optional
if true a progress-bar is created, default false.
- wrapcallable, 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
(self)¶ Return self with summed quantities
This forces the
__call__
routine to return all k-point values summed.See also
Notes
All invocations of sub-methods are added these keyword-only arguments:
- etabool, optional
if true a progress-bar is created, default false.
- wrapcallable, 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)
>>> E = np.linspace(-2, 2, 100) >>> dist = get_distribution('gaussian', smearing=0.1) >>> def wrap(es, parent, k, weight): ... DOS = es.DOS(E, distribution=dist) * weight ... PDOS = es.PDOS(E, distribution=dist) * weight ... occ = es.occupation() ... spin_moment = (es.spin_moment(E, distribution=dist) * occ.reshape(-1, 1)).sum(0) * weight ... return oplist([DOS, PDOS, spin_moment]) >>> bz = BrillouinZone(hamiltonian) >>> DOS, PDOS, spin_moment = bz.assum().eigenstate(wrap=wrap)
-
asyield
(self)¶ Return self with yielded quantities
This forces the
__call__
routine to return a an iterator which may yield the quantities calculated.See also
Notes
All invocations of sub-methods are added these keyword-only arguments:
- etabool, optional
if true a progress-bar is created, default false.
- wrapcallable, 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)
-
call
(self, func, *args, **kwargs)¶ Call the function func and run as though the function has been called
This is a wrapper to call user-defined functions not attached to the parent object.
The below example shows that the equivalence of the call.
- Parameters
- funccallable
method used
- *args :
arguments passed to func in the call sequence
- **kwargs :
keyword arguments passed to func in the call sequence
Examples
>>> H = Hamiltonian(...) >>> bz = BrillouinZone(H) >>> bz.eigh() == bz.call(H.eigh)
-
property
cell
¶
-
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
- nint
number of points in the grid. If trs is
True
this may be smaller than n- displfloat, optional
the displacement of the grid
- sizefloat, optional
the total size of the Brillouin zone to sample
- centeredbool, optional
if the points are centered
- trsbool, optional
whether time-reversal-symmetry is applied
- Returns
- knp.ndarray
the list of k-points in the Brillouin zone to be sampled
- wnp.ndarray
weights for the k-points
-
static
in_primitive
(k)¶ Move the k-point into the primitive point(s) ]-0.5 ; 0.5]
- Parameters
- karray_like
k-point(s) to move into the primitive cell
- Returns
- kall k-points moved into the primitive cell
-
iter
(self, ret_weight=False)¶ An iterator for the k-points and (possibly) the weights
- Parameters
- ret_weightbool, optional
if true, also yield the weight for the respective k-point
- Yields
- kptk-point
- weightweight of k-point, only if ret_weight is true.
-
property
k
¶ A list of all k-points (if available)
-
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
- scSuperCell, or SuperCellChild
the supercell used to construct the k-points
- N_or_dkint
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.
- kRfloat
radius of the k-point. In 1/Ang
- normalarray_like of float
normal vector to determine the circle plane
- origoarray_like of float
origo of the circle used to generate the circular parameterization
- loopbool, optional
whether the first and last point are equal
- Returns
- BrillouinZonewith 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 separationsGenerator 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
- scSuperCell, or SuperCellChild
the supercell used to construct the k-points
- funccallable
method that parameterizes the k-points, must at least accept two arguments,
sc
(super-cell object containing the unit-cell and reciprocal cell) andfrac
(current parametrization fraction, between 0 and(N-1)/N
. It must return a k-point in 3 dimensions.- Nint
number of k-points generated using the parameterization
- argslist of arguments
arguments passed directly to func
- kwargsdictionary of arguments
keyword arguments passed directly to func
-
property
rcell
¶
-
replace
(self, k, mp)[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
- karray_like
k-point in this object to replace
- mpMonkhorstPack
object containing the replacement k-points.
- Raises
- SislErrorif the size of the replacement
MonkhorstPack
grid is not compatible with the k-point spacing in this object.
- SislErrorif the size of the replacement
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))
-
set_parent
(self, parent)¶ Update the parent associated to this object
- Parameters
- parentobject or array_like
an object containing cell vectors
-
tocartesian
(self, k)¶ Transfer a k-point in reduced coordinates to the Cartesian coordinates
- Parameters
- klist of float
k-point in reduced coordinates
- Returns
- kin units of 1/Ang
-
toreduced
(self, k)¶ Transfer a k-point in Cartesian coordinates to the reduced coordinates
- Parameters
- klist of float
k-point in Cartesian coordinates
- Returns
- kin units of reciprocal lattice vectors ]-0.5 ; 0.5] (if k is in the primitive cell)
-
property
weight
¶ Weight of the k-points in the
BrillouinZone
object
-
write
(self, sile, *args, **kwargs)¶ Writes k-points to a
tableSile
.This allows one to pass a tableSile or a file-name.