sisl.physics.brillouinzone module¶

Different tools for contsructing k-points and paths in the Brillouin zone

class sisl.physics.brillouinzone.BrillouinZone(sc)[source]¶

Bases: sisl.supercell.SuperCellChild

A class to construct Brillouin zone related quantities

It takes a super-cell as an argument and can then return the k-points in non-reduced units from reduced units.

Attributes

`cell`	Returns the inherent `SuperCell` objects `cell`
`n_s`	Returns the inherent `SuperCell` objects `n_s`
`nsc`	Returns the inherent `SuperCell` objects `nsc`
`rcell`	Returns the inherent `SuperCell` objects `rcell`
`sc_off`	Returns the inherent `SuperCell` objects `sc_off`
`vol`	Returns the inherent `SuperCell` objects `vol`

Methods

`__call__`(k[, reduced])	Return the k-point in 1/Ang coordinates
`add_vacuum`(vacuum, axis)	Add vacuum along the `axis` lattice vector
`is_orthogonal`()	Return true if all cell vectors are linearly independent
`k`(kb)	Return the k-point in 1/Ang coordinates
`kb`(k)	Return the k-point in reduced coordinates
`sc_index`(args, *kwargs)	Call local `SuperCell` object `sc_index` function
`set_nsc`(nsc)	Set the number of super-cells in the `SuperCell` object
`set_sc`(sc)	Overwrites the local supercell
`set_supercell`(sc)	Overwrites the local supercell

Initialize a BrillouinZone object from a given SuperCell

Parameters:

sc : SuperCell or array_like

the attached supercell

Attributes

`cell`	Returns the inherent `SuperCell` objects `cell`
`n_s`	Returns the inherent `SuperCell` objects `n_s`
`nsc`	Returns the inherent `SuperCell` objects `nsc`
`rcell`	Returns the inherent `SuperCell` objects `rcell`
`sc_off`	Returns the inherent `SuperCell` objects `sc_off`
`vol`	Returns the inherent `SuperCell` objects `vol`

Methods

`__call__`(k[, reduced])	Return the k-point in 1/Ang coordinates
`add_vacuum`(vacuum, axis)	Add vacuum along the `axis` lattice vector
`is_orthogonal`()	Return true if all cell vectors are linearly independent
`k`(kb)	Return the k-point in 1/Ang coordinates
`kb`(k)	Return the k-point in reduced coordinates
`sc_index`(args, *kwargs)	Call local `SuperCell` object `sc_index` function
`set_nsc`(nsc)	Set the number of super-cells in the `SuperCell` object
`set_sc`(sc)	Overwrites the local supercell
`set_supercell`(sc)	Overwrites the local supercell

k(kb)[source]¶: Return the k-point in 1/Ang coordinates

kb(k)[source]¶: Return the k-point in reduced coordinates

class sisl.physics.brillouinzone.PathBZ(sc, points, divisions)[source]¶

Bases: sisl.physics.brillouinzone.BrillouinZone

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

Attributes

`cell`	Returns the inherent `SuperCell` objects `cell`
`n_s`	Returns the inherent `SuperCell` objects `n_s`
`nsc`	Returns the inherent `SuperCell` objects `nsc`
`rcell`	Returns the inherent `SuperCell` objects `rcell`
`sc_off`	Returns the inherent `SuperCell` objects `sc_off`
`vol`	Returns the inherent `SuperCell` objects `vol`

Methods

`__call__`(k[, reduced])	Return the k-point in 1/Ang coordinates
`add_vacuum`(vacuum, axis)	Add vacuum along the `axis` lattice vector
`is_orthogonal`()	Return true if all cell vectors are linearly independent
`k`(kb)	Return the k-point in 1/Ang coordinates
`kb`(k)	Return the k-point in reduced coordinates
`lineark`()	A 1D array which corresponds to the delta-k values of the path
`sc_index`(args, *kwargs)	Call local `SuperCell` object `sc_index` function
`set_nsc`(nsc)	Set the number of super-cells in the `SuperCell` object
`set_sc`(sc)	Overwrites the local supercell
`set_supercell`(sc)	Overwrites the local supercell

Instantiate the PathBZ by a set of special points separated in divisions

Parameters:

sc : SuperCell or array_like

the unit-cell of the Brillouin zone

points : array_like of float

a list of points that are the corners of the path

divisions : 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 points.

Attributes

`cell`	Returns the inherent `SuperCell` objects `cell`
`n_s`	Returns the inherent `SuperCell` objects `n_s`
`nsc`	Returns the inherent `SuperCell` objects `nsc`
`rcell`	Returns the inherent `SuperCell` objects `rcell`
`sc_off`	Returns the inherent `SuperCell` objects `sc_off`
`vol`	Returns the inherent `SuperCell` objects `vol`

Methods

`__call__`(k[, reduced])	Return the k-point in 1/Ang coordinates
`add_vacuum`(vacuum, axis)	Add vacuum along the `axis` lattice vector
`is_orthogonal`()	Return true if all cell vectors are linearly independent
`k`(kb)	Return the k-point in 1/Ang coordinates
`kb`(k)	Return the k-point in reduced coordinates
`lineark`()	A 1D array which corresponds to the delta-k values of the path
`sc_index`(args, *kwargs)	Call local `SuperCell` object `sc_index` function
`set_nsc`(nsc)	Set the number of super-cells in the `SuperCell` object
`set_sc`(sc)	Overwrites the local supercell
`set_supercell`(sc)	Overwrites the local supercell

lineark()[source]¶

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

This is meant for plotting

Examples

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