# dispersion{}¶

calculate the \(\mathbf{k_{||}}\) and \(\mathbf{k_{\tiny{superlattice}}}\) (if applicable) dispersion. The energy dispersion E(**k**) along the specified paths and for the specified **k** space resolutions are completely independent from the **k** space resolution that was used within the self-consistent cycle where the k.p density has been calculated. The latter is specified in `k_integration{ }`

.

- path{ }
Calculate dispersion along custom path in k-space. Multiple instances are allowed.

- name

- value
string

name of the dispersions which also defines the names of the output files.

- point{ }
specifies points in the path through k-space. At least two k points have to be defined. Line between two such points is called segment.

- k

- value
3D float vector

k-point represented by vector \([k_x, k_y, k_z]\). The units are \(nm^{-1}\).

For 1D simulation the \(\mathbf{k_{||}}\) space is a \(k_y-k_z\) plane so \(k_y\), \(k_z\) can be freely choosed. \(k_x\) can only be different from zero, if a periodic boundary condition along the x-direction is defined and the quantum region extends over the whole x-domain.

for 2D simulation the \(\mathbf{k_{||}}\) space is a \(k_z\) axis so \(k_z\) can be freely choosed. \(kx\) can only be different from zero if a periodic boundary condition along the x-direction is defined and the quantum region extends over the whole x-domain. \(k_y\) can only be different from zero if a periodic boundary condition along the y-direction is defined and the quantum region extends over the whole y-domain.

for 3D simulation the \(\mathbf{k_{||}}\) space is empty. \(k_x\) can only be different from zero if a periodic boundary condition along the x-direction is defined and the quantum region extends over the whole x-domain. \(k_y\) can only be different from zero if a periodic boundary condition along the y-direction is defined and the quantum region extends over the whole y-domain. \(k_z\) can only be different from zero if a periodic boundary condition along the z-direction is defined and the quantum region extends over the whole z-domain.

- spacing

- value
float

specifies approximate spacing for intermediate points in the path segments in \(nm^{-1}\). Excludes

`num_points`

.- num_points

- value
integer > 1

specifies number of points (intermediate + two corner points) for each single path segment. Excludes

`spacing`

.- lines{ }
calculate dispersions along some predefined paths of high symmetry in k-space, e.g. [100], [110], [111] and their equivalents (in total maximally 13).

- name

- value
string

name of the dispersions which also defines the names of the output files.

- spacing

- value
float

specifies approximate spacing for intermediate points in the path segments in \(nm^{-1}\).

- k_max

- value
float

specifies a maximum absolute value (radius) for the k-vector in \(nm^{-1}\).

- full{ }
calculate dispersion in 1D/2D/3D k-space depending on simulation dimensionality and pereodic boundary conditions.

- name

- value
string

name of the dispersion which also defines the name of the output file.

- kxgrid{ }
specifies a

`grid{...}`

in k-space for a 1D/2D/3D plot of the energy dispersion E(kx, ky, kz). allowed only, if simulation is periodic along x-direction and current quantum region extends over the whole x-domain. The options are same as grid{}- kygrid{ }
The options are same as

`kxgrid{ }`

.- kzgrid{ }
The options are same as

`kxgrid{ }`

.- superlattice{ }
(convenience keyword) Calculate superlattice dispersion \(E(k_{SL})\) along periodic directions. The intervals are set automatically to \([-\pi/L_i, \pi/L_i]\), where \(L_i\) is the simulation domain range along periodic directions with \(i = x,y,z\).

- name

- value
string

name of the dispersion which also defines the name of the output file.

- num_points_x

- value
any integer > 1

specifies number of points along x direction in

kspace where dispersion is calculated. The simulation must be periodic along the x direction in direct space.- num_points_y

- value
any integer > 1

specifies number of points along y direction in

kspace where dispersion is calculated. The simulation must be periodic along the y direction in direct space.- num_points_z

- value
any integer > 1

specifies number of points along z direction in

kspace where dispersion is calculated. The simulation must be periodic along the z direction in direct space.- num_points

- value
any integer > 1

(convenience keyword) Specifies number of points along all appropriate directions in k space.

- output_dispersions{ }
output all defined dispersions.

- max_num

- value
any integer between 1 and 9999

number of bands to print out

- output_masses{ }
output effective masses calculated from the dispersions.

- max_num

- value
any integer between 1 and 9999

output effective masses calculated from the dispersions.