# 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 k space 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 k space 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 k space 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.