pythtb.TBModel.k_uniform_mesh#

TBModel.k_uniform_mesh(mesh_size, *, gamma_centered=False, include_endpoints=True)[source]#

Generate a uniform grid of k-points in reduced (fractional) coordinates.

The grid spans the interval \([0,1)\) along each periodic crystal direction and always contains the origin. The total number of k-points is the product of the entries in mesh_size.

Parameters:

mesh_sizearray_like: The number of k-points along each periodic direction. Its length must equal the number of periodic dimensions of the model. For example, mesh_size = [n1, n2, n3] produces a 3D mesh with n1 x n2 x n3 points.
gamma_centeredbool, optional: If True, the mesh is centered around the Gamma point, spanning the interval \([-0.5, 0.5)\) along each periodic direction. Default is False.

Added in version 2.0.0.
include_endpointsbool, optional: If True, the mesh includes the endpoint at 1.0 (or 0.5 if gamma_centered=True) along each periodic direction. Default is True.

Added in version 2.0.0.

Returns:

k_pointsnumpy.ndarray

An array of shape (n1, n2, ..., dim_k) where the final index runs over the reduced-coordinate components of each k-vector.

If mesh_size = [n1, n2, ..., nD] and the model has dim_k = D, then the returned array has shape (n1, n2, ..., nD, D).

Notes

This uniform mesh is suitable for evaluating model quantities on a regular Brillouin-zone sampling grid, e.g. via solve_ham().

Examples

Construct a 10x20x30 mesh for a model with three periodic directions:

>>> k_points = my_model.k_uniform_mesh([10, 20, 30])
>>> k_points.shape
(10, 20, 30, 3)

Solve the model on the mesh:

>>> evals = my_model.solve_ham(k_points)