Irreducible K-Points N¶

This module contains the classes that deals with irreducible K-Points at arbitrary order, as well as a method that finds the points that fit in a given supercell.

Except for the get_tpoins method, most of the algorithms used in this code will go under a complete overhaul. The basic concept remains. The new algorithm will be similar to that of the kmesh module.

[1]:

import numpy as np
from coordinate_tools import coord_to_string as c2s
from irreducible_kpts_n import get_tpoints, ibz_mesh_n, k_mesh_n

get_tpoints¶

This is the method that finds all the points that fit in a given cell, it is used by the k-points finders here as well as the supercell constructors in the periodica. The detailed algorithm is described appendix D of the paper PhysRevB.100.014303.

function get_tpoints(supa, vol=None, decimals=6)¶

supa: 2d array of integers, coordinate_parse compatible format The supercell to find the points that fit in. The dimension of this matrix determines the dimension of the points.
vol: int, optional The volume of the supercell, if provided, will check if the volume match that of the supercell matrix
decimals: int, optional The decimal point of the error tolerence for handling floating point precision issues.

Examples:

[2]:

tpoints = get_tpoints("2 -1;  -1 2")
tpoints

[2]:

array([[0, 0],
       [1, 0],
       [0, 1]])

[3]:

tpoints = get_tpoints("2 -1 0;  -1 2 0;  0 0 1")
tpoints

[3]:

array([[0, 0, 0],
       [1, 0, 0],
       [0, 1, 0]])

[4]:

tpoints = get_tpoints("2 -1 0 0;  -1 2 0 0; 0 0 -1 2; 0 0 2 -1")
tpoints

[4]:

array([[0, 0, 0, 0],
       [1, 0, 0, 0],
       [0, 1, 0, 0],
       [0, 0, 0, 1],
       [1, 0, 0, 1],
       [0, 1, 0, 1],
       [0, 0, 1, 0],
       [1, 0, 1, 0],
       [0, 1, 1, 0]])

Irreducible K-Points at arbitrary order with symmetry¶

While k_mesh_n handles the permutation symmetry of the K-Points, ibz_mesh_n utilizes k_mesh_n to account for both point and permutation symmetry.

class k_mesh_n(supa,order,tetra=False,tol=1.0E-6)¶

order: int The order of the system, as well as the number of k-point that forms a single Q.
tol: float Error tolerence for floating point precision issues.

class ibz_mesh_n(supa,pgn,lattice_vecs,order=2,tetra=True,tol=1.0E-6)¶

pgn: Point_Group or str The point group of the system.
lattice_vecs: array of floats The lattice vectors of the system.
tetra: bool, optional, default to True, deprecated

Key attributes: - ksets_ibz_trans: OrderedDict The permutation and point operation that transforms to a given k-point from the matching irreducible k-point (The point symmetry is actually from the given point to the irreducible). - ksets_ibz_fraction: List of nested tuple of Fraction The irreducible Q. The one without “_fraction” suffix is the integer version (p point). - ksets_ibz_map_fraction: The map between Q and irreducible Q.