KMesh

This is the new version of the irreducible_kpts, and has the up to date algorithms that is implemented in the new version of the software suite.

The main concept of the code is to dramatically reduce the speed bottle neck that is currently in the irreducible_kpts, irreducible_kpts_n and tetrahedrom codes, re-think the algorithms. One major point is to utilize the newly developed t-point finder algorithm and have the ability to index points at constant complexity to reduce indexing time cost. We also need to get rid of the “tetra” flag that is in the old irreducibe k-points code, which is mostly redundant and confusing. Update irreducible points finder algorithm to expoit vectorization and achive execution speed similar to even faster than the Fortran implementation in the old code.

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class KMesh(supa, pgn=“C1”, lattice_vecs=np.eye(3), strict_symmetry=True, decimal=6)

K-vectors that fit in a given supercell with symmetry.

Parameters

• supa : str or array of int Super cell matrix
• pgn : str or Point_Group object The point group from which the symmetry is applied.
• lattice_vecs : array of float, optional, default identity The lattice vectors.
• strict_symmetry : bool, optional, default True Whether to impose strict symmetry, when imposed K-point rotation to non-grid point is not allowed.
• decimal : int, optional, default 6 The decimal points for tolerance.

Attributes

• kvecs_int : array of int, shape(self.vol, 3) Integer form of K-vectors in the K-mesh
• kvecs_ibz_kvec_index_map : array of int, shape(self.vol,) Index of irreducible K-vectors in the original K-vector list of each K-vectors in the K-mesh.
• kvecs_ibz_kvec_index : array of int, shape(self.vol,) Index of irreducible K-vectors in the original K-vector list.
• kvecs_ibz_map : array of int, shape(self.vol,) Index of the irreducible K-vectors in the irreducible K-vector list of each K-vectors in the K-mesh.
• kvecs_ibz_mult : array of int, shape(self.vol,) The multiplicity of each irreducible K-vectors.
• kvecs_ibz_trans : array of str, shape(self.vol,) The point group transformations that transform the K-vectors in to their corresponding irreducible K-vectors.
• kvecs_ibz_int : array of int, shape(self.vol, 3) Irreducible K-vectors in integer form.

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class DiagKMesh(supa, pgn, lattice_vecs)

K-vectors of diagonal supercells with symmetry

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class Tetrahedra(DiagKMesh):

K-vectors for tetrahedron integration of the reciprocal space

Attributes

• tet_kvec_ind : array of int, shape(self.vol * 6, 4) Tetrahedra in terms of indices of irreducible K-vectors in the irreducible K-vector list.
• itet_kvec_ind : array of int, shape(N, 4) Irreducible tetrahedra in terms of indices of irreducible K-vectors in the irreducible K-vector list.
• itet_map : array of int, shape(self.vol * 6, ) The index of irreducible tetrahedra of each tetradedron.
• itet_mult : array of int, shape(N) The multiplicity of each irreducible tetrahedra.

import numpy as np
from kmesh import KMesh, DiagKMesh, Tetrahedra

lattice_vecs = np.array([[np.sqrt(3)/2, 0.5, 0], [np.sqrt(3)/2, -0.5, 0], [0, 0, 10]])

kmesh1 = KMesh(supa="2 -1 0; -1 2 0; 0 0 1", pgn="D6h", lattice_vecs=lattice_vecs)

kmesh1.kvecs_fraction

array([[Fraction(0, 1), Fraction(0, 1), Fraction(0, 1)],
       [Fraction(2, 3), Fraction(1, 3), Fraction(0, 1)],
       [Fraction(1, 3), Fraction(2, 3), Fraction(0, 1)]], dtype=object)

# Find the index of a k-point at constant time complexity O(1)
kmesh1.get_index_Fraction(kmesh1.kvecs_fraction[2])

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