Contents

Modulation

class spgrep_modulation.modulation.Modulation(primitive_symmetry, supercell, dynamical_matrix, qpoint, nac_q_direction=None, factor=15.633302300230191, degeneracy_tolerance=0.0001, seed=0)[source]

Generate modulated cells based on dynamical matrix of phonon.

Generate modulated cells based on dynamical matrix of phonon.

Parameters

  • primitive_symmetry (phonopy.structure.symmetry.Symmetry) – phonopy’s Symmetry object for primitive cell

  • supercell (phonopy.structure.cells.Supercell) – phonopy’s supercell object to apply modulation

  • dynamical_matrix (phonopy.harmonic.dynamical_matrix.DynamicalMatrix) – phonopy’s dynamical matrix object

  • qpoint (array, (3, )) –

  • nac_q_direction – Used to calculate dynamical matrix around Gamma point if specified

  • factor (float) – Unit conversion

  • degeneracy_tolerance (float) – Absolute tolerance to groupby phonon frequencies in factor unit

  • seed (int) – Seed value for sampling modulation from degenerated modes

property dynamical_matrix

Return Phonopy’s dynamical matrix.

property primitive_symmetry

Return Phonopy’s symmetry for primitive cell.

property little_rotations

Return rotations of little group at qpoint.

property little_translations

Return translations of little group at qpoint.

property primitive

Return Phonopy’s primitive cell.

property supercell

Return Phonopy’s supercell without modulations.

property qpoint

Return qpoint.

property unit_conversion_factor

Return unit conversion for frequencies.

property degeneracy_tolerance

Return absolute tolerance to detect degenerated bands.

property eigenspaces

Return list of (eigenvalue, degenerated eigenvectors, irrep formed by the eigenvectors) of dynamical matrix.

frequency_index is the index of eigenspaces. Each frequency_index corresponds to a eigenvalue of the dynamical matrix, \(\omega_{\alpha s}^{2}\). Here, \(\alpha\) specifies irrep up to unitary equivalence and \(s\) distinguishes the irrep among equivalent irreps. eigenspaces[frequency_index] is a tuple with

  • eigenvalue: float, eigenvalue of the dynamical matrix \(\omega_{\alpha s}^{2}\)

  • eigenvectors: array, (dim, num_atoms, 3), eigenvectors[lambda, kappa, :] is an eigenvector \(\mathbf{e}(\kappa; \mathbf{q}\alpha s \lambda)\).

  • irrep: array, (little_order, dim, dim), representation matrices of the irrep \(\tilde{\Gamma}^{\mathbf{q}\alpha s}\)

get_modulated_supercell_and_modulation(frequency_index, amplitudes, arguments, return_cell=True)[source]

Return modulated cell and modulation with given amplitudes and arguments.

Parameters

  • frequency_index (int) – Index of considered eigenmodes in Modulation.eigenspaces. See Modulation.eigenspaces().

  • amplitudes (list[float], (dim, )) –

  • arguments (list[float], (dim, )) – in radian

  • return_cell (bool = True) –

get_modulated_supercells(frequency_index, maximal_displacement=0.11, max_size=1)[source]

Return modulated cells with randomly sampled arguments.

Parameters

  • frequency_index (int) – Index of considered eigenmodes in Modulation.eigenspaces. See Modulation.eigenspaces().

  • maximal_displacement (int) – Amplitude of modulation is chosen so that the maximal displacement in returned modulation is equal to maximal_displacement. Same unit as Modulation.primitive.cell.

  • max_size (int) – Number of returned modulated structures when degenerated eigenmodes are specified.

Returns

cells

Return type

list of PhonopyAtoms

get_high_symmetry_modulated_supercells(frequency_index, maximal_displacement=0.11)[source]

Return modulated cells corresponding to one-dimensional order-parameter directions of an isotropy subgroup.

Parameters

  • frequency_index (int) – Index of considered eigenmodes in Modulation.eigenspaces. See Modulation.eigenspaces().

  • maximal_displacement (int) – Amplitude of modulation is chosen so that the maximal displacement in returned modulation is equal to maximal_displacement. Same unit as Modulation.primitive.cell.

Returns

cells

Return type

list of PhonopyAtoms

Return Modulation class with supercell matrix.

eigvals_to_frequencies(eigvals)[source]

Convert eigenvalue to frequency.

apply_modulation_to_supercell(modulation)[source]

Apply modulation to supercell.

API Reference Irreps