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Usage:

Given HDF5 input file 'h5_inp' (see below), use as follows (while in 'src' directory):

>>> from exciton_tb.exciton_tb import ExcitonTB

>>> extb = ExcitonTB('/path/to/h5_inp')

>>> extb.create_matrix_element_hdf5('name_of_matrix_element.hdf5')

>>> bse_hamiltonian = extb.get_bse_eigensystem_direct(solve=False)

>>> bse_eigensystem = extb.get_bse_eigensystem_direct(solve=True)

Input file:

hdf5 format with subdivisions:

Resource for h5py usage: http://docs.h5py.org/en/stable/

  • 'crystal': details about the crystal including

    • 'alat': lattice parameter

    • 'avecs': Real Space Lattice vectors

      • 'a1' : First lattice vector

      • 'a2' : Second lattice vector

    • 'gvecs': Reciprocal Space Lattice vectors

      • 'b1' : First reciprocal lattice vector

      • 'b2' : Second reciprocal lattice vector

    • 'motif': list of vectors for all positions in the cell

    • 'n_atoms': number of atoms in cell

    • 'n_spins': 1 to treat either spinless system or to not split the system into two spins. 2 to construct bse_hamiltonians for spin-up transitions and spin-down transitions.

    • 'n_orbs': total number of orbitals in the cell (not including spin)

    • 'orb_pattern': list of orbitals per atom repeat e.g. [3, 3, 5]

    • 'positions': Periodic supercell lattice vector list

    • 'trunc_alat': Distance to use in the potential near R=0

  • 'eigensystem': eigenvalue and eigenvector data

    • 'convention': Either 1 or 2, ref. https://www.physics.rutgers.edu/pythtb/formalism.html

    • 'n_spins': Set to 1 if spin is either unpresent in the calculation, or if the hamiltonian cannot be split into separable blocks corresponding to different spins. Set to 2 if the eigenvectors for different spins are calculated separately and can be placed in eigenvectors as blocks half the size.

    • 'eigenvalues': Eigenvalues for each k point. Eigenvalues from the same k point should exist in the same row in numerical order, such that the shape of 'eigenvalues' is (n_kpoints, n_states). If the eigensystem is divided by spin (a spin-separable hamiltonian), then the order of eigenvalues should have increasingly ordered spin down eigenvalues first followed by increasingly ordered spin up eigenvalues.

    • 'eigenvectors': Eigenvectors for each k point. Eigenvectors from the same k-point should be in a block of size (eigenvector_length, n_states), and these should be stacked row-wise for different k points, such that 'eigenvectors' is of size (n_kpoints*eigenvector_length, n_states). Note if different k points have different numbers of states associated with them, then the number of columns should be the largest number of states at a single k point, and for k points with less states, the latter states should appear as zeros on the right-most columns.

    • 'eigenvectors_real': Real part of the eigenvectors, see 'eigenvectors' for structural information

    • 'eigenvectors_imag': Imaginary part of the eigenvectors, see 'eigenvectors' for structural information

    • 'is_complex': True to treat the 'eigenvectors' as complex entities, otherwise, set this to False and specify 'eigenvectors_real' and 'eigenvectors_imag'

    • 'k_grid': list of reciprocal vectors that are used for the calculations

    • 'n_k': size of kgrid i.e. the grid will be nk times nk

    • 'n_con': number of conduction band states. (Not needed if 'selective' is True)

    • 'n_val': number of valence band states (Not needed if 'selective' is True)

  • 'selective': The number of bands to be used in the system are limited to avoid using all transitions when calculating the excitons, and instead to use a limited subset of bands. set to True or False.

  • 'band_edges': If selective is True, the minvalence band and max conduction band

    • 'num_states': number of states included in each eigensystem

    • 'k(idx)' idx of the kpt in the k_grid. (Note if n_spins is 2, and we wish to treat the spins separately, the values of 'vb_num' and 'cb_num' will be a list of 2 values for each spin)

      • 'vb_num': number of valence bands

      • 'cb_num': number of conduction bands

  • 'velocity_matrix': (Optional) If the conductivity of imaginary part of the dielectric function is required then the velocity matrices, will be placed here. The velocity matrix must be calculated at the same k points that are used in the calculation, and included in this file in the same order as the k points appear in 'eigensystem/k_grid'

    • 'k(idx)' Place velocity matrix here. idx of the kpt in the k_grid.