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24: Tellurium — gyrotropic effects

  • Outline: Calculate the gyrotropic effects in trigonal right-handed Te Similar to the calculations of 1

  • Directory: tutorials/tutorial24/ Files can be downloaded from here

  • Input files

    • Te.scf The pwscf input file for ground state calculation

    • Te.nscf The pwscf input file to obtain Bloch states on a uniform grid

    • Te.pw2wan The input file for pw2wannier90

    • Te.win The wannier90 input file

To make things easy, the tutorial treats Te without spin-orbit

  1. Run pwscf to obtain the ground state of tellurium

    Terminal
    pw.x < Te.scf > scf.out

  2. Run pwscf to obtain the Bloch states on a uniform 3x3x4 k-point grid

    Terminal
    pw.x < Te.nscf > nscf.out

  3. Run wannier90 to generate a list of the required overlaps (written into the Te.nnkp file).

    Terminal
    wannier90.x -pp Te

  4. Run pw2wannier90 to compute:

    • The overlaps \(\langle u_{n{\bf k}}\vert u_{m{\bf k}+{\bf b}}\rangle\) (written in the Te.mmn file)

    • The projections for the starting guess (written in the Te.amn file)

    • The matrix elements \(\langle u_{n{\bf k}+{\bf b}_1}\vert H_{\bf k}\vert u_{m{\bf k}+{\bf b}_2}\rangle\) (written in the Te.uHu file)

    • The spin matrix elements \(\langle \psi_{n{\bf k}}\vert \sigma_i\vert \psi_{m{\bf k}}\rangle\) (would be written in the Te.spn file, but only if spin-orbit is included, which is not the case for the present tutorial)

    Terminal
    pw2wannier90.x < Te.pw2wan > pw2wan.out

  5. Run wannier90 to compute the MLWFs.

    Terminal
    wannier90.x Te

  6. Add the following lines to the wannier90.win file:

    Input file
    gyrotropic=true
gyrotropic_task=-C-dos-D0-Dw-K
fermi_energy_step=0.0025
fermi_energy_min=5.8
fermi_energy_max=6.2
gyrotropic_freq_step=0.0025
gyrotropic_freq_min=0.0
gyrotropic_freq_max=0.1
gyrotropic_smr_fixed_en_width=0.01
gyrotropic_smr_max_arg=5
gyrotropic_degen_thresh=0.001
gyrotropic_box_b1=0.2 0.0 0.0
gyrotropic_box_b2=0.0 0.2 0.0
gyrotropic_box_b3=0.0 0.0 0.2
gyrotropic_box_center=0.33333 0.33333 0.5
gyrotropic_kmesh=50 50 50

  7. Run postw90 to compute the gyrotropic properties: tensors \(D\), \(\widetilde{D}\), \(K\), \(C\) (See the User Guide):

    Terminal
    postw90.x Te # (1)!
mpirun -np 8 postw90.x Te  # (2)!
    1. serial execution
    2. example of parallel execution with 8 MPI processes

    The integration in the \(k\)-space is limited to a small area around the H point. Thus it is valid only for Fermi levels near the band gap. And one needs to multiply the results by 2, to account for the H' point. To integrate over the entire Brillouin zone, one needs to remove the gyrotropic_box_\(\ldots\) parameters

  8. Now change the above lines to

    Input file
    gyrotropic=true
gyrotropic_task=-NOA
fermi_energy=5.95
gyrotropic_freq_step=0.0025
gyrotropic_freq_min=0.0
gyrotropic_freq_max=0.3
gyrotropic_smr_fixed_en_width=0.01
gyrotropic_smr_max_arg=5
gyrotropic_band_list=4-9
gyrotropic_kmesh=50 50 50

    and compute the interband natural optical activity

    Terminal
    postw90.x Te # (1)!
mpirun -np 8 postw90.x Te  # (2)!
    1. serial execution
    2. example of parallel execution with 8 MPI processes

  1. S. S. Tsirkin, P. Aguado Puente, and I. Souza. Gyrotropic effects in trigonal tellurium studied from first principles. ArXiv e-prints, October 2017. arXiv:1710.03204. ↩