26: Gallium Arsenide — Selective localization and constrained centres

• Outline: Application of the selectively localised Wannier function (SLWF) method to gallium arsenide (GaAs), following the example in Ref. ¹, which is essential reading for this tutorial tutorial.

• Directory: tutorials/tutorial26/ Files can be downloaded from here

• Input files:

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

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

  • GaAs.pw2wan The input file for pw2wannier90

  • GaAs.win The wannier90 and postw90 input file

 

1. Run pwscf to obtain the ground state of Gallium Arsenide

   Terminal

   pw.x < GaAs.scf > scf.out
   

2. Run pwscf to obtain the ground state of Gallium Arsenide

   Terminal

   pw.x < GaAs.nscf > nscf.out
   

3. Run Wannier90 to generate a list of the required overlaps (written into the GaAs.nnkp file)

   Terminal

   wannier90.x -pp GaAs
   

4. Run pw2wannier90 to compute:

   • The overlaps \(\langle u_{n\bf{k}}|u_{n\bf{k+b}}\rangle\) between Bloch states (written in the GaAs.mmn file)

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

   Terminal

   pw2wannier90.x < GaAs.pw2wan > pw2wan.out
   

5. Inspect the .win file.

   • Make sure you understand the new keywords corresponding to the selective localisation algorithm.

   • Run wannier90 to compute the SLWFs, in this case using one objective Wannier function.

   Terminal

   wannier90.x GaAs
   

   To constrain the centre of the SLWF you need to add slwf_constrain = true and\ slwf_lambda = 1 to the input file and uncomment the slwf_centres block. This will add a penalty functional to the total spread, which will try to constrain the centre of the SLWF to be on the As atom (as explained in Ref. ¹, particularly from Eq. 24 to Eq. 35).

   Look at the value of the penalty functional, is this what you would expect at convergence? Does the chosen value of the Lagrange multiplier slwf_lambda give a SLWF function centred on the As atom?

   Alternatively, you can modify the slwf_centres block to constrain the centre of the SLWF to be on the Ga atom. Do you need a different value of slwf_lambda in this case to converge? Take a look at the result in Vesta and explain what you see. Do these functions transform like the identity under the action of the \(T_d\) group?

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1. Runzhi Wang, Emanuel A. Lazar, Hyowon Park, Andrew J. Millis, and Chris A. Marianetti. Selectively localized wannier functions. Physical Review B, 10 2014. doi:10.1103/PhysRevB.90.165125. ↩↩