[Wannier] Sign and shape of Wannier functions with num_iter = 0

[Choi, Moon-ki]

Hello all,


I am computing the tight-binding (TB) Hamiltonian of a monolayer MoS₂ (1×1 unit cell with three atoms) using Quantum ESPRESSO + Wannier90. I'm using d orbitals for Mo and p orbitals for S atoms.



Here is a snippet of my wannier90 settings:
```
num_iter         =  0
dis_num_iter     =  0
…
wannier_plot = True
…
begin projections
  Mo:d:z=0,0,1:x=1,0,0
  S:l=1,mr=2:z=0,0,1:x=1,0,0
  S:l=1,mr=3:z=0,0,1:x=1,0,0
  S:l=1,mr=1:z=0,0,1:x=1,0,0
end projections
```
Please note that I have set num_iter =0 because I want to preserve wannier function shape as typical orbital (px py pz dxy …) This configuration enforces the order of the p_x, p_y, p_z orbitals (Actually its p_x, p_x, p_y, p_y, p_z, p_z for two S atoms) . I expected this setup to generate the y-axis as (0,1,0).


Using wannier90 result, I’m analyzing the p–p Hamiltonian matrix (3×3) for two S atoms aligned along the x-axis (let’s call this H_deg0) and after a 60° rotation about the z-axis (H_deg60). I applied the rotation using the operator D(R), where R is the 60° rotation matrix around the z-axis.



Although the absolute values of the rotated Hamiltonian match those of H_deg60, some components (off diagonal terms) show opposite signs, which was unexpected. This discrepancy suggests that the directions of the p_x, p_y, and p_z orbitals used in Wannier90 may not align with the conventional (x, y, z) coordinate system.


I also have visualized the Wannier functions via .xsf files, it seems that the p_y orbital has an opposite sign: the yellow lobes for -y direction and  blue lobes for +y direction. This probably suggests that p_y orbital used in Wannier90 has an opposite sign, generating left-handed coordinate.

In summary, my main questions are:

  1.  Could someone explain how Wannier90 determines the sign and orientation of wannier function?
  2.  Is there a way to constrain the positions of Wannier functions at the center of each atom and enforce their shapes to resemble standard atomic orbitals (e.g., p_x, p_y, p_z, d_z^2, etc.)— to use Wannier90 like LCAO.
Best regards,
------------------
Moon-ki Choi, Ph.D.
Postdoctoral researcher
Material Research Laboratory, University of Illinois Urbana-Champaign
612-229-9732
Personal website: https://sites.google.com/view/moonkichoi/

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