[Wannier] Discrepancy in Z₂ Invariant Results for Bi₂Se₃ Using WannierTools

[Poonam Sharma]

Dear All,
I have performed Z₂ invariant calculations for Bi₂Se₃ using
WannierTools (with VASP). For reference, I followed the example
provided in the official documentation:
https://wannier-tools.readthedocs.io/en/latest/tutorials/Bi2Se3.html
In that example, the Z₂ invariants for the six time-reversal invariant
momentum (TRIM) planes are reported as:

k₁ = 0.0, k₂-k₃ plane: z₂ = 1

k₁ = 0.5, k₂-k₃ plane: z₂ = 0

k₂ = 0.0, k₁-k₃ plane: z₂ = 1

k₂ = 0.5, k₁-k₃ plane: z₂ = 0

k₃ = 0.0, k₁-k₂ plane: z₂ = 1

k₃ = 0.5, k₁-k₂ plane: z₂ = 0

However, in my case, using the same POSCAR file from the tutorial
(https://github.com/quanshengwu/wannier_tools) and following the same
procedure, I obtained:

k₁ = 0.0, k₂-k₃ plane: z₂ = 1

k₁ = 0.5, k₂-k₃ plane: z₂ = 0

k₂ = 0.0, k₁-k₃ plane: z₂ = 1

k₂ = 0.5, k₁-k₃ plane: z₂ = 0

k₃ = 0.0, k₁-k₂ plane: z₂ = 0

k₃ = 0.5, k₁-k₂ plane: z₂ = 1

So, for the k₃ direction, my results are exactly the opposite of those
reported in the example.
Here is my POSCAR file:
Bi2Se3
1.0
-2.069  -3.583614  0.000000
 2.069  -3.583614  0.000000
 0.000   2.389075  9.546667
Bi   Se
 2   3
Direct
 0.3990    0.3990    0.6970
 0.6010    0.6010    0.3030
 0     0     0.5
 0.2060    0.2060    0.1180
 0.7940    0.7940    0.8820

I'm unable to figure out why this discrepancy is occurring. I am using
VASP.6.4.3, and my projection part is coming completely fine (perfect
overlapping).
Also, when I am using the provided wannier90_hr.dat file and
calculated the  Z₂ values, it is coming correct with VASP.6.4.3. I am
new to these calculations, please suggest as I am not getting why this
is happening. If my output files are required, plet let me know.