Surface function setting

[YJsun00]

Hi!
I'm a beginner and tried bulk Bi2Se3 with first principle (vasp) as an exercise. I found that when I used the different orientations of the POSCAR for system, the result (Z2 invariant) is different. I set the surface function as f(s, t) = [0, s/2, t] and f(s, t) = [0.5, s/2, t]
When POSCAR is:

Bi2Se3
1.0
4.104248 0.000000 9.579474
1.965714 3.602890 9.579474
0.000000 0.000000 10.421669

The result of Z2 is 0 for both while when POSCAR is:

2.0714999999999995 1.1959810826263095 9.545333333
2.0714999999999995 1.1959810826263095 9.545333333
0.0000000000000000 -2.3919621652526191 9.545333333

The result is 1 for f(s, t) = [0, s/2, t]
Can I get some advice on how to generate surfaces according to the POSCAR? Thanks in advance!
Here is the structure of Bi2Se3. It's rhombohedral.

[greschd]

The result of Z2 is 0 for both while when POSCAR is:

2.0714999999999995 1.1959810826263095 9.545333333
2.0714999999999995 1.1959810826263095 9.545333333
0.0000000000000000 -2.3919621652526191 9.545333333

I presume there's a typo here, since the first two vectors are the same?

For the first unit cell, one of the two indices should be 1 - that should be true regardless of unit cell, as long as it is a primitive cell. Maybe there is a problem with convergence, or some other input parameter?
For example, a common mistake is not adjusting the number of bands in the inputs to both VASP and Wannier90. If you use parallelism with VASP, you may also need to account for the fact that VASP may add additional bands to "fill up" the processors, and adjust the exclude_bands parameter in Wannier90.

[YJsun00]

Thanks for the response and sorry about the typo...There should be a minus for 2.071499. I'm sure that all the other parameters are the same.
I'm not so sure whether I should change the surface function or not when the unit cell is changed. Could you please explain more in detail about the surface function f(t1. t2)? Thank you!

[greschd]

It may or may not be important, but the volume for the second unit cell is quite a bit lower for the second unit cell -- are you sure the two structures are equivalent?

The surface function is given in reduced coordinates, so the chosen function should work for both unit cells. There are more details about this definition in this section of the tutorial, or around eq. (23) in the Z2Pack book chapter.

[YJsun00]

Thanks a lot! The structures are different but I thought it wouldn't be a big problem at first. They are both rhombohedral structures with the lattice constant: (a=b=c=10.42167Ang, alpha=beta=gamma=23.1293deg) for the 1st one and (a=b=c=9.84047Ang, alpha=beta=gamma=24.3043deg) for the 2nd.
Now I'm sure that it's not because of the basis vectors. I rotated the vectors of the first one to the same direction as the second and the result would still be 0.
As for me, It's still a little weird because I'm expecting the same result due to their very similar structures.

[greschd]

As for me, It's still a little weird because I'm expecting the same result due to their very similar structures.

It might be instructive to interpolate between the two structures, and see how things change. If the invariant calculation is correct, there should be a point where the band gap closes and the invariant changes.

[YJsun00]

That is a good point! I'll try later. Thanks!