Dear Patric,
For the Z2 calculation, the surface should go only across half the Brillouin zone. So, the surface should probably be lambda s, t: [s / 2, t, 0].
The reason for this is that the second half is a mirror image of the first. When you go across the full BZ, the result for the Z2 invariant will always be zero.
Best regards,
Dominik
On 28.09.2018 12:04, Yifan GAO wrote:
Dear Dominik,
Thanks for your reply! I'm really a rookie in this area.
Now I'm testing silicene(10.1103/PhysRevLett.107.076802) with Z2Pack. I successfully get the edge states by wannier90 calculation. The Z2 invariant should be 1 according to the reference. I set /num_band=num_wann=8/ to integrate the bands under the fermi level and chose /lambda s, t: (s, t, 0)/ and to calculate lines along ky.
The result given by Z2Pack shows Z2 = 0. I don't know if there's anything wrong with my calculation?
All the parameters are similar to the Bi example. I changed /search_shell/ in range of 24~96 in order to finish the calculation.
Best regards,
Patric
*From:* Dominik Gresch greschd@phys.ethz.ch *Sent:* Thursday, September 27, 2018 11:22:31 AM *To:* Yifan GAO; z2pack@lists.phys.ethz.ch *Subject:* Re: topological invariants calculation on 2D system
Dear Patric,
When calculating 2D invariants, the only Chern and Z2 invariants that can be calculated are those on the 2D Brillouin zone itself. Since you are using VASP, the 2D system is represented as a 3D system, where one dimension is very long in real space, and correspondingly very narrow in reciprocal space. As a result, the bands will be almost flat in that direction. So, the surface you need to choose for calculating the 2D invariant should be extended in the remaining two dimensions.
As a simple examle, if your unit cell is
a_1 = (1, 0, 0)
a_2 = (0, 1, 0)
a_3 = (0, 0, 200)
then you want the surface to span k_x and k_y, e.g. lambda s, t: (s, t, 0) for a Chern number. The k_z value can be chosen to be zero, but it could really be anything since the system should not depend on k_z.
Best regards,
Dominik
On 27.09.2018 14:38, Yifan GAO wrote:
Hello,
I don't quite understand how can I get the topological invariants, like Z2 and Chern, within a 2D system? I'm feeling puzzled when building the surface.
BTW I'm using vasp.
Thank you,
Patric