topological invariants calculation on 2D system
greschd at phys.ethz.ch
Thu Sep 27 20:22:31 CEST 2018
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.
On 27.09.2018 14:38, Yifan GAO wrote:
> 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,
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