General setup for Vasp

[Dominik Gresch]

Dear Jiaduo Zhu,

In the example of Bi for VASP, we used a POTCAR file with ZVAL = 5 -- 
with SOC, this gives an occupancy of 10 electrons per UC. For the Z2Pack 
calculation, we choose to look at the 10 lower bands. Note that this is 
not necessarily the same as the occupied bands, especially in the case 
of semimetals with indirect band gap. However, it is still possible to 
calculate the topology of these bands, so long as there is no direct 
band gap closure. Since we study only the 10 lowest bands, we use 
exclude_bands 11 - 15 in the wannier90.win file.

The topology of a Dirac cone can usually be determined by studying a 
sphere surrounding the Dirac cone. However, unlike the case for Weyl 
nodes, it is not enough to just determine the Chern number on this 
sphere, since the two superimposed Weyl nodes which make up the Dirac 
node have opposite contributions to the Chern number. For this reason, 
it is necessary to utilize the symmetry which stabilizes the Dirac cone 
in determining its topological nature. See 
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.075146, 
Section V.D for an example of applying Z2Pack to a Dirac semimetal. Now 
to answer your question -- it is indeed correct to exclude the higher 
energy bands. If both the energy bands above and below the Dirac node 
were to be considered, their effects would cancel out to give a trivial 
topology.

Since you seem to be interested in 2D materials, it might be possible / 
necessary to instead consider just a line around the Dirac node. Since 
the Dirac node is effectively a 'line node' in a 2D system (being 
extended in the third dimension). As a result, the Berry phase around it 
should be half-integer for a Weyl node. Again, the symmetry stabilizing 
the Dirac node would need to be considered to see how this translates to 
the Dirac node.

It is not entirely true that the KPOINTS setup is always '1 1 7' -- 
Z2Pack automatically increases the number of k-points along the line 
which it is currently calculating until convergence in the Wannier 
charge centers is reached. As such, you should not have to directly 
change the k-mesh setting. If you wish to change how the number of 
k-points is changed (maybe for performance reasons, or to increase the 
maximum number of k-points along the line), you can change the 
'iterator' keyword in z2pack.surface.run: 
http://z2pack.ethz.ch/doc/2.0/surface.html#z2pack.surface.run

And finally, there is unfortunately no other example for 2D systems 
available at the moment.

Best regards,

Dominik Gresch


On 06.04.2017 11:49, 朱家铎 wrote:
> Dear sir,
>
> I would like to calculate z2 invariants of a 2D system under VASP. There are a few issues, which confused me.
> 1. I tried the example of Bi for vasp. But SOC needs more bands than the posted INCAR which contains only 15 bands. So, the results never comes out. And I am also confused the exclude bands in the wannier90.win, because the fermi level can be pined by the Dirac cones usually. In this case, I would like to know if it is correct to exclude the higher energy band of the Dirac cone?
>
> 2. The KPOINTS setup is always 1 1 7 (I followed examples of Bi) , Is there suggestions for the correct k-mesh setting? ps: I tried ‘z2pack.fp.kpoint.vasp(5)’ , the message shows the kpt
>   can not be int.
> 3. Is there a more general example for 2D system, for example Graphene.
>
> Thank you for the kind help!
>
> Jiaduo Zhu