Z2 invariant for 2D material (or a semi-infinite slab)

koushik pal koushik.pal.physics at gmail.com
Fri Nov 24 18:33:57 CET 2017

Dear Dominik,

Thanks a lot for this clear explanation.

Best regards,

On Fri, Nov 24, 2017 at 3:07 AM, Dominik Gresch <greschd at phys.ethz.ch>

> Dear Koushik,
> Two-dimensional materials are characterized by a single Z2 invariant,
> since there is only a single plane in k-space. This is exactly the case
> described in the Kane-Mele paper: https://journals.aps.org/prl/a
> bstract/10.1103/PhysRevLett.95.146802
> For Z2Pack, there are examples showing the BHZ model:
> https://github.com/Z2PackDev/Z2Pack/blob/dev/current/example
> s/hm/bhz_model/bhz.py
> and a simple 2D tight-binding model: http://z2pack.ethz.ch/doc/2.1/
> examples/tb.html
> For the cases where your model is actually three-dimensional, you can just
> choose a fixed kz because your model should not depend on kz if it is
> effectively two-dimensional.
> Best regards,
> Dominik
> On 24.11.2017 05:30, koushik pal wrote:
>> Hello All,
>> I was wondering if it's possible to calculate Z2 invariant
>> for a 2D material (or a semi-infinite slab) using the Z2Pack code.
>> Let's say I have  a slab model with (001) surface orientation
>> (i.e. vacuum is along the z-direction of the slab). To determine
>> the topological invariant of  this (001) slab,  shall I calculate the
>> Z_2 invariant for kz=0 and kz=0.5 planes, and take their difference
>> modulo 2?
>> The problem here is the following.  As this is a slab, kz=0.5 plane
>> does not have any physical meaning. So I don't know if Z2 invariant
>> on kz=0.5 plane has some significance.
>> Please correct me if I am missing something here, and suggest me
>> ways to calculate Z2 invariant for such a slab.
>> Thanks in advance.
>> Best regards,
>> Koushik
>> Graduate student
>> Bangalore, India
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