[Wannier] Integration over the half Brillouin zone

Jonathan Yates jonathan.yates at materials.ox.ac.uk
Tue Sep 16 18:03:55 CEST 2014

On 16 Sep 2014, at 06:32, 고운 <rhdnsi at hanmail.net> wrote:

> Dear experts
> I am trying to use Wannier90 for the quantum spin Hall (QSH) phase in graphene and silicene.
> According to Kane and Melle, the Berry curvature sould be integrated over the half Brillouin zone
> (but not over the full Brillouin zone) for the spin Chern number or spin Hall conductivity in the QSH phase.
> Wannier90 calculates the anomalous Hall conductivity (AHC) by integrating the Berry curvature over
> the full Brillouin zone. Since the quantized AHC is the Chern number in units of e^2/h, I expect that
> the AHC calculated by integration of the Berry curvature over the half Brillouin zone gives the spin Chern
> number in the QSH phase. 
> The problem is how to integrate the Berry curvature over the half Brillouin zone (but not over the full Brillouin zone) in Wannier90.
> How can i overcome the problem? Is there a tricky way or a simple modification of the code?

I think it is well worth your while reading the relevant sections of the code and seeing how they implement the physical equations. The Berry phase routines are largely the work of Ivo Souza, and they are very clearly presented and commented. In your case the key routine is in scr/postw90/berry.f90

 In that file you will find a simple loop over points in the Brillouin Zone - I suspect it would not be hard to modify this to do what you want. You will also see from the code that there is an undocumented feature which allows you to read the points from a file (be aware that this will not work for all properties - you need to think carefully to see if this is appropriate for your problem).

Note this is a practical answer - I haven’t tried to think about the physics of your question.


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