[Wien] Confirming Chern z2 topological invariants using BerryPhase

[Rubel, Oleg]

Dear Burhan,

Thank you for trying wcc.py.

Fig. 4 in https://doi.org/10.48550/arXiv.2303.16306 plots evolution of Wannier charge centers (bands 61-78 gives that total of 18 WCCs) stored in wcc.csv file (the sample is shown and discussed on page 6 of the preprint paper). You can compare your result with our wcc.csv available from https://zenodo.org/record/7761199

Your table listed below gives the total phase (essentially a sum of those 18 WCCs). Bi2Se3 is a centrosymmetric material and, thus, the total phase = 0. Therefore, this table is not useful here. But if you try a Chern insulator, the table should show a 2pi jump.

For the speed of light you need to search older posts in the mailing list. I found suggestions there.

I hope it will help
Oleg

> -----Original Message-----
> From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> On Behalf Of
> Burhan Ahmed
> Sent: Wednesday, July 26, 2023 1:40 PM
> To: wien at zeus.theochem.tuwien.ac.at
> Subject: [Wien] Confirming Chern z2 topological invariants using BerryPhase
> 
> 	Caution: External email.
> 
> 
> Dear experts, I want to reproduce the results for the confirmation of Chern
> and Z2 topological invariants as calculated in the manuscript “Software
> implementation for calculating Chern and ℤ2 topological invariants of
> crystalline solids with WIEN2k all-electron density functional package” by
> Gomez, et. al. https://doi.org/10.48550/arXiv.2303.16306 (DOI:
> 10.48550/arXiv.2303.16306).
> 
> 
> 
> For this I have tried with the tutorial by Rubel available in
> https://github.com/rubel75/BerryPI  When I run the wcc.py in my case
> directory (where I have done my PBE+SOC calculation)  I got the following
> results
> 
> Total Berry phase on each Wislon loop for bands 61-78:
> 
> ------------------------------------------------------
> 
> i           k            Phase wrap.    Phase unwrap.
> 
>                             (rad)           (rad)
> 
> ------------------------------------------------------
> 
> 1  [0.000, 0.000, ***]     56.549           0.000
> 
> 2  [0.000, 0.026, ***]     56.549          -0.000
> 
> 3  [0.000, 0.053, ***]     56.549          -0.000
> 
> 4  [0.000, 0.079, ***]     56.549           0.000
> 
> 5  [0.000, 0.105, ***]     56.549           0.000
> 
> 6  [0.000, 0.132, ***]     56.549          -0.000
> 
> 7  [0.000, 0.158, ***]     56.549          -0.000
> 
> 8  [0.000, 0.184, ***]     56.549          -0.000
> 
> 9  [0.000, 0.211, ***]     56.549           0.000
> 
> 10  [0.000, 0.237, ***]     56.549          -0.000
> 
> 11  [0.000, 0.263, ***]     56.549           0.000
> 
> 12  [0.000, 0.289, ***]     56.549          -0.000
> 
> 13  [0.000, 0.316, ***]     56.549          -0.000
> 
> 14  [0.000, 0.342, ***]     56.549          -0.000
> 
> 15  [0.000, 0.368, ***]     56.549          -0.000
> 
> 16  [0.000, 0.395, ***]     56.549          -0.000
> 
> 17  [0.000, 0.421, ***]     56.549          -0.000
> 
> 18  [0.000, 0.447, ***]     56.549           0.000
> 
> 19  [0.000, 0.474, ***]     56.549           0.000
> 
> 20  [0.000, 0.500, ***]     56.549           0.000
> 
> ------------------------------------------------------
> 
> Here "***" refer to the direction of the Wilson loop.
> 
> 
> 
> Where the value of wrap. remains constant in my case. I don't know what the
> mistake I have done. Also in the manuscript by Gomez and Rubel there is a plot
> in Figure 4 (a,b,c,d). I want to know how to plot this graph (is it from .csv
> file?). Also they have performed a reduce SOC calculation by increasing the
> speed of light from 137 to 300. In which file/step we can change the value of
> c.
> 
> 
> 
> Dear experts if possible please upload a video tutorial my mentioning the steps
> on how to confirm Chern and Z2 topological invariants by Berryphse. It will be
> a great help for the researchers.
> 
> 
> 
> 
> 
> 
> 
> Regards
> 
> Burhan Ahmed
> 
> Research Scholar, AUS
> 
>