Chern Number Calculations

[Ali Dehghan]

Dear WT development team and all users,

First of all, let me thank you for creating such a useful package. Hope for further progress.

My question is about the calculation of Chern number for a 3D bulk compound. In calculations of the Chern number, I encountered a strange case.

For Nk1=Nk2=Nk3=61, the results are
# Chern number for 6 planes
k1=0.0, k2-k3 plane:            0
k1=0.5, k2-k3 plane:            0
k2=0.0, k1-k3 plane:            0
k2=0.5, k1-k3 plane:            0
k3=0.0, k1-k2 plane:            0
k3=0.5, k1-k2 plane:            0

For Nk1=Nk2=Nk3=221, the results are
# Chern number for 6 planes
k1=0.0, k2-k3 plane:            1
k1=0.5, k2-k3 plane:            0
k2=0.0, k1-k3 plane:           -1
k2=0.5, k1-k3 plane:            0
k3=0.0, k1-k2 plane:            1
k3=0.5, k1-k2 plane:            0

For Nk1=Nk2=Nk3=121, the results are
# Chern number for 6 planes
k1=0.0, k2-k3 plane:            1
k1=0.5, k2-k3 plane:            0
k2=0.0, k1-k3 plane:           -1
k2=0.5, k1-k3 plane:            0
k3=0.0, k1-k2 plane:            0
k3=0.5, k1-k2 plane:            0

what’s happened? Why the results depend on the Nk? Which is true?

please let me know your comments.

Best wishes,

Ali

 

• This topic was modified 5 years, 10 months ago by Ali Dehghan.

[Brook]

Hi Ali,

Could you please post the Wilson loop plots which can be generated by

“gnuplot wanniercenter3D_Chern.gnu”?

 

There could be Weyl point happening which would generate the singularity of the Berry curvature. You could check with the “FindNodes_calc=T” by setting Nk1=10;Nk2=10;Nk3=10.

 

By the way, when using Chern_3D_calc=T, you don’t have to set Nk3. Only Nk1 and Nk2 are relevant.

 

 

[Ali Dehghan]

Dear QuanSheng,

Thanks for prompt reply. Please find the attached files and let me know your useful comments.

Best wishes,

Ali

• This reply was modified 5 years, 10 months ago by Ali Dehghan.

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