Chern Number Calculations

[Ali Dehghan]

Dear Dr. QuanSheng and all users,

Hope you are well. I was interested to study the topological properties of a compound in 3D half-Heusler structure. To start, I performed an accurate DFT calculation (with Quantum-Espresso) and extracted the spin-polarized band structure according to the band.pdf attachment file. This figure reveals that one of two spin channel (majority-channel) has two important characteristics: 1) the Dirac behavior in Gamma point and 2) the band inversion of d- and p-orbitals in the ascending order of energy (first the d-states and then the p-states are occupied). As you probably know, these two indications are necessary for a topological (or Chern) insulator. In the following, using the Wannier90 and then Wanniertools, I tried to calculate the Chern number of the compound. I should mention that the band structure calculations with these codes produced expected results. Contrary to my expectation, the chern number became zero. That’s why I doubted my calculations. I request that you, if possible, please check whether the input files are correct or not. Any suggestions are welcome. Please find the attached files.

I would appreciate your prompt response.

Sincerely yours,

Ali Dehghan,

Shiraz university, Iran.

[Brook]

Hi Ali,

It’s not the problem with your input files. It’s about physics.

The Chern number should be Zero for each TRIM plane. That’s because the inversion is not caused by the spin-orbit coupling, i.e. the inversion is trivial.

Best regards,

QuanSheng

[Ali Dehghan]

​Dear Dr. QuanSheng,

Thanks for your reply despite your busy scientific schedule. If I understood correctly, once we have a Chern insulator when the band inversion was caused by the SOC. This is interesting and important to me. Can you provide a good reference for this claim, please? Your advice will be greatly appreciated.

Thanks again for your time and consideration.

Sincerely yours,

Ali Dehghan,

Shiraz University, Iran.

• This reply was modified 4 years, 7 months ago by Ali Dehghan.

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