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Non-Integer Chern Number (CN)?
Date: 2021/05/26 00:50
Name: Simba   <pshubham2805@gmail.com>

Hello Team,

I want to know, are these post-processing codes calB and Z2FH valid for 2D materials and especially ones with "inversion symmetry broken"? The paper is titled with the Bulk or 3D but inside it, the process is done for 2D and then 3D.

I am asking this because I am getting a non-integer CN for my 2D-non-inversion symmetric system and as much as I know the CN is an integer, which is not the case here. Can someone physically explain this?

My second query is that is it necessary to have Band.dispersion tag turn on with the specified k-path for the calculation of Z2 invariants and Chern number in *.dat file or else it is not necessary and the Z2FH code can directly calculate Z2 and Chern number?

Again I am asking this because when I turn on the band.disperion I am getting non-zero Z2=(1, 0, 0, 0) while without the band.dispersion I am getting Z2=(0,0,0,0). Can someone resolve the discrepancy? What if my system is 2D as I specified earlier? There should be only one Z2 invariant. Which one I should choose among four (1, 0, 0, 0)?

It would be a great help if someone can clarify these.


Thank You,
Simba
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Re: Non-Integer Chern Number (CN)? ( No.1 )
Date: 2021/05/29 03:28
Name: Naoya Yamaguchi

Dear Simba,

>Again I am asking this because when I turn on the band.disperion I am getting non-zero Z2=(1, 0, 0, 0) while without the band.dispersion I am getting Z2=(0,0,0,0).
At least, the `Band.dispersion` keyword can't affect results of the post-processing programs.

Regards,
Naoya Yamaguchi
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Re: Non-Integer Chern Number (CN)? ( No.2 )
Date: 2021/06/02 01:58
Name: Hikaru Sawahata  <sawahata@cphys.s.kanazawa-u.ac.jp>

Dear Simba,

Thank you for the question.

>I want to know, are these post-processing codes calB and Z2FH valid for 2D materials and especially ones with "inversion symmetry broken"?

The answer is yes, please see the references.
http://www.openmx-square.org/openmx_man3.9/node184.html
http://www.openmx-square.org/openmx_man3.9/node187.html

>I am getting a non-integer CN for my 2D-non-inversion symmetric system

If you get a non-integer CN, the system is metallic (energy bands are degenerated) or it includes some calculation error.

>Again I am asking this because when I turn on the band.disperion I am getting non-zero Z2=(1, 0, 0, 0) while without the band.dispersion I am getting Z2=(0,0,0,0).

I think your input file includes some mistakes. Have you calculated example files?
http://www.openmx-square.org/openmx_man3.9jp/node188.html

Regards,
Hikaru Sawahata
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Re: Non-Integer Chern Number (CN)? ( No.3 )
Date: 2021/06/03 19:57
Name: Simba  <pshubham2805@gmail.com>

Thank you so much Dear Naoya and Hikaru for your response.
Could you please explain what Z2 = (1,1,0,0) means? My system is 2D and for 2D there should be only one Z2 invariant, why there are 2.
Am I missing something? Please correct me if I am, related to code or theory.

Thank you


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Re: Non-Integer Chern Number (CN)? ( No.4 )
Date: 2021/06/03 20:01
Name: Simba  <pshubham2805@gmail.com>

Dear Hikaru Sawahata,

As you said

>If you get a non-integer CN, the system is metallic (energy bands are degenerated) or it includes some calculation error.

My question is if the system is metallic then why I am getting non-zero Z2 which is (1, 1, 0, 0). It would be great if you could clarify this.

Thank you.
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Re: Non-Integer Chern Number (CN)? ( No.5 )
Date: 2021/06/03 22:01
Name: Simba  <pshubham2805@gmail.com>

Dear Naoya and Developers,

I am getting different results with and without band.dispersion. Why this is so? I tried several times and I am getting different Z2. with band dispersion 'on' it is (1,1,0,0) and without the it is (1, 0, 1, 1).

Kindly explain.

Thank you

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Re: Non-Integer Chern Number (CN)? ( No.6 )
Date: 2021/06/04 14:21
Name: Naoya Yamaguchi

Dear Simba,

>I am getting different results with and without band.dispersion. Why this is so? I tried several times and I am getting different Z2. with band dispersion 'on' it is (1,1,0,0) and without the it is (1, 0, 1, 1).
In No. 5, you said that Z2 invariants are (1, 1, 0, 0) for `on` and (1, 0, 1, 1) for `off`.

>Again I am asking this because when I turn on the band.disperion I am getting non-zero Z2=(1, 0, 0, 0) while without the band.dispersion I am getting Z2=(0,0,0,0).
However, in No. 3, you said that Z2 invariants are (1, 0, 0, 0) for `on` and (0, 0, 0, 0) for `off`.

The above two cases implies that the change of values didn't come from the difference of the `Band.Dispersion` switch.
And, I guess that different parameters for input keywords can cause different results.

Regards,
Naoya Yamaguchi
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