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Computing Z2 invariant for 1D graphene nanoribbons (GNRs) by Z2FH
Date: 2020/12/10 07:20
Name: Yubin   <yubin.fu@tu-dresden.de>

Dear All,

Hope you are doing well.

Recently I am focusing on computing Z2 invariant for 1D graphene nanoribbons (GNRs). Since I just start learning knowledge about GNRs with topological insulator properties I found that it can be defined by Z2 topological invariant. And the Z2 topological invariants can be calculated through the Fukui-Hatsugai method by using Z2FH in OpenMX. I installed the OpenMX successfully and I tested a task from the literature(Phys. Rev. Lett. 119, 076401). However, when I finished the SCF calculation and run the Z2FH there was an error: Z2FH is only available for non-collinear systems. So here is my question?

1.Does the Z2FH suitable for computing Z2 invariants of 1D GNRs?
2.To avoid the error from the Z2FH I need to perform the non-collinear(spin-polarized) SCF calculation, am I correct? But for the GNRs(3/5/7-armchair GNRs) in the literature there should be no spin or antiferromagnetic properties. How can I do the non-collinear(spin-polarized) SCF calculation?

Hope anyone can solve my problems. Thank you in advance.

Regards,
Yubin
メンテ
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Re: Computing Z2 invariant for 1D graphene nanoribbons (GNRs) by Z2FH ( No.1 )
Date: 2020/12/10 17:22
Name: Hikaru Sawahata  <sawahata@cphys.s.kanazawa-u.ac.jp>

Dear Yubin,

I'm Hikaru Sawahata in Kanazawa university. I checked PRL article briefly.

1. The definition of Z2 invariant in 1D system is different from 2D or 3D system.
Z2 invariant in 1D system (it called "Zak phase") is obtained by carrying out 1D integration on 1D Brillouin zone, and I think it can be computed by not Z2FH but polB (you need to revise the output format).
>1.Does the Z2FH suitable for computing Z2 invariants of 1D GNRs?

2. Your idea is correct, and you should specify as

scf.SpinPolarization nc

You may need to specify the option as

scf.SpinOrbit.Coupling on

because SOC is an important role in many topological phenomena.

If you want to compute antiferromagnetic system, you may need to use "spin constraint method", please see the manual.
http://www.openmx-square.org/openmx_man3.9/node113.html

>2.To avoid the error from the Z2FH I need to perform the non-collinear(spin-polarized) SCF calculation, am I correct? But for the GNRs(3/5/7-armchair GNRs) in the literature there should be no spin or antiferromagnetic properties. How can I do the non-collinear(spin-polarized) SCF calculation?

Regards,

Hikaru Sawahata
メンテ
Re: Computing Z2 invariant for 1D graphene nanoribbons (GNRs) by Z2FH ( No.2 )
Date: 2020/12/10 20:10
Name: Yubin Fu  <yubin.fu@tu-dresden.de>

Dear Hikaru,

Thank you very much for your quick reply and important suggestions.

I repeated the SCF calculation of one 7-AGNR by using the non-collinear(spin-polarized) parameters (scf.SpinPolarization nc,
scf.SpinOrbit.Coupling on).

After the SCF calculation finished I checked the std file and found that:
Sum of MulP: up = 30.00000 down = 30.00000
total= 60.00000 ideal(neutral)= 60.00000
<DFT> Total Spin Moment (muB) = 0.000000000000

That means this GNR is defined as an antiferromagnetic GNR. Then I start the Z2FH calculation. The running is quite well. But the calculated Z2.data is:
Z2 invariant:(x0,xpi,y0,ypi,z0,zpi)=(-0.000000,0.000000,-0.000000,0.000000,0.000000,0.000000)
Z2 invariant:(nu0,nu1,nu2,nu3):(0,0,0,0)

So it means that the Z2 invariant equals to 0, is it correct? From the literature, the Z2 invariant of this GNR should be 1((Phys. Rev. Lett. 119, 076401)). I understand your meaning that the Z2 invariant of 1D GNRs cannot be calculated by Z2FH.

Regarding the polB, I have checked the description. But from the out file of example, I don't know which value can be used to define the Z2 invariant. Could you please give me some more information since I am new to this area?

Thank you very much in advance.

Best regards,
Yubin
メンテ
Re: Computing Z2 invariant for 1D graphene nanoribbons (GNRs) by Z2FH ( No.3 )
Date: 2020/12/13 01:50
Name: Hikaru Sawahata  <sawahata@cphys.s.kanazawa-u.ac.jp>

Dear Yubin,

You have to read and revise the source code polB.c directly. I think "sumpsi[0]" becomes Zak phase.

>Regarding the polB, I have checked the description. But from the out file of example, I don't know which value can be used to define the Z2 invariant. Could you please give me some more information since I am new to this area?

Regards,
Hikaru Sawahata
メンテ

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