[Wien] inversion vs time reversal

[姜若诗]

Dear professor,

Thanks for your reply, which helps me a lot.

But I still feel a little confused about the time reversal symmetry in wien2k, From your answer, I know when the system has not the inversion symmetry but has time reversal symmetry, the symmetry can also produce the (-1, -1, -1) diagonal matrix to reduce the number of k points which need to calculate in the BZ.

However, for example, the case : GaAs, the system is complex, which I can understand, caused by the absence of inversion symmetry. but the system don’t  have the (-1, -1, -1) diagonal matrix,  Is this mean GaAs also without the time reversal symmetry?  

Is the (-1 -1 -1) diagonal both shows if the system has the inversion symmetry or the time reversal symmetry?  But the (-1 -1 -1) diagonal matrix absent cause the system has not only inversion symmetry, but also the time reversal symmetry?

By the way, why the system is complex when the system without the inversion symmetry? As I know ,the result of inversion symmetry is : <r| -k, j> = <-r | k, j> , Only the time reversal symmetry has some relationship with the complex conjugate:  <r|- k, j> = <r |k, j >*.  Do you have some relevant references of this ? 

Looking forward to your reply.

Sincerely,
Jasmine. 

From: Peter Blaha
Sent: Thursday, February 6, 2020 7:31 PM
To: wien at zeus.theochem.tuwien.ac.at
Subject: Re: [Wien] inversion vs time reversal

time inversion symmetry is used in WIEN2k only for the generation of the 
k-mesh when "inversion" is not present (and it is not a magnetic case 
with spin-orbit). In that case we use the fact that 
epsilon(k)=epsilon(-k) and "add" the (-1,-1,-1) diagonal matrix to the 
symmetry operations reducing the full BZ mesh to the IBZ.

Everywhere else, only "inversion" is used (if present), which makes 
wavefunctions "real" and one can use lapw1 instead of lapw1c.

If you try to run Si with (0,0,0) and (1/4,1/4,1/4), you must "trick" 
the initialization procedure, because WIEN2k will normally not allow it, 
because it requires an 4 times larger computational effort.

On 2/6/20 6:26 AM, 姜若诗 wrote:
> Dear professors,
> 
> Do you know how to deal with the inversion symmetry and time reversal 
> symmetry in wien2k, how do you make them different ?
> 
> For example, if the positions of two atoms Si is in (0.125 0.125 0.125) 
> and (0.875 0.875 0.875), the system has inversion and time reversal 
> symmetry, then the point group symmetry matrix has number 48.
> 
> But if the positions are (0 0 0) and (0.25 0.25 0.25), the system 
> doesn’t has the inversion symmetry, with time reversal symmetry left, 
> will the symmetry matrix reduce to number 24, or also number 48?
> 
> In a word, what my question is :  Does the symmetry matrix  (-1 0 0, 0 
> -1 0, 0 0 -1)  show not only the inversion symmetry , but also time 
> reversal symmetry in a system?
> 
> Looking forward to your reply
> 
> Regards,
> 
> Jasmine.
> 
> 
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-- 

                                       P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
Email: blaha at theochem.tuwien.ac.at    WIEN2k: http://www.wien2k.at
WWW:   http://www.imc.tuwien.ac.at/TC_Blaha
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