[Wien] inversion vs time reversal
姜若诗
ruoshijiang at sjtu.edu.cn
Fri Feb 7 11:33:58 CET 2020
Dear professor, am I understand right?
If the system has inversion symmetry, there is (-1 -1 -1) diagonal matrix and also the system is real.
If the system doesn’t have inversion symmetry, but without magnetism and neglect the spin-orbit interactions( time reversal symmetry present), the system doesn’t have (-1 -1 -1) diagonal matrix and the system is complex, the symmetry operators shows in case.struct is reduced a half(24 sym.ops), but when calculate the k-mesh, we use the time reversal as if inversion present (48 sym.ops) ?
I calculate the GaAs, which with time reversal but without inversion, there are only 24 symmetry operators in case.struct file. Is this the situation that you said?
If I understand right, what the final file you use describes the right symmetry operators, Is case.outputkgen, or in case.struct, with the origin 24 symmetry operators adding another (-1 -1 -1) * 24 sym.ops?
Regards,
Jasmine.
--------------------------------------------------GaAs.struct-------------------------------------------------
GaAs
F LATTICE,NONEQUIV.ATOMS: 2
MODE OF CALC=RELA unit=bohr
10.683000 10.683000 10.683000 90.000000 90.000000 90.000000
ATOM 1: X=0.00000000 Y=0.00000000 Z=0.00000000
MULT= 1 ISPLIT= 2
Ga NPT= 781 R0=0.00005000 RMT= 2.30 Z: 31.000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM 2: X=0.25000000 Y=0.25000000 Z=0.25000000
MULT= 1 ISPLIT= 2
As NPT= 781 R0=0.00005000 RMT= 2.30 Z: 33.000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
24 NUMBER OF SYMMETRY OPERATIONS
1 0 0 0.00000000
0-1 0 0.00000000
0 0-1 0.00000000
1
1 0 0 0.00000000
0 0-1 0.00000000
0-1 0 0.00000000
2
0 1 0 0.00000000
-1 0 0 0.00000000
0 0-1 0.00000000
3
0 0 1 0.00000000
-1 0 0 0.00000000
0-1 0 0.00000000
4
0 1 0 0.00000000
0 0-1 0.00000000
-1 0 0 0.00000000
5
0 0 1 0.00000000
0-1 0 0.00000000
-1 0 0 0.00000000
6
0-1 0 0.00000000
1 0 0 0.00000000
0 0-1 0.00000000
7
0 0-1 0.00000000
1 0 0 0.00000000
0-1 0 0.00000000
8
-1 0 0 0.00000000
0 1 0 0.00000000
0 0-1 0.00000000
9
-1 0 0 0.00000000
0 0 1 0.00000000
0-1 0 0.00000000
10
0-1 0 0.00000000
0 0-1 0.00000000
1 0 0 0.00000000
11
0 0-1 0.00000000
0-1 0 0.00000000
1 0 0 0.00000000
12
0 0 1 0.00000000
0 1 0 0.00000000
1 0 0 0.00000000
13
0 1 0 0.00000000
0 0 1 0.00000000
1 0 0 0.00000000
14
-1 0 0 0.00000000
0 0-1 0.00000000
0 1 0 0.00000000
15
-1 0 0 0.00000000
0-1 0 0.00000000
0 0 1 0.00000000
16
0 0 1 0.00000000
1 0 0 0.00000000
0 1 0 0.00000000
17
0 1 0 0.00000000
1 0 0 0.00000000
0 0 1 0.00000000
18
0 0-1 0.00000000
0 1 0 0.00000000
-1 0 0 0.00000000
19
0-1 0 0.00000000
0 0 1 0.00000000
-1 0 0 0.00000000
20
0 0-1 0.00000000
-1 0 0 0.00000000
0 1 0 0.00000000
21
0-1 0 0.00000000
-1 0 0 0.00000000
0 0 1 0.00000000
22
1 0 0 0.00000000
0 0 1 0.00000000
0 1 0 0.00000000
23
1 0 0 0.00000000
0 1 0 0.00000000
0 0 1 0.00000000
24
From: Peter Blaha
Sent: Friday, February 7, 2020 4:02 PM
To: wien at zeus.theochem.tuwien.ac.at
Subject: Re: [Wien] inversion vs time reversal
> 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?
As I said: WITHOUT magnetism and neglecting Spin-orbit interactions,
time reversal is always present.
Therefore, when we calculate the IBZ k-mesh, we use not only the 24
symops of this space group, but multiply every operation also with
inversion and use 48 sym.ops.
> 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?
The (-1,-1,-1) diagonal matrix (in case.struct) shows, that we have
INVERSION symmetry. Time reversal has nothing to do with the local
symmetry, but depends on ... (see above).
> 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 ?
Now it becomes quite basic:
We use plane waves, right ? These are complex functions psi= exp**(i k r).
However, this can be expanded into cos (k r) + i sin (k r)
With inversion we know that psi (r) = psi (-r).
Since sin (k r) is "odd"; (sin (k r) .ne. sin (k -r)), we know that
this term must vanish and we can replace exp**(i k r) by cos (k r)
and this is purely "real".
>
> Looking forward to your reply.
>
> Sincerely,
>
> Jasmine.
>
> *From: *Peter Blaha <mailto:pblaha at theochem.tuwien.ac.at>
> *Sent: *Thursday, February 6, 2020 7:31 PM
> *To: *wien at zeus.theochem.tuwien.ac.at
> <mailto: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.
>
> >
>
> >
>
> > _______________________________________________
>
> > Wien mailing list
>
> > Wien at zeus.theochem.tuwien.ac.at
>
> > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
>
> > SEARCH the MAILING-LIST at:
> http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
>
> >
>
> --
>
> P.Blaha
>
> --------------------------------------------------------------------------
>
> 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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--
P.Blaha
--------------------------------------------------------------------------
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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