[Wien] Doubt regarding the inter-band velocity term from the OPTIC module.
Nestoklon Mikhail
nestoklon at gmail.com
Sun May 26 11:07:01 CEST 2024
Dear Vivek,
0) I recommend you to read instructions for "mstar" which gives more
explanations than UG of optic.
1) If your system does not have an inversion center (I suspect that TaAs
does not), the calculation of velocity with spin-orbit needs an additional
step in mimicking the spin-polarized calculations [1].
This is explained in UG, check paragraph 8.20.1
2) To have all matrix elements calculated, ask optic to compute all 9: line
3 of case.inop should be 9, and lines 4-12: 1 2 3 4 5 6 7 8 9 respectively.
3) The results are in file case.mommat2 or case.mommat2up file.
4) As for your question about half of matrix elements calculated, the
others are complex conjugated.
Sincerely yours,
Mikhail Nestoklon
[1] $ cp case.vsp case.vspup
$ cp case.vsp case.vspdn
$ cp case.vectorso case.vectorsoup
$ cp case.energyso case.energysoup
$ x lapw2 -fermi -so -up
$ x optic -so -up
On Sat, 25 May 2024 at 23:29, VIVEK PANDEY <vivek6422763 at gmail.com> wrote:
> Dear Wien2K community,
> I am currently using the latest version of the WIEN2k package
> (*Version: WIEN2k_23.2*). At certain point of my work, I am in need of
> velocity term ( *<nk|vx|mk>* ), where *nk* and *m*k are the indices of
> Bloch states. Here, *n* & *m* denotes the band-indices and *k* stands for
> the particular *k*-point of the Brillouin zone. I found from here (
> https://triqs.github.io/dft_tools/latest/faqs/faqs.html#x-optic-does-not-write-a-case-pmat-file)
> that one can obtain the velocity term using the *x optic* module. For
> this, I need to modify the *case.inop* file as mentioned in the above
> link. The velocity term will be contained in the *case.pmat* file.
>
> I have performed the calculations on TaAs. My *TaAs.inop *file look-like:
>
> 100 1 number of k-points, first k-point
> -0.2 0.2 9999 Emin, Emax for matrix elements, NBvalMAX
> 2 number of choices (columns in *outmat): 2: hex or tetrag.
> case
> 1 Re xx
> 3 Re zz
> ON ON/OFF writes MME to unit 4
> 1
>
> So, as mentioned in the *TaAs.inop *file, I want to calculate the
> velocity term for 100 *k*-points. These *k*-points are already contained
> in my *TaAs.klist* file.
>
> After running the command: *x optic -so*, the obtained *TaAs.pmat* file
> look-like (I am providing the data of initial 2 *k*-points):
>
> 1 67 68
> 0.000000000000 0.000000000000 0.000000000000 1
> (-1.617771001625472E-004,1.226564556964964E-008)
> (-1.439040550334954E-004,-1.379984625073599E-008)
> (3.785649513346538E-011,-1.299045946281420E-005)
> (-3.656362974619897E-003,4.416165542701399E-003)
> (4.419121064225817E-003,3.653538690785011E-003)
> (2.453482640439684E-007,-8.805238041136547E-009)
> (1.617766828253836E-004,-1.226567120783516E-008)
> (1.439043262718125E-004,1.378900067924048E-008)
> (7.662998780467998E-012,8.582197920130107E-009)
> 2 67 68
> 0.100000000000 0.100000000000 0.000000000000 2
> (1.395573059329797E-002,3.799018979369327E-007)
> (1.395573021772884E-002,-3.799076130893441E-007)
> (5.130244989109358E-010,-5.404839562596613E-006)
> (1.657834175714330E-002,3.964486338191684E-003)
> (1.657834294376005E-002,-3.964481019261168E-003)
> (-2.893793368690930E-010,1.776652555720962E-003)
> (1.918588062557931E-002,-2.109479429269941E-007)
> (1.918588071334665E-002,2.109422247967537E-007)
> (-5.090469730277025E-010,-5.689825446102657E-006)
>
> I can see that at both these *k*-points, there falls two bands (indices:
> 67 & 68) within the energy window considered in the *TaAs.inop* file.
>
> To understand the data in the *TaAs.pmat* file, I analysed another file
> that was produced, namely *TaAs.symmat. *The data for the first two *k*-point
> in this file look-like:
>
> SO 2 Re <x><x> Re <z><z> ALL
>
> KP: 1 NEMIN NEMAX : 67 68 dE: -0.2 0.2 K: 1
>
> 67 67 0.123929E-18 0.168529E-09
> 67 68 0.000000E+00 0.000000E+00
> 68 68 0.123929E-18 0.168529E-09
>
> KP: 2 NEMIN NEMAX : 67 68 dE: -0.2 0.2 K: 2
>
> 67 67 0.109837E-02 0.123092E-09
> 67 68 0.000000E+00 0.000000E+00
> 68 68 0.109837E-02 0.123092E-09
>
> It is seen from the *TaAs.symmat *file that at each *k*-point, there are
> data for three pairs of bands (67-67, 67-68 & 68-68). If the *TaAs.pmat *file
> corresponds to these combinations of bands, then at each *k*-point, there
> should be 9 lines. This is because, corresponding to each pair of bands,
> there will be three components of velocity (vx, vy & vz). The results
> obtained in *TaAs.pmat* file seems to be consistent with this.
>
> Here, I want to ask my question. In the *TaAs.pmat* file, I am getting
> the data for *<67 k|vx|68 k> *but not the data for *<68 k|vx|67 k>. Why?
> Will they both be same or anyway related to each other?*
>
> After going through the WIEN2k userguide, I found a line mentioning: "*The
> program optic generates the symmetrized squared momentum matrix elements*".
> Does it mean that for the above given case, the code is making a 2x2
> velocity matrix (for the two band-indices 67 & 68 ) and then it is
> symmetrizing the matrix by following the formula (A+A_Transpose)/2 ? If
> this is the case, then the inter-band (*n* not equal to *m*) velocity
> will not be correct in the *TaAs.pmat* file. How can I obtain the correct
> value of the inter-band velocity?
>
> Kindly help me with this. Also, please correct me if I am misinterpreting
> something at some point.
>
> *Thanks and Regards*
>
> *Yours Sincerely*
> Vivek Pandey
> Research Scholar
> Indian Institute of Technology, Mandi
> Himachal Pradesh, India
>
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