[Wien] Doubt regarding the inter-band velocity term from the OPTIC module.
VIVEK PANDEY
vivek6422763 at gmail.com
Sun May 26 15:01:20 CEST 2024
Dear Mikhail,
Thank you for your reply. It was helpful in clearing my doubts.
Sincerely yours
Vivek
On Sun, 26 May, 2024, 2:37 pm Nestoklon Mikhail, <nestoklon at gmail.com>
wrote:
> 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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