Symmetry Problems of the Transport Tensor

[Molakeshi]

When I repeated the example of Si given in the document, I successfully calculated the result according to the steps in it, but when I checked the transport tensor output in T0.300E+03, I found that the symmetry of the tensor was not well met. For example
”
drag_el_alphabyT_tot：
-0.6868439640E+02 0.2817398099E-01 0.2817328942E-01
0.2817536425E-01 -0.6868439719E+02 -0.2817135391E-01
0.2817166961E-01 -0.2817263822E-01 -0.6868398772E+02

drag_el_sigmaS_tot:
-0.7889824040E+02 0.3272308989E+00 0.3271797398E+00
0.3272513156E+00 -0.7889827281E+02 -0.3271496146E+00
0.3271394922E+00 -0.3271540024E+00 -0.7891607079E+02
“
I checked the output and found that the program correctly identified the symmetry of Si:
“___________________________________________________________________
_______________________________Analyzing symmetry...
Crystal symmetry group = Fd-3m
Spacegroup number = 227
Number of crystal symmetries (without time-reversal) = 48
”
According to the symmetry of Si, the non-diagonal term should be 0 and the numerical result should be quite small, but the calculated result is not. I don’t know where the problem lies, and I look forward to your reply!

[nakib]

Dear Molakeshi,

Thanks a lot for creating this issue. Your numbers are slightly different from what is quoted in the output file. Nevertheless, they are not too far off from those numbers. Below I quote the output that I get in the file drag_el_alphabyT_tot:

  0   -0.6485384256E+02    0.1753024234E-32    0.0000000000E+00    0.0000000000E+00   -0.6485384256E+02    0.0000000000E+00    0.0000000000E+00    0.0000000000E+00   -0.6485384256E+02
  1   -0.6471289036E+02    0.2694873144E-01    0.2694929379E-01    0.2694909542E-01   -0.6471289111E+02   -0.2694881279E-01    0.2694905680E-01   -0.2694927684E-01   -0.6471250996E+02
  2   -0.6472983875E+02    0.3019795820E-01    0.3019793257E-01    0.3019952273E-01   -0.6472983974E+02   -0.3019634709E-01    0.3019634317E-01   -0.3019771659E-01   -0.6472941623E+02
  3   -0.6473128672E+02    0.3026928712E-01    0.3026937006E-01    0.3027100138E-01   -0.6473128773E+02   -0.3026758150E-01    0.3026761744E-01   -0.3026910262E-01   -0.6473086397E+02
  4   -0.6473128450E+02    0.3027703168E-01    0.3027711261E-01    0.3027877762E-01   -0.6473128553E+02   -0.3027529711E-01    0.3027533030E-01   -0.3027684233E-01   -0.6473086150E+02
  5   -0.6473133525E+02    0.3027724391E-01    0.3027732631E-01    0.3027899520E-01   -0.6473133628E+02   -0.3027550688E-01    0.3027553743E-01   -0.3027705577E-01   -0.6473091212E+02
  6   -0.6473132862E+02    0.3027759735E-01    0.3027768265E-01    0.3027935241E-01   -0.6473132965E+02   -0.3027585937E-01    0.3027588989E-01   -0.3027741098E-01   -0.6473090550E+02
  7   -0.6473133313E+02    0.3027757429E-01    0.3027766155E-01    0.3027933157E-01   -0.6473133417E+02   -0.3027583668E-01    0.3027586687E-01   -0.3027738997E-01   -0.6473090999E+02

As you can see, the RTA solution has the expected cubic symmetry (we can say that 0.1753024234E-32 is practically zero). During the course of the iteration, the symmetry becomes less accurate. Looking at values in the final iteration, the diagonal numbers are still identical up to many decimal places. The off-diagonal elements are much smaller (~0.05%) compared to the diagonal.

As for why this might be happening, it is difficult to say. I "resymmetrize" the response functions after every iteration step, and also symmetrize the transport tensors. However, perhaps there is always room for improvement regarding this symmetrization procedure.

I will keep this issue up until my group or some community member takes a look at it at some point. Feel free to contribute your solution, if you can find one.

Best regards,
Nakib

[Molakeshi]

Dear Nakib,

Thank you very much for your detailed explanation. I will continue to monitor this issue and will share any potential solutions if I find them.

Thank you again for your time and support—it is much appreciated!

Best regards
Molakeshi