[Wien] Fwd: non-symmorphic space group and electric field with spin-orbit coupling calculations

[Martin Gmitra]

Dear Wien2k users,

We would like to investigate effect of electric field on spin-orbit
coupling in a non-magnetic system within slab geometry. Depending on
initial atomic position within unit cell we can obtain after initialization
either monoclinic Bravais lattice with symmorphic space group (6 [P m];
point group Cs) or triclinic with non-symmorphic space group (28 [P m a 2];
point group C2v).

Both the sets should provide equivalent results, but we observe a
difference in spin-orbit coupling band splittings. To do a cross-check we
have run an additional calculation for the third case with (manually)
reduced symmetry to get P1 spacegroup with unit local rotation matrices.
The results equal with the monoclinic symmorphic space group case.

Does it mean that the non-symmorphic space group is not implemented for
electric field calculations?

It is true that results should not depend on local rotation matrices?

Some outputs from symmetry analysis are below.

Best regards,
Martin Gmitra
Uni Regensburg



FIRST CASE:

 PGLSYM: THE CRYSTAL SYSTEM IS ORTHORHOMBIC
 PGLSYM: ORDER OF LATTICE POINT GROUP (NO BASE) =             8
 PGBSYM: ORDER OF LATTICE SPACE GROUP (WITH BASE) =           2
 PGBSYM: SPACE GROUP IS SYMMORPHIC
 PGBSYM: SPACE GROUP DOES NOT CONTAIN INVERSION

======================================================================

Number and name of space group: 6 (P m) [unique axis c]
- Short - Full - Schoenflies - names of point group:
 m      m      Cs

Number of symmetry operations: 2
Operation: 1
 1.0   0.0   0.0  0.000
 0.0   1.0   0.0  0.000
 0.0   0.0   1.0  0.000

Operation: 2
 1.0   0.0   0.0  0.000
 0.0   1.0   0.0  0.000
 0.0   0.0  -1.0  0.000

============================================================


SECOND CASE:


 PGLSYM: THE CRYSTAL SYSTEM IS ORTHORHOMBIC
 PGLSYM: ORDER OF LATTICE POINT GROUP (NO BASE) =             8
 PGBSYM: ORDER OF LATTICE SPACE GROUP (WITH BASE) =           4
 PGBSYM: NON-SYMMORPHIC SPACE GROUP OR NON-STANDARD ORIGIN OF COORDINATES
 PGBSYM: SPACE GROUP DOES NOT CONTAIN INVERSION


======================================================================

Number and name of space group: 28 (P m a 2)
- Short - Full - Schoenflies - names of point group:
 mm2    mm2    C2v

Number of symmetry operations: 4
Operation: 1
 1.0   0.0   0.0  0.000
 0.0   1.0   0.0  0.000
 0.0   0.0   1.0  0.000

Operation: 2
-1.0   0.0   0.0  0.000
 0.0  -1.0   0.0  0.000
 0.0   0.0   1.0  0.000

Operation: 3
 1.0   0.0   0.0  0.500
 0.0  -1.0   0.0  0.000
 0.0   0.0   1.0  0.000

Operation: 4
-1.0   0.0   0.0  0.500
 0.0   1.0   0.0  0.000
 0.0   0.0   1.0  0.000

============================================================
Note that shift vectors for this space group are defined
only up to the vector { 0, 0, Z }.
Here Z can take any value.
==========================================



THIRD CASE:


Number and name of space group: 1 (P 1)
- Short - Full - Schoenflies - names of point group:
 1      1      C1

Number of symmetry operations: 1
Operation: 1
 1.0   0.0   0.0  0.000
 0.0   1.0   0.0  0.000
 0.0   0.0   1.0  0.000
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