Greetings everyone,

I have a question regarding the effective mass tensor, that I cannot seem to find the solution for:

I have used DFT to calculate the bands/eigenvalues of Silicon. I have done this ones with the conventional unit cell (from materials project):

Si2

1.0

3.8681383004362986 0.0 0.0

1.9340686210409386 3.349905532609194 0.0

1.9340686210409386 1.1166353539288019 3.1583211568194507

Si

2

Direct

0.250000000 0.250000000 0.250000000

0.000000000 0.000000000 0.000000000

As well as the primitive unitcell:

Si8

1.0

5.4687280655 0.0000000000 0.0000000000

0.0000000000 5.4687280655 0.0000000000

0.0000000000 0.0000000000 5.4687280655

Si

8

Direct

0.250000000 0.750000044 0.250000000

-0.000000000 -0.000000000 0.500000000

0.250000000 0.250000000 0.750000044

-0.000000000 0.500000000 0.000000000

0.750000044 0.750000044 0.750000044

0.500000000 0.000000000 0.000000000

0.750000044 0.250000000 0.250000000

0.500000000 0.500000000 0.500000000

Let's look at the gamma point only to keep it simple: I then constructed (using the emc.py script) a cartesian k-point grid around the Gamma point in order to get the effective mass tensor for the gamma point for each definition of the unit cell (Conduction Band). For the primitive, 8 atom unit cell, I get something like:

-20.46496343 0.00000000 0.00000000

0.00000000 -20.46496343 0.00000000

0.00000000 0.00000000 -20.46496343

with all Eigenvalues being 20.465 (the tensors are given in units of 1/m*). As far as I am aware, this is what it should look like in terms of symmetry/degeneracy (the absolute values are not of interest at this point).

If I look at the conventional, 2 atom unit cell, however, I get something like:

0.88345374 -0.00018375 -0.00018375

-0.00018375 0.11245293 -1.46684926

-0.00018375 -1.46684926 2.17115005

with non-degenerate eigenvalues of -0.65, 0.88, 2.93.

I do not understand how this can be. I would understand that the tensors might look different due to different (absolute) orientation in k-space, but the eigenvalues should remain identical, should they not? Otherwise the physics would have changed. Especially in the example of the Gamma point above, I would have assumed to get the exact same tensor, as the effective masses are equal in all directions. Again, the dense grid around the Gamma point is constructed as cartesian cube in both cases.

I feel I am missing something fundamental here in terms of physics, I am grateful for any insight.

Thanks a lot!