Electron-phonon matrix elements rotation

[HaritzGarai]

The rotation of the electron-phonon matrix elements using symmetry is an important feature that adds substantial value to the first release of intw.

At this moment there are some phase differences between the matrix elements computed in this way and the matrix elements computed by rotating the wave functions. I think that Maria was able to remove those phases for a few tests by including some unitary transformation, but it doesn't work always.

Anyway, we are not completely sure if those phases shouldn't appear, and therefore there is some bug somewhere, or if they should be removed by including some unitary transformation. As an intermediate step to check everything, doing the same for the Mmn's could be helpful.

[mblancorey]

We need more tests for this, since the current ones are not sensitive to changes in the code. The tests consist in comparing the rotated element (phase included) with the element calculated explicitly with rotated wavefunctions. The current implementation works for Cu, Si and GaAs, but not with spinors.

The critical cases are TR symmetry, improper elements, fractional translations and spinor rotation:

• TR symmetry seems to be correctly implemented, but it would be good to have tests where the symlink_q includes some TR symmetries.

• I think mirror planes should introduce a -1 in the rotated element, but the tests are not sensitive to this. However, the Mmn rotation suggests it is not necessary.

• Non-symmorphic elements are difficult, since they make the space group symmetries depend on k. In practice, this introduces phases e^ikL, with L a lattice vector. The current implementation works for Si, but the test is insensitive to changes in some signs, etc. It would be good to have a Bi test and see how this combines with TR.

• With spinors, the current tests fail in the phases of the elements.