Dear all,

I have performed some fatband calculations with pawfatbnd=2, in order to get the contribution of each |L,M> state belonging to a certain Cu atom to the bands. My question is the following: is M the quantum number corresponding to the Z component of the orbital angular momentum (Lz)?

The question arises from the tutorial https://docs.abinit.org/tutorial/dmft/ about DMFT. There, they mention that each state |L=2,M> corresponds to a d-type orbital of Vanadium. For example, they affirm that the state |L=2,M=-2> corresponds to the orbital d_xy. However, all d orbitals (and the same happens with p and f orbitals) except the one with M=0 are combinations of states |L=2,M> and |L=2, - M> in such a way that the angular part of the resulting wave function is real. Therefore, I suspect that the label M used in abinit is not the quantum number corresponding to Lz.

In the case that M is not the quantum number corresponding to Lz, which criteria should be used to identify each |L,M> with the corresponding atomic orbital?

Thank you.