[Pw_forum] unitary matrix u

[Kostyantyn Borysenko]

Hello all,

 

I am trying to understand the meaning of some variables in the source code
of QE. Particularly, it is not clear what is the meaning of the (3*nat,
3*nat) matrix u in phonon and electron-phonon calculations. In the output
file generated by the subroutine phq_summary.f90 the columns of this matrix
are referred to as "phonon polarizations" - i.e. they are supposed to be
eigenvectors of the dynamical matrix. 

 

I consider the case when nat = 2 (two atoms in the unit cell), so the
eigenvectors are 6-dimentional (3*nat=6) and there are six of them. I was
told that in the case nat = 2 the components have the following meaning:
(1x, 1y, 1z, 2x, 2y, 2z) - Cartesian components of deviations for both
atoms.

 

Now, in the output file generated by phq_summary.f90 for q=0, regardless of
degeneracy of branches, there is always only one nonzero component. For
instance, the first eigenvector is (-1,0,0,0,0,0). Obviously, all six
eigenvectors are orthonormal, which is how it's supposed to be.

 

But here is what bothers me. For acoustic phonon modes, the unit cell moves
as a whole, i.e. both atoms must move with the same phase. So I expect to
see something like  (1/sqrt(2),0,0, 1/sqrt(2),0,0), instead of
(-1,0,0,0,0,0). For optical branches on the other hand, two atoms have the
opposite phase (the center of mass of the unit cell does not move), so I
would expect to see something like (1/sqrt(2),0,0, -1/sqrt(2),0,0). My
understanding is this: if every eigenvector has only one nonzero component,
it means that in each mode, one atom is not moving at all!

 

Maybe, I misunderstood the meaning of components of the matrix u? 

 

I apologize for this lengthy explanation. And I would really appreciate any
help.

 

Best regards,

 

Kostyantyn Borysenko

Electrical and Computer Engineering Department

North Carolina State University

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