[Pw_forum] Follow up on thread: unitary matrix u

Shela Aboud saboud at gmail.com
Thu Feb 9 21:25:55 CET 2012

I have searched the Pw_forum but was not able to find a response to a
previous post. I am including the portion of the original post that I
am curious about below. I have the same question. After running my
electron-phonon calculations some of my q-points (G-M in graphene)
have only a "-1" for each of the real x,y,z-components of one atom and
zero everywhere else as written under "modes" in the electron-phonon
output file. I assumed "modes" corresponded to the phonon
eigenvectors, but this would imply 6 optical modes at some q values
which is not correct (although along different symmetry lines it looks
like the correct format for eigenvectors).

Thank you,

Part of original Post:

Date: Thu, 14 May 2009 12:05:53 -0400
Subject: [Pw_forum] unitary matrix u
Message-ID: <2C1C44865AA64068BE6465660B5DEA6E at ece.ncsu.edu>

".....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?

Shela Aboud
CEES Sr. Research Scientist
367 Panama St. GES 077A
Stanford University
Stanford, CA 94305-2220
shela.aboud at stanford.edu
(650) 721-2276

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