How to distinguish the modes

Hi Prof. Julian,

I was working on single layer graphene whose primitive unit cell has 2 basis atoms. And thus it gives 6 modes(frequency) for a particular k-point. But these frequencies come out in increasing order in the output from GULP.
Now, I am interested in figuring it out as to which frequncy belongs to which mode (LA,TA,ZA,LO,TO or ZO) ?

(1) One way I look into it is that we can use eigenvectors in order to differentiate between Acoustic and Optical branches by the signs . All the acoustic frequency will have the atoms moving in the same direction and so it belongs to acoustic otherwise it would be optical (am I correct?)

(2) Even if this approach is correct then how to decide out of the acoustic and optical branch that which one is Transverse(T) and which one is Longitudnal(L)?

With regards,

Hi Abhikeern,

(1) At the gamma point this should be exactly true - the acoustic modes are pure translation and so all atoms will be moving together. Away from gamma things are a bit more subtle since there will be some phasing. In order to connect modes away from gamma you need to look at the phonon dispersion curves and then you can link points by the trend (or maximal overlap of the dot product of eigenvectors between successive points if you want to get fancy).
(2) In brief, if you look at gamma where the eigenvectors are real (to keep things simple), the transverse modes are the 2 which are orthogonal to the direction of the dispersion curve, while the longitudinal one is parallel to the dispersion. Of course take care due to degeneracy at gamma which will mix the modes.