I would like to do a phonon band-resolved harmonic sampling, following the recipes from the paper by West and Estreicher (harmonic sampling). In fact, the method presented in the paper is already implemented in some codes devoted to the lattice dynamics (TDEP, fhi-vibes) at finite temperature.
The methodology is described in details in TDEP manual. Thus, I would just point to the equations (2)-(6) in the mentioned manual.
In this approach eigenvectors and eigenvalues of the dynamical matrix computed at the Gamma-point are used. In other words, we got data from the commensurate q-points.
In my case, I would like to do displacements using particular phonon branch. Which means that I should take only those eigenvectors and eigenstates of the dynamical matrix, which are related to the same phonon branch. Consequently, is there anyone who knows a method to assign phonon branch label to the specific eigenvector, eigenvalue? Any hints on how to do that are highly appreciated.
Since I already spend some time trying to figure it out on my own I would share what I have found at the moment. First of all, I looked if phonopy has anything related to this problem. It turned out that in phonopy during the plotting of the phonon dispersion there is a function, which estimates which q-points to connect (estimate_band_connection in the phonopy/phonon) and it works simply based on the scalar product between different eigenvectors at neighboring qpoints. I am not sure that this method is completely reliable, i.e. what do to with band-crossing (use symmetry representation of phonons of this branches?). In addition to that I have found out this paper (How to resolve a phonon-associated property into contributions of basic phonon modes), but this methodology seems to be similar to the one used in Phonopy and I am also not sure if this is what I need.
Sincerely, Nikita Rybin PhD student at the FHI, Berlin